The Debye length for electron in HMB medium can be calculated using its mass *me=9.1∙10- 31kg*, charge *qe=1.6∙10-19C* and Compton's length *λe=2.43∙10-12m*. The effective electron volume,

Our great assumption is the distribution of whole electron mass between the point center (with the smallest point radius near 10-17 -10-18 m, where the whole electron charge is concentrated) and other volume *Ve*. Here we assume that the electron mass is dividing near

*ne* = (*me*/2)/*Ve/m* = 1.35·1043 1/m3. Further we provide the estimation of HMB dipole charge q. The number of charge particles in the electron center *Ne=(me/2)/(m/2)=1.62∙109* and *q=qe/Ne=0.99∙10-28C*. Now we can calculate

*De = sqrt*(*ε0kT/q2/ne*) = 0.5·10-10m. In the spherical symmetric case with single spatial coordinate-radius *r* we come from (4) to

> 2 2 2 *De d d r sh r dr dr*

We shall bring typical solutions of the last equation for polarized electron space (Figure 4). A principal important particularity of distribution presented is potential pit and barrier on

negative electric charge is concentrated on external border, induced by charged electron core during polarizations of its "fur coat". The results presented are valid due to charge symmetry also for description of polarized positron space structure (when changing potential sign on opposite). The scheme of polarized electron space is shown on Figure 5.

Now consider possible building on the same principles of proton and antiproton model. In analogy with electron we suppose that the entire positive proton charge is concentrated in its center, having an estimated size, like electron core size of order 17 10 m. This central nucleus is spherical "droplet" surrounded polarized by HMB in "fluid" aggregate condition. The droplet size defines a typical known proton nuclear size (about 15 0.8 10 m), where

( )*r* break. Herewith an induced

3 = 0.601·10-34 m3.

 *T* , 2 0 0 *D sqrt kT q n* ( /)

**Figure 4.** Potential distribution in electron screening space for two D

The model of hydrogen atom consists of proton with concentrated in its center positive charge and two-layer HMB polarized space in fluid (up to 0.8·10-15m) and gaseous aggregate conditions and having an electron situated in steady stationary state on polarized space external surface (*r0=De=0.5∙10-10*). Herewith for ensuring electron stationary condition in atom there is no need to introduce additional quantum postulates. This condition is provided by potential distribution in the electron and proton models built. The scheme of polarized hydrogen atom space is shown on Figure 7. The potential distribution in the hydrogen atom is present on Figure 8.

**Figure 5.** Scheme of electron screening space

#### **5.2. Physical model of van der Waals polarized atom spheres**

The presence of real existing polarized atom space and their forms close to spherical (van der Waals spheres as Debye screened spheres) is validated by methods of crystal-chemistry and scanning probe microscopy. By means of tunnel microscope needle one can manipulate separate spherical atoms, move them on surfaces, build 3D figures, etc. Atom shape presentation as van der Waals spheres is now broadly used method when studying substance physical-chemical properties.

The previous section offers models of polarized screened spaces partly shielding central concentrated electrical charges that enable demonstrative physical interpretation of van der Waals atom spheres. These spheres are in essence external borders of polarized spaces filled with HMB dipoles Coulomb interaction bound. On such spherical borders with local concentrated induced charges might be stationary placed concentrated charges of another sign (example: hydrogen atom from article previous paragraph).

**Figure 6.** Scheme of proton screening two layer space

**Figure 5.** Scheme of electron screening space

substance physical-chemical properties.

**5.2. Physical model of van der Waals polarized atom spheres**

sign (example: hydrogen atom from article previous paragraph).

The presence of real existing polarized atom space and their forms close to spherical (van der Waals spheres as Debye screened spheres) is validated by methods of crystal-chemistry and scanning probe microscopy. By means of tunnel microscope needle one can manipulate separate spherical atoms, move them on surfaces, build 3D figures, etc. Atom shape presentation as van der Waals spheres is now broadly used method when studying

The previous section offers models of polarized screened spaces partly shielding central concentrated electrical charges that enable demonstrative physical interpretation of van der Waals atom spheres. These spheres are in essence external borders of polarized spaces filled with HMB dipoles Coulomb interaction bound. On such spherical borders with local concentrated induced charges might be stationary placed concentrated charges of another

**Figure 7.** Scheme of hydrogen atom

**Figure 8.** Numerical solution for potential distribution inside hydrogen atom

Possible stationary steady electron position on van der Waals spheres brings about a model of atom electronic shell with STationary ELectron (STEL models). Electronic shells of spherical shape are equidistant to nucleus centre at distances accordingly 0000 1 ,2 ,3 ,4 *rrrr* , etc. (natural row coefficients 1, 2, 3, 4… show, as accepted, main quantum number). The first shell area 2 0 4π*r* is fully occupied by 2 stationary electrons; they rather tightly cover nearly whole area by their own polarized spaces. The following three shells area 2 0 4 4π*r* , 2 0 9 4π*r* and 2 0 16 4π*r* can be occupied by less 8, 18, and 32 stationary electrons (double square of main quantum number); also tightly covering by their own polarized spaces nearly whole disposable area of corresponding shell. The rule stated defines maximum possible electrons number on any electronic shell (its "thick packing"), however electrons number on external shells at once may not reach its maximum value.

Number of ordinal atom element increasing and its nucleus positive charge growing under action of increasing Coulomb forces, the electron shells compress ( 0 *r* decreases) that fully complies with experimental data on atom sizes of different chemical elements. Heat expansion of electronic shells (including external van der Waals spheres) on linear law is described by corresponding solutions change of equation (4) for polarized atom space when changing Debye radius 2 1/2 0 0 *D kT n q* ( /) *T* (since typical gaseous HMB concentration 0 *n* at similar pressure 0 *p* is inversely proportional to temperature *T*).

#### **5.3. STEL model for atoms and molecules**

38 Energy Conservation

shell area 2

and 2

**Figure 8.** Numerical solution for potential distribution inside hydrogen atom

shells at once may not reach its maximum value.

Possible stationary steady electron position on van der Waals spheres brings about a model of atom electronic shell with STationary ELectron (STEL models). Electronic shells of spherical shape are equidistant to nucleus centre at distances accordingly 0000 1 ,2 ,3 ,4 *rrrr* , etc. (natural row coefficients 1, 2, 3, 4… show, as accepted, main quantum number). The first

whole area by their own polarized spaces. The following three shells area 2

0 4π*r* is fully occupied by 2 stationary electrons; they rather tightly cover nearly

0 16 4π*r* can be occupied by less 8, 18, and 32 stationary electrons (double square of main quantum number); also tightly covering by their own polarized spaces nearly whole disposable area of corresponding shell. The rule stated defines maximum possible electrons number on any electronic shell (its "thick packing"), however electrons number on external

Number of ordinal atom element increasing and its nucleus positive charge growing under action of increasing Coulomb forces, the electron shells compress ( 0 *r* decreases) that fully complies with experimental data on atom sizes of different chemical elements. Heat expansion of electronic shells (including external van der Waals spheres) on linear law is described by corresponding solutions change of equation (4) for polarized atom space when

0 4 4π*r* , 2 0 9 4π*r*

Let us give some examples of typical atomic structures within the framework of STationary ELectron (STEL) model. Begin with helium atom and its first electronic shell filled by two electrons. There are two protons and two neutrons in the center of helium atom. On surfaces of first polarized space – helium nucleus border ( 15 *r* ~ 10 m) there are two electrons in steady state due to total potential distribution. The DM polarized space in gaseous condition is situated around nucleus on the space external shell ( 10 *r* ~ 0.5 10 m) with two electrons in steady state. This first electronic shell is tightly "filled" due to the described structures of electron polarized space (also 10 *r* ~ 0.5 10 m). Each electron occupies about half spherical shell around helium atom.

The next is a carbon atom. Its external shell has 4 electrons located in tetrahedral tops (traditional direction of valence links, Figure 9). Oxygen atom on external shell contains 6 electrons. The least total potential energy of these electrons is provided by their location in two triangles tops in parallel planes and turned to each other by angle 60° (so called triangle anti-prism, Figure 9).

**Figure 9.** Structures for carbon, oxygen, and neon atoms

An inert gas neon atom has on external shell 8 electrons. The least total potential energy of these electrons forms at their location in square tops turned by angle 45° (square anti-prism, Figure 9). Similar structure to carbon, oxygen, and neon atoms is for atoms of silicon, sulphur, and argon accordingly with the same location of 4, 6, and 8 electrons on the third external shell. One can uncomplicated similar way reproduce stationary electron location on completely filled third shell with 18 electrons of 4 period (5 rows) elements and fourth shell with 32 electrons of 6 period elements of the Mendeleyev table.

The illustrated application of STEL model for electron shells description in some features repeats the known Lewis octets. An important novelty to model STEL is electrons location in anti-prism tops (for oxygen, neon, sulphur, and argon) providing minimum value of total potential energy of external electrons.

Existence of DM polarized spaces of electron, proton, and atomic nucleus allows description from general positions through Coulomb interaction of any available molecular linkages as stationary deterministic structures of shell electrons and nucleus. Here we also use the model STEL. The simplest hydrogen *Н2* molecule presents a 2D quadrangle, in opposite tops of which there are two protons and two electrons (Figure 10). These perimeter concentrated charges are located at distances about Debye radius and partly shielded by HMB polarized space. Potential distribution in polarized hydrogen molecule space might also be found by integrating equation (4). Here the covalence link presents a pair of stationary electrons (not moving on orbits).

For geometric presentation and physical description of molecular links with participation of elements of second and third periods of Mendeleyev table we return to modified Lewis cubic structures and his electron octets. Instead of perfect cubes with electrons in their tops we have square anti-prisms. Bring some typical examples. In asymmetrical water molecule each hydrogen atom is connected by covalence link (pair of socialized electrons) with oxygen atom in neighboring tops of square anti-prism.

Oxygen molecule is united by double covalence link. We have here on the second orbital shells of each atom electron octets in anti-prism tops (Figure 10 ). An example of "twisted" molecule with double covalence link serves the molecule of carbon dioxide (Figure 10).

Similar geometric models with square anti-prism structure (electron octets) and covalence links are typical for carbon compounds. Show, for example, saturated hydrocarbon with filled octet of the electronic shell - methane (Figure 11). Compounds, similar to carbon, of third period silicon element with four valency electrons on the following third electronic shell are also comfortable to present in the form of geometric models with square antiprisms; with the only difference - in covalence links participate electrons of silicon third external electronic shell.

Within the framework of STEL model it is natural ("classical") way to represent models of hydrogen links, when on the first, nearest to proton (hydrogen ion) shell are stationary localized two electrons simultaneously belonging to two negative ions. For instance, hydrogen difluoride *HF*2 possesses linear structure *FHF* ; its steadiness is obliged to the proton linking two negative fluorine ions by Coulomb interaction (Figure11 ).

**Figure 11.** Structures for CH4 and HF2 molecules

moving on orbits).

external electronic shell.

hydrogen difluoride *HF*2

**Figure 10.** Structures for H2, O2 and CO2 molecules

oxygen atom in neighboring tops of square anti-prism.

Existence of DM polarized spaces of electron, proton, and atomic nucleus allows description from general positions through Coulomb interaction of any available molecular linkages as stationary deterministic structures of shell electrons and nucleus. Here we also use the model STEL. The simplest hydrogen *Н2* molecule presents a 2D quadrangle, in opposite tops of which there are two protons and two electrons (Figure 10). These perimeter concentrated charges are located at distances about Debye radius and partly shielded by HMB polarized space. Potential distribution in polarized hydrogen molecule space might also be found by integrating equation (4). Here the covalence link presents a pair of stationary electrons (not

For geometric presentation and physical description of molecular links with participation of elements of second and third periods of Mendeleyev table we return to modified Lewis cubic structures and his electron octets. Instead of perfect cubes with electrons in their tops we have square anti-prisms. Bring some typical examples. In asymmetrical water molecule each hydrogen atom is connected by covalence link (pair of socialized electrons) with

Oxygen molecule is united by double covalence link. We have here on the second orbital shells of each atom electron octets in anti-prism tops (Figure 10 ). An example of "twisted" molecule with double covalence link serves the molecule of carbon dioxide (Figure 10).

Similar geometric models with square anti-prism structure (electron octets) and covalence links are typical for carbon compounds. Show, for example, saturated hydrocarbon with filled octet of the electronic shell - methane (Figure 11). Compounds, similar to carbon, of third period silicon element with four valency electrons on the following third electronic shell are also comfortable to present in the form of geometric models with square antiprisms; with the only difference - in covalence links participate electrons of silicon third

Within the framework of STEL model it is natural ("classical") way to represent models of hydrogen links, when on the first, nearest to proton (hydrogen ion) shell are stationary localized two electrons simultaneously belonging to two negative ions. For instance,

proton linking two negative fluorine ions by Coulomb interaction (Figure11 ).

possesses linear structure *FHF* ; its steadiness is obliged to the

The ionic link presents Coulomb ion interaction when external electrons of one atom complement more filled external shell of another atom. Here it is also comfortable for elements of second and third periods of the Table to consider electron octets of external shells with geometric approach in the form of anti-prisms. Typical examples serve sodium chloride and sulphureous magnesium.

Now describe from used deterministic positions and STEL model metallic links when atom external shells are partly filled by electrons. Metallic links are realized through links of electronic shells nearest to the external shell, through one or several electrons, which begin to belong simultaneously to two nearby atoms. Then electrons of external blank shells and "spare" electrons of binding shell (if and when before links this shell was filled) become not connected with concrete atom and easy moving. Examples are schematic traditional 2D presentations of metallic electronic links for lithium and natrium (Figure 12). For nickel subsequent to the second filled electronic shell with 8 electrons octet follows the third shell with 16 electrons that is complemented up to 18 electrons by attaching nearby atom two electrons realizing metallic link.

**Figure 12.** Schemes of metal linkages for Li and Na

Special consideration has fulfilled for hydrocarbon valence linkages in benzoyl C6H6 and naphthalene C10H8 molecules. We give the molecule images, their detail structures (Figure 13) and also electronic and structural formulas (Figure 14). It should be emphasized that the benzoyl ring has internal linkages between carbon atoms through three stationary electrons.

The next examples are related to borohydrogen molecules B2H2, B6H6, B4H10 (Figure 15). The complex B2H2 has special type of internal four electrons linkage and outer four valence linkages, similar the carbon and silicon atoms.

**Figure 13.** Benzoyl C6H6 and naphthalene C10H8 molecules and their form

**Figure 14.** Electronic and structural formulas of benzoyl C6H6 and naphthalene C10H8 molecules

**Figure 15.** Complex B2 H2 and molecules B2 H6 and B4 H10

In the approach presented any molecular links are realized by stationary electrons of external orbits by means of electric (Coulomb) interaction with partial screening electron and nucleus "point" charges by DM polarized particles. Electric potential distribution is described in this approach by the same equation (4) with stationary electrons distribution providing minimum of total potential energy. The principle of minimum total potential energy brings about electrons stationary localization in geometric anti-prism tops that provides maximum repulsion of electrons on electronic shells. Anti-prism foundations turning are a base for shaping heliciform circuits of complex molecules (in particular, RNA and DNA molecules).

It follows to emphasize in the section conclusion that stated physical models allow looking from new positions at known ways of modeling chemical links. These methods may include the Lewis model and diagrams and Van der Waals sphere model for revealing intermolecular contacts.

#### **5.4. Examples of weak and strong interactions**

Following our methodology we show now shortly the scheme of neutron as a positive nuclear of proton with Debye screening (up to *r0=0.8∙10-15m*) by liquid layer of HMB dipoles and stationary electron, presenting on boundary of Debye region (Figure 16). Decay of neutron gives naturally proton, electron and antineutrino, which presents itself isolated soliton in DM gaseous medium. Exact soliton solutions for neutrino and antineutrino were obtained in papers [92-95].

**Figure 16.** Scheme of neutron

42 Energy Conservation

**Figure 13.** Benzoyl C6H6 and naphthalene C10H8 molecules and their form

**Figure 15.** Complex B2 H2 and molecules B2 H6 and B4 H10

**5.4. Examples of weak and strong interactions**

and DNA molecules).

intermolecular contacts.

**Figure 14.** Electronic and structural formulas of benzoyl C6H6 and naphthalene C10H8 molecules

In the approach presented any molecular links are realized by stationary electrons of external orbits by means of electric (Coulomb) interaction with partial screening electron and nucleus "point" charges by DM polarized particles. Electric potential distribution is described in this approach by the same equation (4) with stationary electrons distribution providing minimum of total potential energy. The principle of minimum total potential energy brings about electrons stationary localization in geometric anti-prism tops that provides maximum repulsion of electrons on electronic shells. Anti-prism foundations turning are a base for shaping heliciform circuits of complex molecules (in particular, RNA

It follows to emphasize in the section conclusion that stated physical models allow looking from new positions at known ways of modeling chemical links. These methods may include the Lewis model and diagrams and Van der Waals sphere model for revealing

Following our methodology we show now shortly the scheme of neutron as a positive nuclear of proton with Debye screening (up to *r0=0.8∙10-15m*) by liquid layer of HMB dipoles The STEL model with solution (4) allows us to simulate also an internal nuclear structure. Figure 17 shows the typical nuclear structures for deuterium, tritium, helium 3He and 4He. Potential distribution for deuterium was calculated (Figure 18). Figure 19 present the nuclear structure of 4Li, 5Li and 6Li.

**Figure 17.** Internal structures of deuterium, tritium and helium 3He and 4He

**Figure 18.** Numerical solution for potential distribution inside deuterium

**Figure 19.** Internal structures of Lithium 4Li, 5Li and 6Li

#### **6. Additional experimental confirmations**

*"Experience is and a source of knowledge and a criterion of truth.". Francis Bacon (1620)*

In the last section of the chapter we would like to demonstrate additional experimental confirmations of our simulation and first of all the HMB (DM) medium presence in Cosmic space and on Earth. Here, as good examples, one can select wide experimental data on solid bodies, deoxyribonucleic acid (DNA) molecules, some aeronautics and astronautics.

#### **6.1. Hooke's, Dulong–Petit's and thermal expansion laws**

The solid body is characterized by structural rigidity and resistance to changes of shape or volume. The atoms in a solid are tightly bound to each other, either in a regular geometric lattice (crystalline solids) or irregularly (an amorphous solid). The forces between the atoms in a solid can take a variety of forms but today we take into account mainly electrostatic bonds. For example, a crystal of sodium chloride (common salt) is made up of ionic sodium and chlorine, which are held together by ionic bonds. In diamond or silicon, the atoms share electrons and form covalent bonds. In metals, electrons are shared in metallic bonding. Some solids, particularly most organic compounds, are held together with van der Waals forces resulting from the polarization of the electronic charge cloud on each molecule. The dissimilarities between the types of solid result from the differences between their bonding. New our item is the presence inside bodies (similar by containers) HMB (DM) medium with own pressure, which play the same important role also as electrostatic bonds and steady solid forms result by equilibrium between HMB medium pressure and electrostatic atomic forces.

**Hooke's law.** Hooke's law was found in 1610. The most commonly encountered form of this law is probably the spring equation, which relates the force exerted by a spring to the distance it is stretched by a spring constant *k*, measured in force per length

*F = - k∆x*. The negative sign indicates that the force exerted by the spring is in direct opposition to the direction of displacement. It is called a "restoring force", as it tends to restore the system to equilibrium. In equilibrium state electrostatic forces and internal HMB medium pressure forces equal (the first equation in the system (3)). HMB pressure is increasing (or decreasing) proportional of displacement *x* (as for ideal gas case).

The potential energy stored in a spring is given by *Pe = k∆x2/2,* which comes from adding up the energy it takes to incrementally compress the spring. That is, the integral of force over displacement. (Note that potential energy of a spring is always non-negative.) This energy is internal energy of HMB gaseous medium and also can be calculated using our gas dynamics modeling.

For HMB gaseous medium we have the state equation *pV=NkT.* When *T=const* and *N=const*  the value *pV=const.* For the pressure increasing *∆p* with the change volume *∆V=V(1-∆x/l)* one can be written

$$(p + \Delta p)V(1 - \Delta \mathbf{x}/\mathbb{I}) = \mathbf{N}kT$$

and

44 Energy Conservation

**Figure 18.** Numerical solution for potential distribution inside deuterium

**Figure 19.** Internal structures of Lithium 4Li, 5Li and 6Li

**6. Additional experimental confirmations**

*"Experience is and a source of knowledge and a criterion of truth.".*

In the last section of the chapter we would like to demonstrate additional experimental confirmations of our simulation and first of all the HMB (DM) medium presence in Cosmic space and on Earth. Here, as good examples, one can select wide experimental data on solid

bodies, deoxyribonucleic acid (DNA) molecules, some aeronautics and astronautics.

*Francis Bacon (1620)*

$$
\Delta p \approx \Delta \ge l \text{ } \nu kT.
$$

Hence Young's modulus

$$E = \Delta p / \Delta \mathbf{x} / l \approx \mathbf{n}kT.$$

As an example we determine the concentration *n* on boundary polarized space for aluminum with *E=70GPa* and the Debye temperature *T=394 K*

#### *n≈E/kT*=1.31031 1/m3.

**Dulong–Petit's law.** The Dulong–Petit law, a chemical law proposed in 1819 by French physicists P.L. Dulong and A.T. Petit, states the classical expression for the molar specific heat capacity of a crystal. Experimentally the two scientists had found that the heat capacity per weight (the mass-specific heat capacity) for a number of substances became close to a constant value, after it had been multiplied by number-ratio representing the presumed relative atomic weight of the substance. These atomic weights had shortly before been suggested by Dalton. In modern terms, Dulong and Petit found that the heat capacity of a mole of many solid substances is about 3*R*, where *R* is the modern constant called the universal gas constant. Dulong and Petit were unaware of the relationship with *R*, since this constant had not yet been defined from the later kinetic theory of gases. The value of 3*R* is about 25 joules per kelvin, and Dulong and Petit essentially found that this was the heat capacity of crystals, per mole of atoms they contained. HMB theory gives theoretical base for this law (see point 3.2 of the chapter).

**Thermal expansion law.** To a first approximation, the change in length measurements of an object ("linear dimension" as opposed to, e.g., volumetric dimension) due to thermal expansion is related to temperature change by a "linear expansion coefficient". It is the fractional change in length per degree of temperature change. The point 4.1 presents detail modeling of this law. Heat expansion of electronic shells (including external van der Waals spheres) on linear law is described by corresponding solutions change of equation (4) for polarized atom space when changing Debye radius 2 1/2 0 0 *D kT n q* ( /) *T* (since typical gaseous HMB concentration 0 *n* at similar pressure 0 *p* is inversely proportional to temperature *T*). This law works well as long as the linear-expansion coefficient does not change much over the change in temperature.

#### **6.2. Deoxyribonucleic acid "flash" memory**

Deoxyribonucleic acid (DNA) is a nucleic acid containing the genetic instructions used in the development and functioning of all known living organisms. The DNA segments carrying this genetic information are called genes. Likewise, other DNA sequences have structural purposes, or are involved in regulating the use of this genetic information. Along with ribonucleic acid and proteins, DNA is one of the three major macromolecules that are essential for all known forms of life. DNA consists of two long polymers of simple units called nucleotides, with backbones made of sugars and phosphate groups joined by ester bonds. These two strands run in opposite directions to each other and are therefore anti-parallel. Attached to each sugar is one of four types of molecules called nucleobases (informally, *bases*). It is the sequence of these four nucleobases along the backbone that encodes information. This information is read using the genetic code, which specifies the sequence of the amino acids within proteins. The code is read by copying stretches of DNA into the related nucleic acid RNA in a process called transcription. Within DNA cells is organized into long structures called chromosomes. During cell division these chromosomes are duplicated in the process of DNA replication, providing each cell its own complete set of chromosomes.

Hydrogen bonds play an important role in maintaining two circuits of DNA molecule heliciform structure (Figure 20). This distribution provides minimal summary potential energy. The principle of minimal potential energy leads to stationary localization of electrons in antiprism vertexes (the point 4.3 of the chapter). The turn of antiprism bases lead serves as a basis for forming of spiral complex molecules (in this case DNA, RNA). Common polarized space of HMB medium in DNA molecule presents a base of "flash" memory. Figure 20 shows the polarized space for *N---H---N* bond. We can propose HMB is elementary bit of information for the development and functioning of living organisms.

**Figure 20.** Hydrogen bonding N---H---N of DNA molecule

46 Energy Conservation

this law (see point 3.2 of the chapter).

change much over the change in temperature.

**6.2. Deoxyribonucleic acid "flash" memory**

*n≈E/kT*=1.31031 1/m3. **Dulong–Petit's law.** The Dulong–Petit law, a chemical law proposed in 1819 by French physicists P.L. Dulong and A.T. Petit, states the classical expression for the molar specific heat capacity of a crystal. Experimentally the two scientists had found that the heat capacity per weight (the mass-specific heat capacity) for a number of substances became close to a constant value, after it had been multiplied by number-ratio representing the presumed relative atomic weight of the substance. These atomic weights had shortly before been suggested by Dalton. In modern terms, Dulong and Petit found that the heat capacity of a mole of many solid substances is about 3*R*, where *R* is the modern constant called the universal gas constant. Dulong and Petit were unaware of the relationship with *R*, since this constant had not yet been defined from the later kinetic theory of gases. The value of 3*R* is about 25 joules per kelvin, and Dulong and Petit essentially found that this was the heat capacity of crystals, per mole of atoms they contained. HMB theory gives theoretical base for

**Thermal expansion law.** To a first approximation, the change in length measurements of an object ("linear dimension" as opposed to, e.g., volumetric dimension) due to thermal expansion is related to temperature change by a "linear expansion coefficient". It is the fractional change in length per degree of temperature change. The point 4.1 presents detail modeling of this law. Heat expansion of electronic shells (including external van der Waals spheres) on linear law is described by corresponding solutions change of equation (4) for

gaseous HMB concentration 0 *n* at similar pressure 0 *p* is inversely proportional to temperature *T*). This law works well as long as the linear-expansion coefficient does not

Deoxyribonucleic acid (DNA) is a nucleic acid containing the genetic instructions used in the development and functioning of all known living organisms. The DNA segments carrying this genetic information are called genes. Likewise, other DNA sequences have structural purposes, or are involved in regulating the use of this genetic information. Along with ribonucleic acid and proteins, DNA is one of the three major macromolecules that are essential for all known forms of life. DNA consists of two long polymers of simple units called nucleotides, with backbones made of sugars and phosphate groups joined by ester bonds. These two strands run in opposite directions to each other and are therefore anti-parallel. Attached to each sugar is one of four types of molecules called nucleobases (informally, *bases*). It is the sequence of these four nucleobases along the backbone that encodes information. This information is read using the genetic code, which specifies the sequence of the amino acids within proteins. The code is read by copying stretches of DNA into the related nucleic acid RNA in a process called transcription. Within DNA cells is organized into long structures called chromosomes. During cell division these chromosomes are duplicated in the process of

0 0 *D kT n q* ( /)

*T* (since typical

polarized atom space when changing Debye radius 2 1/2

DNA replication, providing each cell its own complete set of chromosomes.

#### **6.3. High temperature air breathing engine data**

The united mathematical model (1) of the entire engine flow path is considered below (details present in [87, 88]). The typical flow passage of aviation gas turbine engine in meridional plane (z,r) is shown in figure 21. The main parts of engine (here it is a turbojet bypass engine with afterburner) are: fan (low pressure compressor), high pressure compressor (with a few variable guide vanes), main angular combustor chamber, high pressure turbine, low pressure turbine, afterburner, secondary contour, variable-area nozzle. A simulation of working fluid (air or gas) moving is fulfilled in the whole flow of engine including core and bypass duct. We use in this case equation system (1) with thin layer viscous approaches and differential turbulence models.

Results of flow simulation for bypass gas turbine engine show on figure 22-24. The engine was investigated in detail experimentally. Both the whole engine and the core engine were tested. The experiments demonstrated significant discrepancy between the tested and design engine parameters for a number of working points. In became apparent first of all in

the decreased flow capacity of the compressor, and led finally to increased turbine inlet temperatures, decreasing thrust etc. Examples of compressor and turbine flows are shown on figure 23 and 24.

**Figure 21.** Air Breathing engine scheme (bypass turbojet)

**Figure 22.** Examples of steady and unsteady calculations in turbojet engine

Channel flow with heat addition simulation is presented on figure 25. We can see temperature and pressure distributions inside channel and on up and down walls.

**Figure 23.** Static pressure distributions in the centrifugal compressor

on figure 23 and 24.

**Figure 21.** Air Breathing engine scheme (bypass turbojet)

**Figure 22.** Examples of steady and unsteady calculations in turbojet engine

Channel flow with heat addition simulation is presented on figure 25. We can see

temperature and pressure distributions inside channel and on up and down walls.

the decreased flow capacity of the compressor, and led finally to increased turbine inlet temperatures, decreasing thrust etc. Examples of compressor and turbine flows are shown

**Figure 24.** Mach number contours in high pressure two stage turbine

**Figure 25.** Pressure distributions in channel walls with intensive heat addition

#### **6.4. Astrophysics examples**

Let's demonstrate now possible application our modeling within the frame of classical mechanics approach for two astrophysics phenomena (gamma ray bursts and cosmic jets).

**Gamma ray bursts.** A good theoretic model of gamma-bursts can be represented by the above considered superluminal soliton solutions of rather big amplitude, which move in the dark matter medium without changing their shapes and loss of energy. We also give calculated solutions of the decomposition task of initial contraction for sequence of soliton solutions (Figure 26). As a result of such decomposition a sequence solitons with decreasing amplitude and propagation velocity is formed. The similar solutions can simulate the effects of gamma-bursts after glowing, which later reaches an observer (with the delay of several years).

**Figure 26.** Gamma-ray burst and afterglow simulation

50 Energy Conservation

**Figure 25.** Pressure distributions in channel walls with intensive heat addition

Let's demonstrate now possible application our modeling within the frame of classical mechanics approach for two astrophysics phenomena (gamma ray bursts and cosmic jets).

**Gamma ray bursts.** A good theoretic model of gamma-bursts can be represented by the above considered superluminal soliton solutions of rather big amplitude, which move in the dark matter medium without changing their shapes and loss of energy. We also give calculated solutions of the decomposition task of initial contraction for sequence of soliton

**6.4. Astrophysics examples**

**Cosmic extragalactic jets.** Further using our modeling we can imagine a quasar center (of an active galaxy) like a jet engine combustion chamber form which in the born opposite directions and perpendicular to the galaxy disk the two supercritical jets are breaking out. The combustion processes of "sub baryon fuel" are going on in the quasar center at huge temperatures and pressures. Such a "sublimation" of dark holes seems more natural (than their quantum evaporation) and is well described from the standpoint of classical mechanics (obviously, an adequate definition of state equation is required). Figure 27 displays a scheme of an active galaxy with two superluminal jets flowing from its center in opposite directions. The calculation results (on equations (1)) of several "barrels" for such extragalactic jets are given (as constant pressure lines).

**Figure 27.**  Conclusion**

### **Author details**

Mikhail Ja. Ivanov *Gas Dynamics Department, Central Institute of Aviation Motors, Moscow, Russia*

#### **Acknowledgement**

Author expresses his sincere thanks to V.I. Kokorev and B.O. Muravyov for their help in preparation of the chapter.

#### **8. References**

[8] Chernin A.D. Dark energy and universe antigravitation. Uspekhi Fizicheskikh Nauk 2008; 178(3), 267-300.

52 Energy Conservation

**7. Conclusion**

for Light and Dark Matter theory.

molecule structures).

demonstrated.

**Acknowledgement**

preparation of the chapter.

**Author details**

Mikhail Ja. Ivanov

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4. Additional empirical confirmations of the GUT are Hooke's, Dulong–Petit's, thermal expansion laws and interaction of radiation and matter. In the plane of practical applications the corrected theory of high temperature air breathing engines is

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### **Barotropic and Baroclinic Tidal Energy**

Dujuan Kang

56 Energy Conservation

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http://dx.doi.org/10.5772/52293

**1. Introduction**

Oceans cover approximately 71% percent of the Earth's surface, which makes them the largest solar energy collector in the world. On the other hand, the seawater moves constantly at different scales ranging from large-scale ocean currents down to centimeter-scale turbulent motions. These movements create a huge store of kinetic energy in the ocean. The ocean energy is clean and renewable. Therefore, a better understanding of the physical processes that govern the ocean movements is crucial to utilize the ocean energy more efficiently.

The tides are one of the major sources of energy to mix the interior ocean. The barotropic tidal energy is converted into heat through a series of important mixing processes. When the barotropic tides flow over rough topographic features, a portion of the barotropic energy is lost directly through local mixing, while the other portion is converted into baroclinic energy through the generation of internal (baroclinic) tides. This generated baroclinic energy either dissipates locally or radiates into the open ocean, and then cascades into smaller scales along the internal wave spectrum and finally turns into deep ocean turbulence (Figure 1). In the past decade significant efforts have been made to understand these tidal mixing processes and the associated energy distributions. Munk & Wunsch (1998) proposed a global tidal energy flux budget as shown in Figure 1. Of the 3.5 TW (1 TW = 1012 W) total tidal energy lost in the ocean, approximately 2.6 TW is dissipated in shallow marginal seas through bottom friction, while the remaining portion is lost in the deep ocean. Egbert & Ray (2000, 2001) have confirmed that approximately 1 TW, or 25–30% of the global total tidal energy is lost in the deep ocean by inferring dissipation from a global tidal model. They found the tides lose much more energy in the open ocean, generally in regions with rough topographic features (Figure 2). Field observations also showed that turbulent mixing is several order of magnitude larger over rough topography than over smooth abyssal plains [18]. This evidence has led to the interest in internal tides as a major source of energy for deep-ocean mixing. Both analytical and numerical investigations have also been performed to estimate the tidal energy flux budget [1, 9, 17, 20].

This chapter focuses on the numerical investigation of tidal energy in the ocean. The problem of how and where the ocean tides distribute their energy is discussed using a numerical study

© 2012 Kang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Kang, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Figure 1.** Global energy flux budget based on Munk and Wunsch (1998). The tides and winds are the two major sources of energy to mix the ocean. The tides contribute 3.5 TW of energy with 2.6 TW dissipated in shallow marginal seas and 0.9 TW lost in the deep ocean. The winds provide 1.2 TW of additional mixing power to maintain the global abyssal density distribution.

**Figure 2.** Global tidal energy loss rate derived from satellite altimetry sea-surface elevation data (Egbert and Ray, 2001).

of the tidal energetics in the Monterey Bay area along the central west coast of the United States. The purpose of this work is twofold: first, to provide a theoretical framework for the accurate evaluation of tidal energy budget and, second, to conduct numerical simulations of barotropic and baroclinic tides for a given region in the ocean and estimate the tidal energy budget based on the theoretical framework. A brief derivation of the barotropic and baroclinic energy equations is presented in Section 2. Subsequent sections focus on the numerical simulations which include the model setup and tidal dynamics in Section 3, and the energetics analysis in Section 4. The characteristics of tidal energy conversion is examined in Section 5. Finally, conclusions are summarized in Section 6.

#### **2. Theoretical framework**

2 Energy Conservation

**!**

**(")**

**Figure 1.** Global energy flux budget based on Munk and Wunsch (1998). The tides and winds are the two major sources of energy to mix the ocean. The tides contribute 3.5 TW of energy with 2.6 TW dissipated in shallow marginal seas and 0.9 TW lost in the deep ocean. The winds provide 1.2 TW of

**Figure 2.** Global tidal energy loss rate derived from satellite altimetry sea-surface elevation data (Egbert

of the tidal energetics in the Monterey Bay area along the central west coast of the United States. The purpose of this work is twofold: first, to provide a theoretical framework for the

**-**

additional mixing power to maintain the global abyssal density distribution.

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and Ray, 2001).

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In order to study the energetics of barotropic and baroclinic tides, we derive the barotropic and baroclinic energy equations as a theoretical framework for the numerical evaluation of the tidal energy budget in subsequent sections. Here we provide a brief description of the equations. More detailed derivation can be found in Kang (2010).

The derivation is based on the three-dimensional Reynolds-averaged Navier-Stokes equations under the Boussinesq approximation, along with the density transport equation and the continuity equation,

$$\frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} = -2\boldsymbol{\Omega} \times \mathbf{u} - \frac{1}{\rho\_0} \nabla p - \frac{g}{\rho\_0} \rho \mathbf{k} + \nabla\_H \cdot (\nu\_H \nabla\_H \mathbf{u}) + \frac{\partial}{\partial z} \left( \nu\_V \frac{\partial \mathbf{u}}{\partial z} \right), \tag{1}$$

$$\frac{\partial \rho}{\partial t} + \mathbf{u} \cdot \nabla \rho = \nabla\_H \cdot (\kappa\_H \nabla\_H \rho) + \frac{\partial}{\partial z} \left( \kappa\_V \frac{\partial \rho}{\partial z} \right) \,, \tag{2}$$

$$
\nabla \cdot \mathbf{u} = \mathbf{0},
\tag{3}
$$

where **u** = (*u*, *v*, *w*) is the velocity vector and **Ω** is the Earth's angular velocity vector. *ν* and *κ*, in units of m2 s−1, are the eddy viscosity and eddy diffusivity, respectively. ( )*H* and ( )*V* are the horizontal and vertical components of a variable or operator. The total density is given by *ρ* = *ρ*0 + *ρb* + *ρ*� , where *ρ*0 is the constant reference density, *ρb* is the background density, and *ρ*� is the perturbation density due to wave motions. The pressure is split into its hydrostatic (*ph*) and nonhydrostatic (*q*) parts with *p* = *ph* + *q*, where the hydrostatic pressure can be further decomposed with *ph* = *p*0 + *pb* + *p*� . To obtain the barotropic and baroclinic, the velocity is also split into its barotropic and baroclinic parts as **u** = **U** + **u**� . Accordingly, the kinetic energy density, in units of J m−3, is decomposed as

$$E\_k = \underbrace{\frac{1}{2}\rho\_0 \left(\mathcal{U}^2 + \mathcal{V}^2\right)}\_{E\_{\rm i0}} + \underbrace{\frac{1}{2}\rho\_0 \left(\mathcal{U}^2 + \mathcal{V}^2 + w^2\right)}\_{E\_k'} + \underbrace{\rho\_0 \left(\mathcal{U}u' + \mathcal{V}v'\right)}\_{E\_{\rm i0}},\tag{4}$$

where *Ek*0 is the barotropic horizontal kinetic energy density, *E*� *k* is the baroclinic kinetic energy density, and *E*� *k*0 is the cross term which vanishes upon depth-integration. Following Gill (1982), the perturbation potential energy due to surface elevation, in units of J m−2, is given by

$$
\overline{E\_{p0}} = \frac{1}{2} \rho\_0 g \eta^2 \,\text{\,\,\,}\tag{5}
$$

in which *η* is the free surface elevation. The available potential energy density, in units of J m−3, is defined as

$$E\_p' = \int\_{z-\zeta}^{z} g\left[\rho\_b(z) + \rho'(z) - \rho\_b(z')\right] dz',\tag{6}$$

where *ζ* is the vertical displacement of a fluid particle due to wave motions. This definition is an exact expression of the local APE because it computes the true active potential energy between the perturbed and unperturbed density profiles [12, 14].

Applying the variable decompositions and the boundary conditions, we obtain the depth-integrated barotropic and baroclinic energy equations as

$$\frac{\partial}{\partial t} \left( \overline{E\_{k0}} + \overline{E\_{p0}} \right) + \nabla\_H \cdot \overline{\mathbf{F}\_0} = -\overline{\mathbf{C}} - \overline{\mathbf{c}\_0} - D\_0 \tag{7}$$

$$
\frac{\partial}{\partial t} \left( \overline{E\_k'} + \overline{E\_p'} \right) + \nabla\_H \cdot \overline{\mathbf{F}'} = \overline{\mathbf{C}} - \overline{\mathbf{c}'} - D' \,, \tag{8}
$$

where the depth-integrated barotropic and baroclinic energy flux terms, with the small unclosed terms neglected, are given by

$$\overline{\mathbf{F}\_0} = \underbrace{\mathbf{U}\_H \overline{\mathbf{E}\_{k0}}}\_{\text{Aduction}} + \underbrace{\mathbf{U}\_H H \rho\_0 g \eta}\_{\text{Pressure work}} + \mathbf{U}\_H \overline{p'} + \mathbf{U}\_H \overline{\eta} \underbrace{-\overline{\nu\_H \nabla\_H E\_{k0}}}\_{\text{Diffusion}} \tag{9}$$

$$\overline{\mathbf{F}'} = \underbrace{\overline{\mathbf{u}\_H E\_k'} + \overline{\mathbf{u}\_H E\_{k0}'}}\_{\text{Aduction}} + \overbrace{\overline{\mathbf{u}\_H E\_p'}}\_{\text{Pressure work}} + \underbrace{\overline{\mathbf{u}\_H' p'} + \overline{\mathbf{u}\_H' q}}\_{\text{Pressure work}} + \underbrace{\overline{\nu\_H \nabla\_H E\_k'} - \overline{\kappa\_H \nabla\_H E\_p'}}\_{\text{Diffusion}} \tag{10}$$

in which the contributions from energy advection, pressure work, and diffusion have been labeled. The definitions of the barotropic-to-baroclinic conversion rate (*C*), the dissipation rates (*�*0 and *�*� ) and the bottom drag terms (*D*0 and *D*� ) are not listed here. Please refer to Kang (2010) for details.

The time-averaged forms of equations (7) and (8) are given by

$$\frac{1}{T}\Delta\overline{E\_0} + \nabla\_H \cdot \left<\overline{F\_0}\right> = -\left<\overline{\mathbf{C}}\right> - \left<\overline{\mathbf{c}\_0} + D\_0\right>\,. \tag{11}$$

$$
\frac{1}{T}\Delta \overline{E'} + \nabla\_H \cdot \left< \overline{\mathbf{F}'} \right> = \left< \overline{\mathbf{C}} \right> - \left< \overline{\mathbf{c}'} + D' \right> \tag{12}
$$

where �·� = 1 *T t*+*T t* (·) *dτ* is the time-average of a quantity over a time interval *T*. For a periodic system with period *T*, Δ*E*0 and Δ*E*� tend to zero and thus the first term in equations (11)-(12) vanishes. The remaining terms describe the energy balance associated with tidal dissipation processes. The ∇*H* · **F**0 term represents the total barotropic energy that is available for conversion to baroclinic energy, *C* represents the portion of the barotropic energy that is converted into baroclinic energy, and the ∇*H* · **F**� term represents the portion of the converted baroclinic energy that radiates from the conversion site. Local dissipation occurs along with the conversion and radiation processes, and they are measured by the barotopic (− �*�*0 + *D*0�) and baroclinic (− *�*� + *D*� ) dissipation terms, respectively. This approach presents an exact measure of the barotropic-to-baroclinic tidal energy conversion.

#### **3. Numerical simulations**

We can implement the theoretical framework into a numerical ocean model and then use it to analyze the tidal energy budget. In this section, we provide an example of the numerical investigation of the tidal energetics in the Monterey Bay area along the central west coast of the United States.

#### 60 Energy Conservation Barotropic and Baroclinic Tidal Energy 5 Barotropic and Baroclinic Tidal Energy 61

**Figure 3.** Bathymetry map of Monterey Bay and the surrounding open ocean. The black ∗ indicates a field observation station K. The domain outside the white box indicates the area affected by the sponge layers in the simulations. The solid black line indicates the vertical transaction along which baroclinic velocities are shown in Figure 5.

#### **3.1. Model setup**

4 Energy Conservation

where *ζ* is the vertical displacement of a fluid particle due to wave motions. This definition is an exact expression of the local APE because it computes the true active potential energy

Applying the variable decompositions and the boundary conditions, we obtain the

where the depth-integrated barotropic and baroclinic energy flux terms, with the small

+**U***H Hρ*0*gη* + **U***H p*� + **U***Hq* Pressure work

*H p*� + **u**�

 Pressure work

in which the contributions from energy advection, pressure work, and diffusion have been labeled. The definitions of the barotropic-to-baroclinic conversion rate (*C*), the dissipation

> = − *C*

periodic system with period *T*, Δ*E*0 and Δ*E*� tend to zero and thus the first term in equations (11)-(12) vanishes. The remaining terms describe the energy balance associated with tidal

of the converted baroclinic energy that radiates from the conversion site. Local dissipation occurs along with the conversion and radiation processes, and they are measured by the

> *�*� + *D*�

approach presents an exact measure of the barotropic-to-baroclinic tidal energy conversion.

We can implement the theoretical framework into a numerical ocean model and then use it to analyze the tidal energy budget. In this section, we provide an example of the numerical investigation of the tidal energetics in the Monterey Bay area along the central west coast of

*C*

*Hq*

*t* (·) *dτ* is the time-average of a quantity over a time interval *T*. For a

−*νH*∇*HE*�

+ ∇*H* · **F**0 = −*C* − *�*0 − *D*0 , (7)

+ ∇*H* · **F**� = *C* − *�*� − *D*� , (8)

−*νH*∇*HEk*0 Diffusion

 Diffusion

term represents the total barotropic energy that is

 **F**�  *k* − *κH*∇*HE*�

) are not listed here. Please refer to

− �*�*0 + *D*0� , (11)

represents the portion of the barotropic

) dissipation terms, respectively. This

, (12)

term represents the portion

*p*

, (9)

, (10)

between the perturbed and unperturbed density profiles [12, 14].

depth-integrated barotropic and baroclinic energy equations as

*Ek*0 + *Ep*0

*k*0 + **u***HE*�

) and the bottom drag terms (*D*0 and *D*�

*p*

 **F**0

 **F**� = *C* − *�*� + *D*�

+**u**�

*∂ ∂t*

**F**0 = **U***HEk*0 Advection

*k* + **u***HE*�

 Advection

The time-averaged forms of equations (7) and (8) are given by

*T* Δ*E*0 + ∇*H* ·

*T* Δ*E*� + ∇*H* ·

energy that is converted into baroclinic energy, and the ∇*H* ·

 **F**0

1

1

available for conversion to baroclinic energy,

barotopic (− �*�*0 + *D*0�) and baroclinic (−

unclosed terms neglected, are given by

**F**� = **u***HE*�

rates (*�*0 and *�*�

where �·� = 1

*T t*+*T*

dissipation processes. The ∇*H* ·

**3. Numerical simulations**

the United States.

Kang (2010) for details.

*∂ ∂t E*� *k* + *E*� *p*

> Monterey Bay is featured by the prominent Monterey Submarine Canyon (MSC), numerous ridges, smaller canyons, and a continental slope and break region. This area is exposed to the large- and meso-scale variations of the California Current System as well as the tidal currents. Energetic internal wave activity has been observed in MSC and the surrounding region. Due to the complex bathymetry, tidal mixing processes in this area are of great interest. Our simulation domain extends approximately 200 km north and south of Moss Landing, and 400 km offshore (Figure 3), which is large enough to allow the evolution of offshore-propagating waves.

> The ocean model we employ for this study is the SUNTANS model of Fringer *et al.* (2006). The resolution of the horizontal unstructured grid smoothly transitions from roughly 80 m within the Bay to 11 km along the offshore boundary. In the vertical, there are 120 z-levels with thickness stretching from roughly 6.6 m at the surface to 124 m in the deepest location, which provides better vertical resolution in the shallow regions. In total, the mesh consists of approximately 6 million grid cells in 3D.

> The initial free-surface and velocity field are initialized as quiescent throughout the domain. The initial stratification is specified with horizontally-homogeneous temperature and salinity profiles. At the coastline, we apply the no-flow condition, while at the three open boundaries the barotropic velocities are specified with the OTIS global tidal model [2]. A sponge layer is imposed at each of the open boundaries to absorb the internal waves and minimize the

#### 6 Energy Conservation 62 Energy Conservation

reflection of baroclinic energy into the domain. More model setup details and the validation of the model skill can be found in Kang and Fringer (2012).

#### **3.2. Tidal dynamics**

**Figure 4.** Sea surface elevation at *t* = 18*TM*2 from *M*2 forced barotropic run (left) and baroclinic run (right). Bathymetry contours are spaced at -200, -500, -1000, -1500, -2000, -2500, -3000, -3500 m.

Monterey Bay is exposed to predominantly semidiurnal *M*2 tide. Therefore we carry out two sets of *M*2 forced simulations, one with homogeneous density to investigate the barotropic tides only, while the other with vertical stratification to study the baroclinic tides. Each simulation is run for 18 *M*2 tidal cycles. Sea-surface elevations from such two runs are illustrated in Figure 4. This comparison highlights the modulation of baroclinic tides to the barotropic flow field, particularly near rough bottom topography.

Figure 5 demonstrates the vertical distribution of baroclinic velocities along a transect indicated in Figure 3. It can be seen clearly that baroclinic tides are generated at Sur Platform and then radiate to the north and south in the form of tidal beams.

#### **4. Tidal energetics**

We evaluate the depth-integrated, time-averaged barotropic and baroclinic energy equations (11) and (12) for the energy analysis in this section. They are averaged over the last six *M*2 tidal cycles of the 18-*M*2-cycle baroclinic simulation. Because the system is periodic, the first term in equation (11)-(12) tends to zero upon period-averaging. We therefore obtain the balance relations

$$
\nabla\_H \cdot \langle \mathbf{F}\_0 \rangle = -\left\langle \overline{\mathbf{C}} \right\rangle - \left\langle \overline{\mathbf{c}\_0} + D\_0 \right\rangle \ , \tag{13}
$$

$$
\nabla\_H \cdot \left< \overline{\mathbf{F}}' \right> = \left< \overline{\mathbf{C}} \right> - \left< \overline{\mathbf{c}'} + D' \right> \,. \tag{14}
$$

The model computes all the energy terms in the barotropic and baroclinic equations. In the following analysis, the conversion rate, *C* , and the energy flux divergence terms, ∇*H* · **F**0

**Figure 5.** Vertical structure of the East-West (a) and North-South (b) baroclinic velocities along the transect indicated in Figure 3.

and ∇*H* · **F**� , are from direct model outputs. However, the barotropic and baroclinic dissipation rates are inferred from the above balance relations as in Niwa and Hibiya (2004).

#### **4.1. Horizontal structure**

6 Energy Conservation

reflection of baroclinic energy into the domain. More model setup details and the validation

**Figure 4.** Sea surface elevation at *t* = 18*TM*2 from *M*2 forced barotropic run (left) and baroclinic run (right). Bathymetry contours are spaced at -200, -500, -1000, -1500, -2000, -2500, -3000, -3500 m.

barotropic flow field, particularly near rough bottom topography.

and then radiate to the north and south in the form of tidal beams.

∇*H* · **F**0

∇*H* · **F**� = *C* − � + *D*�

following analysis, the conversion rate,

Monterey Bay is exposed to predominantly semidiurnal *M*2 tide. Therefore we carry out two sets of *M*2 forced simulations, one with homogeneous density to investigate the barotropic tides only, while the other with vertical stratification to study the baroclinic tides. Each simulation is run for 18 *M*2 tidal cycles. Sea-surface elevations from such two runs are illustrated in Figure 4. This comparison highlights the modulation of baroclinic tides to the

Figure 5 demonstrates the vertical distribution of baroclinic velocities along a transect indicated in Figure 3. It can be seen clearly that baroclinic tides are generated at Sur Platform

We evaluate the depth-integrated, time-averaged barotropic and baroclinic energy equations (11) and (12) for the energy analysis in this section. They are averaged over the last six *M*2 tidal cycles of the 18-*M*2-cycle baroclinic simulation. Because the system is periodic, the first term in equation (11)-(12) tends to zero upon period-averaging. We therefore obtain the balance

The model computes all the energy terms in the barotropic and baroclinic equations. In the

− �0 + *D*0� , (13)

, and the energy flux divergence terms, ∇*H* ·

. (14)

 **F**0

 = − *C*

> *C*

of the model skill can be found in Kang and Fringer (2012).

**3.2. Tidal dynamics**

**4. Tidal energetics**

relations

The left panel of Figure 6 illustrates the horizontal distribution of the depth-integrated baroclinic energy flux vectors, **F**� . Large energy fluxes are seen in the vicinity of rough topographical features, such as the MSC, the Sur Ridge-Platform region, and the Davidson Seamount. The right panel of Figure 6 shows the horizontal distribution of the depth-integrated barotropic-to-baroclinic conversion rate, *C* . Red color represents positive energy conversion rate, which implies generation of internal tides, and negative energy conversion rate (blue color) represents energy transfer from the baroclinic tide to the barotropic tide. Negative energy conversion is due to the phase difference between locally-

**Figure 6.** Depth-integrated, period-averaged baroclinic energy flux, **F**� (left), and barotropic-to-baroclinic conversion rate, *C* (right). Darker bathymetry contours are 200 m and 3000 m isobaths.

and remotely-generated baroclinic tides, and therefore indicates multiple generation sites [23]. Significant negative conversion occurs within the MSC because the locally generated baroclinic tides interact with those generated at the North Sur Platform region. Large baroclinic energy can be seen radiating from North Sur Platform into the MSC following the canyon bathymetry from the figure. Figure 6 also shows that most of the generation is contained within the 200-m and 3000-m isobaths. The baroclinic energy flux divergence, ∇*H* · **F**� , and the baroclinic dissipation rate, ∇*H* · **F**� − *C* , are shown in Figure 7's left and right panels, respectively. Large baroclinic energy dissipation occurs near the locations of strong internal tide generation.

#### **4.2. Energy flux budget**

The total power within a region is obtained by area-integrating the period-averaged and depth-integrated energy terms to give

$$\text{BT } \text{ Input} = -\sum \nabla\_H \cdot \left< \overline{\mathbf{F}\_0} \right> \,\Delta A\_\prime \tag{15}$$

$$\text{Conversion} = \sum \langle \overline{\mathbb{C}} \rangle \,\Delta A \,\, \tag{16}$$

$$\text{BC} \cdot \text{Radiation} = \sum \nabla\_H \cdot \left< \overline{\mathbf{F}}' \right> \,\Delta A\_\prime \tag{17}$$

$$\text{BT}\cdot\text{Dissipation} = \sum \left(\nabla\_H \cdot \left<\overline{\mathbf{F}\_0}\right> + \left<\overline{\mathbf{C}}\right>\right)\,\Delta A\,\,\tag{18}$$

$$\text{BC}\cdot\text{Dissipation} = \sum \left(\nabla\_H \cdot \left<\overline{\mathbf{F}}'\right> - \left<\overline{\mathbf{C}}\right>\right)\Delta A\_\prime \tag{19}$$

where ∑ implies summation of the grid cells within a particular region and Δ*A* is the area of each grid cell.

 -

> **F**�

(left), and

, are shown in Figure 7's left

Δ*A* , (15)

Δ*A* , (17)

Δ*A* , (18)

Δ*A* , (19)

Δ*A* , (16)

(right). Darker bathymetry contours are 200 m and 3000 m

**Figure 6.** Depth-integrated, period-averaged baroclinic energy flux,

, and the baroclinic dissipation rate, ∇*H* ·

*C*

and remotely-generated baroclinic tides, and therefore indicates multiple generation sites [23]. Significant negative conversion occurs within the MSC because the locally generated baroclinic tides interact with those generated at the North Sur Platform region. Large baroclinic energy can be seen radiating from North Sur Platform into the MSC following the canyon bathymetry from the figure. Figure 6 also shows that most of the generation is contained within the 200-m and 3000-m isobaths. The baroclinic energy flux divergence,

and right panels, respectively. Large baroclinic energy dissipation occurs near the locations of

The total power within a region is obtained by area-integrating the period-averaged and

*C*

∇*H* · **F**0 + *C*

 ∇*H* · **F**� − *C*

where ∑ implies summation of the grid cells within a particular region and Δ*A* is the area of

BT Input = − ∑ ∇*H* ·

Conversion = ∑

BC Radiation = ∑ ∇*H* ·

BT Dissipation = ∑

BC Dissipation = ∑

 **F**� − *C*

 **F**0

 **F**�

barotropic-to-baroclinic conversion rate,

strong internal tide generation.

depth-integrated energy terms to give

**4.2. Energy flux budget**

each grid cell.

isobaths.

∇*H* · **F**�

>

>

**Figure 7.** Depth-integrated, period-averaged baroclinic energy flux divergence, ∇*H* · **F**� (left), and baroclinic dissipation rate, ∇*H* · **F**� − *C* (right).

As Figure 6 indicated, most of the baroclinic energy generation is within the 200-m and 3000-m isobaths. We now depict the energy budget for the shelf and slope regions bounded by the 200-m and 3000-m isobaths Figure 8. Barotropic energy is lost at a rate of 147 MW to the slope region and approximately 87% of this energy is converted into baroclinic energy. Most of this generated baroclinic energy is dissipated locally, while the remaining portion (38%) is radiated. The shelf region acts as a baroclinic energy sink because it dissipates both the energy generated locally and the portion flowing into it from the slope region.

Two efficiency parameters are defined to examine the characteristics of baroclinic energy conversion and radiation, respectively,

$$
\eta\_{\mathcal{C}} = \frac{\text{Conversion}}{\text{BT Input}}\,,\tag{20}
$$

$$
\eta\_r = \frac{\text{BC Ratio}}{\text{Conversion}}.\tag{21}
$$

Figure 9 compares the conversion and radiation efficiency for five subdomains (a)-(e). Subdomain (a), a 200 km × 230 km domain, is used to represent the Monterey Bay area because it includes all typical topographic features in this area. This comparison demonstrates that the tidal energy conversion and radiation depend strongly on topographic features. The Davidson Seamount and the Northern shelf-break region are the most efficient topographic features to convert (∼ 94%) barotropic energy into baroclinic energy and then let it radiate out into the open ocean (> 75%). The Sur Platform region also converts a large portion (88%) and radiates more than half of the barotropic energy as baroclinic energy. The MSC acts as an energy sink because it does not radiate energy but instead absorbs the baroclinic energy from the Sur Platform region.

**Figure 8.** Schematic of the *M*2 tidal energy budget for the two subdomains bounded by the 0-m, 200-m and 3000-m isobaths.

**Figure 9.** Efficiency of the *M*2 baroclinic energy conversion and radiation for the five subdomains indicated in the left figure.

#### **4.3. Energy flux contributions**

10 Energy Conservation

**Figure 8.** Schematic of the *M*2 tidal energy budget for the two subdomains bounded by the 0-m, 200-m

**Region** *-*

(a) All 88% 42% (b) Shelf Break 94% 76% (c) Submarine Canyon 71% -62% (d) Ridge Platform 88% 61% (e) Seamount 95% 81%

and 3000-m isobaths.

indicated in the left figure.

(b) North Shelf Break

(c) MSC

(a)

(d) Sur Region

(e) Davidson Seamount

**Figure 9.** Efficiency of the *M*2 baroclinic energy conversion and radiation for the five subdomains

**Figure 10.** Baroclinic energy flux contributions from (a) hydrostatic, and (b) nonhydrostatic pressure work in the Monterey Submarine Cayon region.

As discussed in Section 2, our method computes the full energy fluxes and thus allows us to compare the contributions of different components. Here we choose subdomain (a) as our study domain. We found that the component due to hydrostatic pressure work (the traditional energy flux) is the dominant term. If we consider the total energy radiation as 100%, the hydrostatic contribution is ∼ 101% while the other terms account for the remaining -1%. The advection and nonhydrostatic contributions are quite small, which implies that the internal tides in the Monterey Bay area are mainly linear and hydrostatic. Figure 10 shows that the hydrostatic and nonhydrostatic energy fluxes oppose one another within MSC. This occurs because the effect of the nonhydrostatic pressure is to restrict the acceleration owing to the impact of vertical inertia. Hydrostatic models therefore tend to overpredict the energy flux particularly for strongly nonhydrostatic flows.

#### **5. Mechanism of energy conversion**

Several nondimensional parameters are generally employed to discuss the character of barotropic-to-braoclinic energy conversion. The first parameter is the steepness parameter defined by

$$
\epsilon\_1 = \frac{\gamma}{s},
\tag{22}
$$

where *γ* is the topographic slope, and *s* is the internal wave characteristic slope. The steepness parameter is used to distinguish between subcritical (*�*1 < 1) and supercritical topography (*�*1 > 1). The topography is referred to as critical when *�*1 = 1.

#### 12 Energy Conservation 68 Energy Conservation

The second nondimensional parameter is the tidal excursion parameter defined by

$$
\varepsilon\_2 = \frac{\mathcal{U}\_0 k\_b}{\omega} \,\,\,\,\,\,\tag{23}
$$

which measures the ratio of the tidal excursion *U*0/*ω* to the horizontal scale of the topography *k*−1 *b* .The excursion parameter is used to examine the nonlinearity of the waves [6, 15, 20]. When *�*2 � 1, linear internal tides are generated mainly at the forcing frequency *ω*. Over subcritical topography (*�*1 < 1) most of the energy generation is in the first mode internal tide, while over critical or supercritical topography (*�*1 ≥ 1), higher modes are generated and their superposition creates internal tidal beams. At intermediate excursion (*�*2 ∼ 1), nonlinearity becomes important, and nonlinear internal wave bores, weak unsteady lee waves, and solitary internal waves may be generated depending on the topographic features. When *�*2 > 1, in addition to bores and solitary internal waves, strong unsteady lee waves may form [22].

Although internal wave generation is a complex process, we can summarize the behavior of the internal wave generation in Monterey Bay by plotting histograms of the conversion and divergence terms as functions of the criticality and excursion parameters. Here we compute the two parameters throughout subdomain (a). The upper and left panels of Figures 11 demonstrate the distribution of conversion as a function of the nondimensional parameters *�*1 and *�*2, respectively. The energy conversion (green bins) occurs predominantly in regions within which *�*1 < 5 and *�*2 < 0.02. Under these conditions, baroclinic tides generated in this region are mainly linear and in the form of internal tidal beams [6, 20, 22]. As expected, conversion of barotropic energy into baroclinic energy peaks for critical topography near *�*1 ∼ 1. More interesting, however, is that there is also a peak in conversion for a particular value of *�*2 ∼ 0.005.

The lower right panel of Figure 11 depicts the distribution of the energy conversion as a function of the two parameters. Energy conversion occurs mainly in regions where *�*1 and *�*2 satisfy a particular relation. When both parameters are small, this relation is linear. As the values of the two parameters increase, the departure is weakly quadratic.

#### **6. Summary**

The tides are one of the main power to mix the ocean, which is the largest energy collector from the Earth-Moon system. A better understanding of how and where the tides lost their energy is very important to the climate and energy study. In this chapter, we present a numerical method to investigate the tidal energy conversion and estimate the tidal energy budget.

A theoretical framework for analyzing tidal energetics is derived based on the complete form of the barotropic and baroclinic energy equations that provide an accurate and detailed energy analysis. Three-dimensional, high-resolution simulations of the tides and waves in the Monterey Bay area are conducted using the hydrodynamic coastal SUNTANS ocean model. Based on the theoretical approach, model results are analyzed to address the question of how the barotropic tidal energy is partitioned between local barotropic dissipation and local generation of baroclinic energy, and then how much of this generated baroclinic energy is lost locally versus how much is radiated away for open-ocean mixing. Subdomain (a), a 200 km × 230 km domain, is used to represent the Monterey Bay area because it includes

*�*2 = *U*0*kb*

which measures the ratio of the tidal excursion *U*0/*ω* to the horizontal scale of the topography

*b* .The excursion parameter is used to examine the nonlinearity of the waves [6, 15, 20]. When *�*2 � 1, linear internal tides are generated mainly at the forcing frequency *ω*. Over subcritical topography (*�*1 < 1) most of the energy generation is in the first mode internal tide, while over critical or supercritical topography (*�*1 ≥ 1), higher modes are generated and their superposition creates internal tidal beams. At intermediate excursion (*�*2 ∼ 1), nonlinearity becomes important, and nonlinear internal wave bores, weak unsteady lee waves, and solitary internal waves may be generated depending on the topographic features. When *�*2 > 1, in addition to bores and solitary internal waves, strong unsteady lee waves may form [22].

Although internal wave generation is a complex process, we can summarize the behavior of the internal wave generation in Monterey Bay by plotting histograms of the conversion and divergence terms as functions of the criticality and excursion parameters. Here we compute the two parameters throughout subdomain (a). The upper and left panels of Figures 11 demonstrate the distribution of conversion as a function of the nondimensional parameters *�*1 and *�*2, respectively. The energy conversion (green bins) occurs predominantly in regions within which *�*1 < 5 and *�*2 < 0.02. Under these conditions, baroclinic tides generated in this region are mainly linear and in the form of internal tidal beams [6, 20, 22]. As expected, conversion of barotropic energy into baroclinic energy peaks for critical topography near *�*1 ∼ 1. More interesting, however, is that there is also a peak in conversion for a particular

The lower right panel of Figure 11 depicts the distribution of the energy conversion as a function of the two parameters. Energy conversion occurs mainly in regions where *�*1 and *�*2 satisfy a particular relation. When both parameters are small, this relation is linear. As the

The tides are one of the main power to mix the ocean, which is the largest energy collector from the Earth-Moon system. A better understanding of how and where the tides lost their energy is very important to the climate and energy study. In this chapter, we present a numerical method to investigate the tidal energy conversion and estimate the tidal energy budget.

A theoretical framework for analyzing tidal energetics is derived based on the complete form of the barotropic and baroclinic energy equations that provide an accurate and detailed energy analysis. Three-dimensional, high-resolution simulations of the tides and waves in the Monterey Bay area are conducted using the hydrodynamic coastal SUNTANS ocean model. Based on the theoretical approach, model results are analyzed to address the question of how the barotropic tidal energy is partitioned between local barotropic dissipation and local generation of baroclinic energy, and then how much of this generated baroclinic energy is lost locally versus how much is radiated away for open-ocean mixing. Subdomain (a), a 200 km × 230 km domain, is used to represent the Monterey Bay area because it includes

values of the two parameters increase, the departure is weakly quadratic.

*ω* , (23)

The second nondimensional parameter is the tidal excursion parameter defined by

*k*−1

value of *�*2 ∼ 0.005.

**6. Summary**

**Figure 11.** Distribution of the barotropic-to-baroclinic energy conversion as a function of steepness parameter *�*1 and excursion parameter *�*2 for subdomain (a).

all typical topographic features in this region. Of the 152 MW energy lost from the barotropic tide, approximately 133 MW (88%) is converted into baroclinic energy through internal tide generation, and 42% (56 MW) of this baroclinic energy radiates away for open-ocean mixing (Figure 12). The tidal energy partitioning depends greatly on the topographic features. The Davidson Seamount and the Northern shelf-break region are most efficient at baroclinic energy generation and radiation. The Sur Platform region converts a large portion and radiates roughly half of the barotropic energy as baroclinic energy. The Monterey Submarine Canyon acts as an energy sink because it does not radiate energy but instead absorbs the baroclinic energy from the Sur Platform region. The energy flux contributions from nonlinear and nonhydrostatic effects are also examined. The small advection and nonhydrostatic contributions imply that the internal tides in the Monterey Bay area are predominantly linear and hydrostatic.

We also investigate the character of tidal energy conversion by examining the energy distribution as a function of two nondimensional parameters, namely the steepness parameter (*�*1 = *γ*/*s*) and the excursion parameter (*�*2 = *U*0*kb*/*ω*). The generation mainly occurs in the regions satisfying *�*1 < 5 and *�*2 < 0.02, indicating that baroclinic tides generated in the Monterey Bay area are mainly linear and in the form of internal tidal beams. The results highlight how description of the conversion process with simple nondimensional parameters produces results that are consistent with theory, in that internal wave energy generation peaks at critical topography (*�*1 ∼ 1). The results also indicate that conversion peaks for a particular excursion parameter (*�*2 ∼ 0.005 for this case). This implies that it may be possible to parameterize conversion of barotropic to baroclinic energy in barotropic models

**Figure 12.** Schematic of the *M*2 tidal energy budget in percentages for subdomain (a) indicated in Figure 9. The bold percentages are relative to the total input barotropic energy, and the thin italic percentages are relative to the generated baroclinic energy.

with knowledge of 1 and 2. For example, a parameterization of internal wave generation based on the steepness parameter has been widely used in global barotropic tidal models [21] and ocean general circulation models [10].

This work outlines a systematic approach to analyze internal tide energetics and estimate tidal energy budget regionally and globally. The results draw a picture of how the *M*2 tidal energy is distributed in the Monterey Bay region. The Monterey Bay area is exposed to the large-scale California Current System and meso-scale eddies and upwelling. The seasonally varying dynamics may affect the stratification and thus the generation and propagation of internal tides in this area. Therefore, it may be necessary to consider seasonal effects of stratification and to include mesoscale effects by coupling with a larger-scale regional model such as ROMS [8, 19].

#### **Acknowledgements**

The author gratefully acknowledge the support of Professor Oliver Fringer at Stanford University and the ONR Grant. I would like to thank Samantha Terker, Drs. Jody Klymak, Robert Pinkel, James Girton, and Eric Kunze for kindly providing the field data. The helpful discussions with Drs. Robert Street, Stephen Monismith, Leif Thomas, and Rocky Geyer are greatly appreciated. I also thank Dr. Steven Jachec for useful help with simulation setup.

#### **Author details**

Dujuan Kang *Institute of Marine and Coastal Sciences, Rutgers University, New Jersey, USA*

#### **7. References**

14 Energy Conservation

**Topography**

**88%** *(100%)*

**12%**

*(58%)* **51%**

**Barotropic Tides**

**100%**

**Baroclinic Tides**

**Deep Ocean Mixing Local Mixing**

**Figure 12.** Schematic of the *M*2 tidal energy budget in percentages for subdomain (a) indicated in Figure 9. The bold percentages are relative to the total input barotropic energy, and the thin italic percentages

with knowledge of 1 and 2. For example, a parameterization of internal wave generation based on the steepness parameter has been widely used in global barotropic tidal models [21]

This work outlines a systematic approach to analyze internal tide energetics and estimate tidal energy budget regionally and globally. The results draw a picture of how the *M*2 tidal energy is distributed in the Monterey Bay region. The Monterey Bay area is exposed to the large-scale California Current System and meso-scale eddies and upwelling. The seasonally varying dynamics may affect the stratification and thus the generation and propagation of internal tides in this area. Therefore, it may be necessary to consider seasonal effects of stratification and to include mesoscale effects by coupling with a larger-scale regional model such as ROMS

The author gratefully acknowledge the support of Professor Oliver Fringer at Stanford University and the ONR Grant. I would like to thank Samantha Terker, Drs. Jody Klymak, Robert Pinkel, James Girton, and Eric Kunze for kindly providing the field data. The helpful discussions with Drs. Robert Street, Stephen Monismith, Leif Thomas, and Rocky Geyer are greatly appreciated. I also thank Dr. Steven Jachec for useful help with simulation setup.

*Institute of Marine and Coastal Sciences, Rutgers University, New Jersey, USA*

**Internal Waves**

are relative to the generated baroclinic energy.

and ocean general circulation models [10].

[8, 19].

**Acknowledgements**

**Author details**

Dujuan Kang

**37%** *(42%)*

#### 16 Energy Conservation 72 Energy Conservation

## **Understanding Energy Conservation: Intersection Between Biological and Everyday Life Contexts**

Vivien Mweene Chabalengula and Frackson Mumba

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/51872

#### **1. Introduction**

16 Energy Conservation

[21] St. Laurent L, Simmons H.L, Jayne S.R (2002) Estimating tidally driven mixing in the

[22] Vlasenko V, Stashchuk N, Hutter K (2005) Baroclinic Tides: Theoretical Modeling and

[23] Zilberman N.V, Becker J.M, Merrifield M.A, Carter G.S (2009) Model estimates of M2 internal tide generation over Mid-Atlantic Ridge topography. J. Phys. Oceanogr. 39:

deep ocean. Geophys. Res. Lett. 29: 2106-2110.

2635-2651.

Observational Evidence. Cambridge University Press.

Energy and energy conservation (which is also the First Law of Thermodynamics) are such closely related concepts that it is almost impossible to discuss one without the other in a closed system (Goldring & Osborne, 1994). Energy is commonly defined as the *capacity to do work* (Lee & Liu, 2010), such as driving metabolic reactions and processes (e.g. photosynthesis, muscle contraction) in biological systems. On the other hand, the energy conservation principle is commonly stated as *energy cannot be created or destroyed* (Raven & Johnson, 1999) in almost all science textbooks. However, many science educators argue that this definition may be confusing among students if supporting concepts such as energy transfer, energy flow, and energy transformation (Mclldowie, 1995; Chabalengula et al, 2012) are not incorporated when defining energy conservation. This is because all energy forms are inter-convertible from one form to another without any *loss*; and any apparent loss of energy can be explained as the conversion/transformation of energy into some other form (Raven & Johnson, 1999; Solomon et al, 1993).

The concepts of energy and energy conservation are central scientific ideas which provide an important key to our understanding of the way things happen in the biological, physical, and technological world (Liu, Ebenezer & Fraser, 2002). Furthermore, energy is one of the science concepts that cuts across all science disciplines, and is experienced in our everyday life situations (Saglam-Arslan & Kurnaz, 2009).

However, the synonymous use of the terms *conservation* and *saving* in everyday language usage causes students to misunderstand the scientific meaning of the energy conservation principle. With the current national and global debates on energy saving reality coming to agenda with energy crisis, many students think of energy conservation as energy saving

© 2012 Chabalengula and Mumba., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 Chabalengula and Mumba., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

because the latter term is used when issues on depleting energy sources are discussed in media and political realms (Tatar & Oktay, 2007). As such, it is imperative that school-going citizens are scientifically literate about what energy conservation is if they are to delineate energy conservation and energy saving. Therefore we propose that it is vital for science educators to determine students' understanding of energy conservation from a scientific (particularly biological context) and an everyday life context. These two contexts are particularly important because they are interrelated in that biological contexts such as jogging and breathing are always experienced by students on each daily basis so much that they can relate to them very well. Therefore, a compilation of students' understanding of energy conservation based on these two contexts would provide a set of energy conservation data that can be used as a basis for science education curriculum development and instructional design in schools (Lee, 2011).

#### **1.1. Energy conservation principle**

According to the energy conservation principle (also known as the first law of thermodynamics), energy cannot be created or destroyed; instead it can be converted from one form to another (Raven & Johnson, 1999; Solomon et al, 1993). All energy forms are inter-convertible from one form to another without any '*loss*'. Any apparent loss of energy can be explained as the conversion of energy into some other form. For example, in biological/living systems, some of the energy is used to drive metabolic processes and some of it dissipates to the atmosphere in the form of heat. Therefore, energy as a conserved quantity at the system level is built upon many supporting concepts such as energy source, energy transfer, energy flow, and energy transformation (Mclldowie, 1995).

The description of energy flow and transformations is frequently used in many biological and technological applications (Ametller & Pinto, 2002; Lin & Hu, 2003). For instance, in biological systems, energy flows from sources such as the sun and moves through a number of carriers to eventual receivers, such as through producers (mostly plants which utilize energy to produce food during photosynthesis) to consumers (animals) in food chains. That is, plant cells transform light energy to chemical energy stored in chemical bonds of food materials. When some herbivores eat the plants, some of this chemical energy is eventually converted to mechanical energy in animals for muscle contraction (useful work), whereas some of it may dissipate to the atmosphere in form of heat energy (Raven & Johnson, 1999). As all these metabolic processes are happening, there is no loss; instead any seemingly loss is explained in terms of energy conversion/transformation. Given the scientific viewpoint of energy conservation especially in biological systems, it is important to remind readers that this concept poses conceptual difficulties among students, as highlighted in the next section.

#### **1.2. Problematic concerns about energy conservation in biology education**

As stated earlier on, the energy conservation principle is commonly stated as energy cannot be created or destroyed in most science textbooks. Due to its common appearance in textbooks and its short definition, Tatar and Oktay (2007) point out that energy conservation is one of the most known science principles among students as it is easy to state and remember. As such when asked to state the energy conservation principle, many students tend to recite it with relative easiness, but they are unable to correctly apply it to biological systems. Therefore, the two problematic aspects that make energy conservation a difficult concept to understand among students are:

74 Energy Conservation

and instructional design in schools (Lee, 2011).

**1.1. Energy conservation principle**

because the latter term is used when issues on depleting energy sources are discussed in media and political realms (Tatar & Oktay, 2007). As such, it is imperative that school-going citizens are scientifically literate about what energy conservation is if they are to delineate energy conservation and energy saving. Therefore we propose that it is vital for science educators to determine students' understanding of energy conservation from a scientific (particularly biological context) and an everyday life context. These two contexts are particularly important because they are interrelated in that biological contexts such as jogging and breathing are always experienced by students on each daily basis so much that they can relate to them very well. Therefore, a compilation of students' understanding of energy conservation based on these two contexts would provide a set of energy conservation data that can be used as a basis for science education curriculum development

According to the energy conservation principle (also known as the first law of thermodynamics), energy cannot be created or destroyed; instead it can be converted from one form to another (Raven & Johnson, 1999; Solomon et al, 1993). All energy forms are inter-convertible from one form to another without any '*loss*'. Any apparent loss of energy can be explained as the conversion of energy into some other form. For example, in biological/living systems, some of the energy is used to drive metabolic processes and some of it dissipates to the atmosphere in the form of heat. Therefore, energy as a conserved quantity at the system level is built upon many supporting concepts such as energy source,

The description of energy flow and transformations is frequently used in many biological and technological applications (Ametller & Pinto, 2002; Lin & Hu, 2003). For instance, in biological systems, energy flows from sources such as the sun and moves through a number of carriers to eventual receivers, such as through producers (mostly plants which utilize energy to produce food during photosynthesis) to consumers (animals) in food chains. That is, plant cells transform light energy to chemical energy stored in chemical bonds of food materials. When some herbivores eat the plants, some of this chemical energy is eventually converted to mechanical energy in animals for muscle contraction (useful work), whereas some of it may dissipate to the atmosphere in form of heat energy (Raven & Johnson, 1999). As all these metabolic processes are happening, there is no loss; instead any seemingly loss is explained in terms of energy conversion/transformation. Given the scientific viewpoint of energy conservation especially in biological systems, it is important to remind readers that this concept poses conceptual difficulties among students, as highlighted in the next section.

**1.2. Problematic concerns about energy conservation in biology education**

As stated earlier on, the energy conservation principle is commonly stated as energy cannot be created or destroyed in most science textbooks. Due to its common appearance in textbooks and its short definition, Tatar and Oktay (2007) point out that energy conservation

energy transfer, energy flow, and energy transformation (Mclldowie, 1995).

The two problems stated above led to our motivation to look at the science education literature and determine the extent to which the science education research has tried to remediate the problems. Two issues became evident: First, a review of the previous instruments aimed at diagnosing students' understanding of energy conservation shows that the focus was mainly in physics and engineering contexts rather than in biological contexts. Second, very few studies have used test items which reflected the everyday life situations despite the findings that students have ideas about energy conservation from this perspective. In our opinion, the students' conceptual difficulties with respect to energy conservation are interrelated and connected to other aspects such as everyday life and science discipline contexts, which have not been sufficiently taken into account in previous diagnostic research.

Therefore in this book chapter, we will present findings from the diagnosis we conducted with 90 university biology students' understanding of energy conservation using the pencil and paper test, reflecting test items phrased in the biological and everyday life situations, we developed specifically for this study.

#### **1.3. Previous studies on students' understanding of energy conservation**

The science education research has shown that students of all ages have conceptual difficulties and misunderstandings related to the meaning of energy conservation (e.g. Goldring & Osborne, 1994; Pinto et al, 2005), and the application of energy conservation in biological systems (e.g. Barak et al, 1997; Eisten & Stavy, 1988; Fetherston, 1999; Gayford, 1986; Goldring & Osborne, 1994; Kesidou et al, 1993; Kruger et al, 1992; Linjse, 1990; Mann, 2003; Solomon, 1982; Trumper, 1997).

Table 1 shows some previous studies (in chronological order) and the corresponding student errors about energy conservation meanings and applications in biological systems. With respect to what energy conservation means, several researchers have found two common errors: energy conservation means energy saving; and energy conservation is

**Table 1.** Summary of students' erroneous ideas about energy conservation

**Note:** \*represents that a corresponding error was observed, but no exact percentages of students holding the error was given.

opposite of energy degradation. With respect to the application of energy conservation, many researchers have found a conceptual failure among students to apply the energy conservation principle (energy cannot be created or destroyed) to biological situations involving energy. That is, the most common errors identified are: energy is created or formed during respiration; energy is used up or consumed during metabolic processes; and energy is lost during physical activities in living organisms. Energy loss and decrease in energy phases are erroneously interpreted as a decrease in its quantity, and not a decrease in energy's usefulness (a correct scientific viewpoint). Scientifically, all energy forms are interconvertible from one form to another without any loss of energy*.* Similarly, in all biological processes there is the same amount of energy before as after an event (Starr &Taggart, 1992). However, as shown in Table 1, previous research shows that many students do not realise that energy is conserved in biological processes and systems. Kesidou et al (1993) explain that students often reject the idea of energy conservation because it seems to contradict everyday experiences and language usage where energy is often viewed as being produced and consumed, but not conserved. As such it is important to point out here that some students who seem to have erroneous ideas about energy conservation may be influenced by a language problem, and not a conceptual one. It is possible that whilst students use terms such as *used up* and *lost,* some of them may use these terms figuratively, and not actually conceptualize energy as not being conserved.

#### **1.4. Aims of the chapter**

76 Energy Conservation

**Some erroneous ideas**

Energy conservation is synonymous to energy

Energy conservation is the opposite of energy

Students' responses to energy-related concepts do not reflect (or if they do, contradict) the idea of energy conservation in biological systems

Energy is **created or formed** during respiration

Energy is **used up or consumed** during processes in living

Energy **loss** & **decrease**

activities (e.g. exercises) in living systems are erroneously interpreted as a decrease in its

holding the error was given.

during physical

things

quantity

Solomon (1982) n=one class

**Errors relating to meaning of energy conservation**

(English

Gayford (1986) n=296

(English

**Errors relating to application of energy conservation in biological systems**

79% 100

**7%**

**Table 1.** Summary of students' erroneous ideas about energy conservation

**Note:** \*represents that a corresponding error was observed, but no exact percentages of students

 A-level biology Eisten et al (1988) n=188

(Isreali high school &

Linjse (1990) n=97

(D t h hi h h l t d t )

Kruger et al (1992) n=159

(English

%

 29%15%

 primary Kesidou et al (1993) n=34

(German

 high school students)

Goldring et al (1994) n=75

(English

31%

30%

 high school students)

Barak et al (1997) n=104

(76 & 28 Israeli high school

Trumper (1997) n=189

(Israeli

pre-service

Fetherston (1999) n=94

(Australian

 high school students)

Mann (2003) n=610

(Australian

 high school students)

Pinto et al (2005) n=20

(Spanish

 high school science

 biology

 school teachers)

university

comprehensive

 school)

**about energy conservation, as identified by different**

**researchers**

saving

degradation

Based on the concerns outlined above, and the previous studies done on students' understanding of energy conservation, the aims of this chapter are three fold: (a) To present the data and results we found on students' understanding of energy conservation in biological and everyday contexts; (b) To develop a diagnostic instrument which can be used to diagnose students' understanding of energy conservation; and (c) To provide suggestions on how biology educators can design their science curriculum and instruction in order to help students understand and apply the concept of energy conservation to biological systems.

The three research questions that guided this study were: (1) Are students able to state the energy conservation principle? (2) To what extent are students able to apply the energy conservation principle to everyday life situations involving biological phenomena? (3) Do students understand what happens to energy during metabolic processes in biological/living organisms?

#### **2. Data collection methods and analysis**

#### **2.1. Sample description**

The sample consisted of 90 first-year biology students at a South African university. There were 40 males and 50 females. All these students were in a pre-medical program in which they were preparing to go to medical school.

#### **2.2. Development of energy conservation diagnostic test**

A survey approach was used for this research, using a pencil-and-paper diagnostic test specifically developed to collect the data. The design of the diagnostic test was based on a process described by Haslam and Treagust (1987). The development of the test involved two main phases: the preparatory and the test formulation phases. The preparatory phase involved three steps. Step 1 involved the drawing up a list of scientifically acceptable propositional knowledge statements about energy conservation and in biological-context. This list was drawn up after interviewing three biology lecturers and then consulting the two prescribed tertiary level textbooks for first-year biology courses at the university where the study was conducted (i.e. Raven & Johnson, 1999; Solomon *et al.,* 1993). The purpose of this step was to draw up the energy conservation conceptual structure that defined this study, and which was used as a guide when constructing the test items, and when marking the answers. The energy conservation conceptual structure we came up with is summarized below:

Step 2 involved compiling a list of common erroneous ideas about energy conservation, reported in the research literature (see Table 1). The purpose of this step was to compile a list of ideas about energy conservation held by students in previous research studies, so these could be included in the diagnostic test to be developed. Step 3 involved defining the content boundaries of the test so that topics which students were expected to know when they enter first year would be included in the test, in order for the test to be used to diagnose prior knowledge as well. The information for this step was acquired through interviews with lecturers who provided data on the prerequisite knowledge required in first year biology.

In the test formulation phase, the diagnostic test had to fulfill two basic criteria: checks basic knowledge about energy conservation; and tests understanding of energy conservation. Testing for understanding is not an easy matter. Various authors have listed criteria that could be used in judging understanding. For example, Sanders and Mokuku (1994) stated that individuals who understand a concept should: know and be able to recognize the name and definition of a concept; be able to define and explain the concept in their own words; be able to recognize instances not previously encountered of the concept; be able to distinguish between and classify instances and non-instances of the concept not previously encountered; and be able to apply the concept to new situations. Through these criteria, it is possible for science educators to determine for sure, their students' understanding level. A number of these criteria were considered when designing the test. For example, the test items were constructed in such a way that students were required to state *energy conservation* in their own words, and to apply their understanding of energy conservation in the closed statements reflecting biological and everyday life scenarios.

#### **2.3. Energy conservation diagnostic test**

78 Energy Conservation

below:

biology.

work.

atmosphere in the form of heat.

contraction, if the plant is eaten by an animal.

**2.2. Development of energy conservation diagnostic test**

A survey approach was used for this research, using a pencil-and-paper diagnostic test specifically developed to collect the data. The design of the diagnostic test was based on a process described by Haslam and Treagust (1987). The development of the test involved two main phases: the preparatory and the test formulation phases. The preparatory phase involved three steps. Step 1 involved the drawing up a list of scientifically acceptable propositional knowledge statements about energy conservation and in biological-context. This list was drawn up after interviewing three biology lecturers and then consulting the two prescribed tertiary level textbooks for first-year biology courses at the university where the study was conducted (i.e. Raven & Johnson, 1999; Solomon *et al.,* 1993). The purpose of this step was to draw up the energy conservation conceptual structure that defined this study, and which was used as a guide when constructing the test items, and when marking the answers. The energy conservation conceptual structure we came up with is summarized

 According to the first law of thermodynamics (the law of conservation of energy), energy cannot be created or destroyed, but it can be converted from one form to another

 Any apparent loss of energy can be explained as the conversion of energy into some other form. For example, during each energy conversion in living systems, some of the energy is used to drive the metabolic processes and some of it dissipates to the

 In biological systems, most reactions of organisms involve a complex series of energy transformations. For example, during photosynthesis, plant cells transform light energy to chemical energy stored in chemical bonds of food materials. Some of this chemical energy may eventually be converted to mechanical energy in animals for muscle

Step 2 involved compiling a list of common erroneous ideas about energy conservation, reported in the research literature (see Table 1). The purpose of this step was to compile a list of ideas about energy conservation held by students in previous research studies, so these could be included in the diagnostic test to be developed. Step 3 involved defining the content boundaries of the test so that topics which students were expected to know when they enter first year would be included in the test, in order for the test to be used to diagnose prior knowledge as well. The information for this step was acquired through interviews with lecturers who provided data on the prerequisite knowledge required in first year

In the test formulation phase, the diagnostic test had to fulfill two basic criteria: checks basic knowledge about energy conservation; and tests understanding of energy conservation. Testing for understanding is not an easy matter. Various authors have listed criteria that could be used in judging understanding. For example, Sanders and Mokuku (1994) stated that individuals who understand a concept should: know and be able to recognize the name

All energy forms are inter-convertible from one form to another without any *loss*.

The test consisted of three questions. Question 1 was an open-ended and aimed at eliciting students' understanding of the energy conservation principle. Actual Question 1 read: *What does the energy conservation principle state?* Question 2 consisted of closed-ended statements phrased in everyday life contexts but reflecting biological phenomena (see Table 3 for the actual statements). These statements were meant to determine the extent to which students are able to apply their understanding of energy conservation in the biological and everyday life situations. The actual Question 2 read: *Below are some statements about energy reflecting everyday life situations and biological phenomena.* Task 1 *(a) For each statement, indicate by placing a tick () in the appropriate box if the statement is scientifically correct or incorrect; (b)Then indicate how sure you are that the answer you have provided is correct by ticking the appropriate box on "Sure", "Think so" or "Guessing"*. Task 2 *(a) If the statement is incorrect, underline the word or phrase in the statement which makes it incorrect; and (b) Then write in a word or phrase which would make the statement correct*. Question 3 was open-ended and was meant to elicit students' conceptual understanding of what happens to energy during metabolic processes in living organisms. The actual question 3 read: *Energy is required to drive metabolic processes (such as breathing, muscle contraction) in living organisms. Explain what you think happens to energy during metabolic processes.*

Quality-control steps taken while the instrument was developed included checks on content validity, and rigorous face validation by three university biology experts. The instrument was piloted with 30 first-year biology students who were not involved in the main study. Piloting is an important quality-control procedure as it enables to check on the suitability of individual test items; to gain feedback on how well participants understood the questions, response procedures and instructions so that questions can be improved (Bell, 1987). The pilot group was requested to indicate whether they had problems understanding what they were required to do in each question and each closed statement. They were also further requested to write down the words or phrases which were not clear to them. The results of the pilot showed that majority of the students who indicated having problems suggested their inability to give answers due to lack of knowledge about energy conservation, and not based on misunderstanding the items. As such all test items were maintained.

#### **3. Data analysis**

The data were analysed using open-coding and reported as frequency counts and percentages. After a line-by-line analysis of each script, categories and sub-categories to which responses would fit well were developed. The categories which had been developed were given to two biology experts for validation. These experts were asked to check for the following: the scientific correctness of the answers given by students, the appropriateness of the categories developed for the student answers, and whether the students' responses were correctly categorised. This was done by giving each expert ten scripts to go through and code independently. Any differences in the coding were discussed collectively, and a common agreement reached. When individuals rate a product, there is always a possibility that some portion of the agreement between them is due to chance. As such, Cohen (1960) recommends using the kappa statistic to assess interrater agreements involving nominal scale. Cohen's Kappa (k) is a coefficient of interrater agreement that takes into consideration agreement by chance. The interrater agreements between the biology educators on the scientific correctness of the answers provided by students are shown in Table 2.

**Table 2.** Interrater agreement values

The percentage of agreement ranged from 87 % to 96% with a corresponding kappa coefficients range of 0.85 to 0.90. The percentage agreement of more than 75% and kappa values above 0.5 are considered to indicate good level of interrater agreement (Chiapetta, Fillman & Sethna, 1991). Therefore, the values in this study can be considered good enough to justify reliability. After the categorization process on the scientific correctness of the responses, frequency counts were conducted to get the actual number of students giving each answer, and to calculate the percentages.

#### **4. Results and discussion**

The results have been presented along with the discussion. This is because certain aspects of energy such as what happens to energy during metabolic processes need to be discussed alongside the scientifically acceptable perceptions so that the reader(s) can have a clearer perspective as to why the authors of the current study categorized some statements as scientifically correct or incorrect.

#### **4.1. Stating the energy conservation principle**

Nearly all students (98%) correctly stated the principle of energy conservation (i.e. energy cannot be created or destroyed). This finding is supported by Tatar et al (2007) who pointed out that this principle is widely known among students due to its easiness in stating and remembering so much that when asked to state it, students do recite it correctly.

80 Energy Conservation

**3. Data analysis**

metabolic processes.

**Table 2.** Interrater agreement values

**4. Results and discussion**

scientifically correct or incorrect.

The data were analysed using open-coding and reported as frequency counts and percentages. After a line-by-line analysis of each script, categories and sub-categories to which responses would fit well were developed. The categories which had been developed were given to two biology experts for validation. These experts were asked to check for the following: the scientific correctness of the answers given by students, the appropriateness of the categories developed for the student answers, and whether the students' responses were correctly categorised. This was done by giving each expert ten scripts to go through and code independently. Any differences in the coding were discussed collectively, and a common agreement reached. When individuals rate a product, there is always a possibility that some portion of the agreement between them is due to chance. As such, Cohen (1960) recommends using the kappa statistic to assess interrater agreements involving nominal scale. Cohen's Kappa (k) is a coefficient of interrater agreement that takes into consideration agreement by chance. The interrater agreements between the biology educators on the

scientific correctness of the answers provided by students are shown in Table 2.

Definitions of energy conservation principle.

each answer, and to calculate the percentages.

**4.1. Stating the energy conservation principle**

Explanations of what happens to energy during

**Test item Percent agreement Kappa value**

The percentage of agreement ranged from 87 % to 96% with a corresponding kappa coefficients range of 0.85 to 0.90. The percentage agreement of more than 75% and kappa values above 0.5 are considered to indicate good level of interrater agreement (Chiapetta, Fillman & Sethna, 1991). Therefore, the values in this study can be considered good enough to justify reliability. After the categorization process on the scientific correctness of the responses, frequency counts were conducted to get the actual number of students giving

The results have been presented along with the discussion. This is because certain aspects of energy such as what happens to energy during metabolic processes need to be discussed alongside the scientifically acceptable perceptions so that the reader(s) can have a clearer perspective as to why the authors of the current study categorized some statements as

Nearly all students (98%) correctly stated the principle of energy conservation (i.e. energy cannot be created or destroyed). This finding is supported by Tatar et al (2007) who pointed

96

0.90

0.85

87

However, majority of the students in this study still reverted back to their everyday understanding of energy being *used up*, *created* or *lost* during activity, when they had to apply this principle in closed-ended biological and everyday context statements. This implies that even though these students can correctly state the energy conservation principle, they do not understand it fully so as to apply it to biological situations.

#### **4.2. Application of energy conservation principle in biological situations**

Students' understanding and application of energy conservation were elicited using the closed statements that involved biological phenomena presented in everyday life situations, as shown in Tables 3 and 4. Table 3 shows students' responses on the correctness of each statement, and their confidence level of their answers. Table 4 shows students' responses on word/phrase they believed made a statement incorrect, as well as the word/phrase they would write-in to make a statement correct. However, one important point to note as one reads the results in this section is that many students (38%) did not attempt to underline the word or phrase making the statement(s) incorrect, or to write in the word or phrase which would correct the statement(s) which they had indicated were incorrect. The possible validity problem associated with this is that it is not clear whether the students who did not give responses did not follow the instructions, or whether this indicated a lack of understanding of the energy conservation principle. As such, it would have been of value to interview some of these students. However, interviews were not conducted because one of the purposes for this study was to develop a pencil-and-paper diagnostic test that could be used to diagnose students understanding of energy conservation, and which biology educators can easily administer. The specific findings pertaining to students' ability to apply the energy conservation principle are provided in the next subsections.

**Table 3.** Students' responses on correctness of statements, and how sure they were about their answers. **Notes:** Figures outside the brackets represent the actual number of students who responded.

\* Statement is scientifically incorrect.

**Table 4.** Students' responses on words/phrases making the statements incorrect, and how they would correct them.

**Note:** \* Statement is scientifically incorrect

82 Energy Conservation

When you are asleep your body does not require any energy because it is not active\*.

During exercise, energy is built up in the body\*.

When living things are active, they lose

\* Statement is scientifically incorrect.

energy\*.

**Statements**

**phenomena**

**reflecting biological**

If you go jogging, energy is used up\*

After exercise, you can build up your energy levels by

resting\*

**6 (7%)** 4 (67%) 2 (33%) 0 **83 (92%)** 71 (86%) 9 (11%) 0

**14 (16%)** 6 (43%) 7 (50%) 0 **74 (82%)** 47 (64%) 23 (31%) 3 (4%)

**53 (59%)** 30 (57%) 18 (34%) 3 (6%) **36 (40%)** 20 (56%) 15 (42%) 0

**Table 3.** Students' responses on correctness of statements, and how sure they were about their answers.

**Notes:** Figures outside the brackets represent the actual number of students who responded.

**Task 1 Task 2**

students

% of who

4 7 4

9 16 10

res

ponded

% of whole

a le

up

**Written-in Word or phrase which makes statement correct**

Acceptable - converted to different forms Unacceptable

Acceptable -do not build

Acceptable -eating(food consumption) Unacceptable -stop using energy

Number of

3

1

15

3

students

% of who

5

2

4 7 4

27

6

responded

% of whole

3

1

16

4

sample

Actual number of

Number of students who did not attempt the test item 34 (38%)

Number of students who responded to the test item 56 (62%)

**Underlined word or phrase which**

**makes statement incorrect**

Incorrect phrase

Incorrect phrase -build up

Incorrect word

#### *4.2.1. Ideas relating to energy being used up when an organism is active*

The idea that energy is *used up* during activities was erroneously accepted by majority of the students. That is, 92% of them erroneously indicated that the statement *If you go jogging, energy is used up,* is correct and most of these students (73 of them) were sure their response was correct. To the contrary, only 6 students correctly indicated that the statement is incorrect. When asked to underline the phrase making the statement incorrect, only four of the six students (who indicated that the statement was incorrect) correctly underlined the phrase *used up*. Three of these students correctly wrote in the phrase "energy is converted into different forms". One student wrote in the word *lost*, however without the added explanation that heat energy is lost to the body during respiration, this answer has to be judged as erroneous.