Ripples are transverse bed forms, which normally have heights of less than 0.04 m and lengths below 0.6 m. Ripples are formed under hydraulically smooth flow conditions. If the flow velocity is great enough to move the individual sand grains but less than another limiting value, the bed is spontaneously deformed into irregular features called dunes. Dunes are formed under hydraulically rough conditions. Dunes have much larger dimensions and may have heights up to several meters and wavelength up to hundreds of meters. Observations and measurements suggest that lengths of dunes are about 3 to 8 times the water depth (Yalin 1977). When the velocity of flow is increased in beds composed of fine sediments (< 0.4 mm), a situation will be reached when dunes can no longer be sustained, and flat bed is formed in which the bed and free surface become flat. With increase in velocity and the Froude number, the water surface becomes unstable, and even small disturbances give rise to stationary surface waves thereby forming trains of long, sinusoidal-shaped waves of sand that are in phase with the surface waves and usually move slowly upstream. These features are called antidunes, and surface waves accompanying them are referred to as stationary waves. At higher velocities and stream powers, the bed reorients itself to create a series of hydraulic jumps for energy dissipation and these bed forms are called as chutes and pools. These high Froude number flows may occur when flash floods sweep down steep gullies of rocky areas. Large quantities of suspended sediment are carried by resulting breaking waves.

Bed Forms and Flow Mechanisms Associated with Dunes 39

The simplification with equilibrium bed forms is that uniformly sized periodic dunes vary only in the streamwise direction and do not change with time. As a first step towards developing a comprehensive understanding of flow in natural channels, researchers have studied the flow field over a train of fixed, well developed dunes. Best et al. (2001) opined that a fixed dune approach doesn't capture the effect of sediment transport on velocity profiles and despite this limitation the simplification of dune morphology to a fixed twodimensional profile does allow investigation of the major features of flow, as has been successfully demonstrated in previous studies of flow over two-dimensional bed forms (e.g. Bennett and Best, 1995; Lyn, 1993; Nelson et al., 1993; Raudkivi, 1966). Such studies also provide a basis for a better understanding of the effects of dune three-dimensionality. The laser-Doppler (LDV) technique has been used in several laboratory fixed sediment bed form investigations (e.g., Balachandar et al., 2007; Balachandar and Patel 2008; Bennett and Best 1995; Coleman et al. 2006; Kadota and Nezu 1999; Lyn 1993; McLean et al. 1994 and 1996; Nelson et al. 1993; Nelson et al. 1995; Van Mierlo and de Ruiter 1988; Venditti and Bennett 2000). These studies have suggested that near-bed turbulence over much of the stoss side of a dune deviates markedly from either classical boundary-layer or wake turbulence. Cellino and Graf (2000) carried out detailed study of sediment-transport flows over mobile bed forms using acoustic Doppler technique. Mendoza and Shen (1990), Johns et al. (1993), Yoon and Patel (1996), Yue et al. (2006), Stoesser et al. (2008) and Noguchi et al., (2009) performed numerical simulations of flow over fixed bed forms by applying sophisticated turbulence

models. Detailed flow characteristics will be discussed in the upcoming sections.

The shape and size of bed forms and flow conditions are inter-related. Significant progress has been made to understand the role played by topography on flow characteristics, separated flow dynamics, internal boundary layer development, and turbulence structures (Smith 1996). Raudkivi (1997) studied the formation and development of ripples. Bennett and Best (1996) and Lopez et al. (2000) studied the ripple to dune transition. Recent experimental and theoretical studies carried out by Coleman and Melville (1996) and Coleman and Fenton (2000) have focused on the bed form initiation process. Coleman and Eling (2000) observed that turbulence may not be an essential feature of the initial instability

Robert and Uhlman (2001) carried out experiments on different bed stages across the rippledune transition and found that turbulence intensity and Reynolds stresses gradually increase throughout the transition. Coleman et al. (2006) studied developing dunes using an innovative experimental approach and double averaging methodology to advance our understanding of the structure of the rough flow near the bed region. They found that flow structure doesn't change as dunes develop in time for a steady flow, even though overall flow structure must change as dunes develop and traditional boundary layer type features can be potentially destroyed. Interesting findings of this work include: (a) friction factor was noted to increase with bed form growth; (b) the location of the separated shear layer reattachment point was determined as approximately 4h downstream of the crest for time averaged flow fields over the developing dunes as compared to 4.2h of previous flows over fixed dunes (Bennett and Best 1995; Kadota and Nezu 1999; Lyn 1993; McLean et al. 1999;); (c) negligible variation of the vertical velocity distribution, spatial fields of Reynolds stresses , form induced stress, skin friction, form drag, bed stress and overall momentum

**2.2 Fully developed (equilibrium) bed forms**

**2.3 Transient bed forms**

of a sediment bed.

### **2.1 Dune geometry**

The upstream side of a dune is commonly referred to as the stoss side (for example, see Figures 3 and 4). The downstream side is usually referred to as the lee face or slipface. Dune height *h* (Figure 4) is most often defined as the difference in elevation between the dune crest and corresponding downstream trough (Gabel 1993, Julien and Klaassen 1995): although sometimes dune height is measured from upstream trough to downstream crest (e.g., Nordin 1971). Dune length, *λ* is the longitudinal distance between subsequent crests or troughs. Dune steepness, *δ* = *h*/*λ*, is the ratio of dune height to length and its value varies between 0.1 to 0.03 (Yalin, 1964). If the aspect ratio of the channel is small, dunes tend to be approximately triangular with straight crests and extend nearly across the width of the channel (Klaassen et al. 1986). On the other hand, when the aspect ratio is large, dunes will be three-dimensional with sinusoidal crests or several crests stretching across the flume.

Fig. 2. Bed forms in alluvial channel (from Vanoni, 1975, copyright permission of ASCE)

### **2.2 Fully developed (equilibrium) bed forms**

38 Sediment Transport – Flow Processes and Morphology

The upstream side of a dune is commonly referred to as the stoss side (for example, see Figures 3 and 4). The downstream side is usually referred to as the lee face or slipface. Dune height *h* (Figure 4) is most often defined as the difference in elevation between the dune crest and corresponding downstream trough (Gabel 1993, Julien and Klaassen 1995): although sometimes dune height is measured from upstream trough to downstream crest (e.g., Nordin 1971). Dune length, *λ* is the longitudinal distance between subsequent crests or troughs. Dune steepness, *δ* = *h*/*λ*, is the ratio of dune height to length and its value varies between 0.1 to 0.03 (Yalin, 1964). If the aspect ratio of the channel is small, dunes tend to be approximately triangular with straight crests and extend nearly across the width of the channel (Klaassen et al. 1986). On the other hand, when the aspect ratio is large, dunes will be three-dimensional with sinusoidal crests or several crests stretching across the flume.

Subcritical flow Supercritical flow Fig. 2. Bed forms in alluvial channel (from Vanoni, 1975, copyright permission of ASCE)

**2.1 Dune geometry**

The simplification with equilibrium bed forms is that uniformly sized periodic dunes vary only in the streamwise direction and do not change with time. As a first step towards developing a comprehensive understanding of flow in natural channels, researchers have studied the flow field over a train of fixed, well developed dunes. Best et al. (2001) opined that a fixed dune approach doesn't capture the effect of sediment transport on velocity profiles and despite this limitation the simplification of dune morphology to a fixed twodimensional profile does allow investigation of the major features of flow, as has been successfully demonstrated in previous studies of flow over two-dimensional bed forms (e.g. Bennett and Best, 1995; Lyn, 1993; Nelson et al., 1993; Raudkivi, 1966). Such studies also provide a basis for a better understanding of the effects of dune three-dimensionality. The laser-Doppler (LDV) technique has been used in several laboratory fixed sediment bed form investigations (e.g., Balachandar et al., 2007; Balachandar and Patel 2008; Bennett and Best 1995; Coleman et al. 2006; Kadota and Nezu 1999; Lyn 1993; McLean et al. 1994 and 1996; Nelson et al. 1993; Nelson et al. 1995; Van Mierlo and de Ruiter 1988; Venditti and Bennett 2000). These studies have suggested that near-bed turbulence over much of the stoss side of a dune deviates markedly from either classical boundary-layer or wake turbulence. Cellino and Graf (2000) carried out detailed study of sediment-transport flows over mobile bed forms using acoustic Doppler technique. Mendoza and Shen (1990), Johns et al. (1993), Yoon and Patel (1996), Yue et al. (2006), Stoesser et al. (2008) and Noguchi et al., (2009) performed numerical simulations of flow over fixed bed forms by applying sophisticated turbulence models. Detailed flow characteristics will be discussed in the upcoming sections.

### **2.3 Transient bed forms**

The shape and size of bed forms and flow conditions are inter-related. Significant progress has been made to understand the role played by topography on flow characteristics, separated flow dynamics, internal boundary layer development, and turbulence structures (Smith 1996). Raudkivi (1997) studied the formation and development of ripples. Bennett and Best (1996) and Lopez et al. (2000) studied the ripple to dune transition. Recent experimental and theoretical studies carried out by Coleman and Melville (1996) and Coleman and Fenton (2000) have focused on the bed form initiation process. Coleman and Eling (2000) observed that turbulence may not be an essential feature of the initial instability of a sediment bed.

Robert and Uhlman (2001) carried out experiments on different bed stages across the rippledune transition and found that turbulence intensity and Reynolds stresses gradually increase throughout the transition. Coleman et al. (2006) studied developing dunes using an innovative experimental approach and double averaging methodology to advance our understanding of the structure of the rough flow near the bed region. They found that flow structure doesn't change as dunes develop in time for a steady flow, even though overall flow structure must change as dunes develop and traditional boundary layer type features can be potentially destroyed. Interesting findings of this work include: (a) friction factor was noted to increase with bed form growth; (b) the location of the separated shear layer reattachment point was determined as approximately 4h downstream of the crest for time averaged flow fields over the developing dunes as compared to 4.2h of previous flows over fixed dunes (Bennett and Best 1995; Kadota and Nezu 1999; Lyn 1993; McLean et al. 1999;); (c) negligible variation of the vertical velocity distribution, spatial fields of Reynolds stresses , form induced stress, skin friction, form drag, bed stress and overall momentum

Bed Forms and Flow Mechanisms Associated with Dunes 41

important in controlling the stability of the bed forms and the entrainment and transport of the sediments. It has been suggested that this macroturbulence has its origin in Kelvin-Helmoltz instabilities in the separating shear layer (Best 2003; Kostaschuk and Church 1993; Muller and Gyr 1987). In particular, Best (2003) and Hyun et al. (2003) provide whole field quantification using particle image velocimetry. As an important step towards better understanding the flow-dune interaction, researchers have analyzed the flow field for the

Fig. 4. Schematic of the flow field. Not to scale, all dimensions in millimeters (from

Using laser-Doppler measurements, Balachandar et al., (2007) analyzed the velocity data at various axial stations between two dune crests and is shown in Figure 5. In the figure, *d1* = flow depth ahead of the crest at *X*/*h* = -2 or 18; X = horizontal distance from the dune crest; *h* = dune height. It was observed that the flow over the dune train was periodic in space insofar as the flow pattern was the same over successive dunes, but there was a significant variation in flow properties along the wavelength of the dune. The velocity profile at *X*/*h* = -2, just ahead of the crest, indicates a log-region, although of a much reduced extent compared with a plane channel flow (see Figure 5a). A region of reverse flow can be seen at *X*/*h* = 4 and the mean reattachment point is located around *X*/*h* = 4.5. It was also observed that the flow in the outer region was not influenced by the local bed geometry, which is shown in Figure 5b. The average vertical velocity is zero at the dune crest, yet flow expansion and separation cause bed wise movement and thus negative velocities over much of the dune. This indicates downward deflection of streamlines (Figure 5c). The positive vertical velocities at *X*/*h* = 12 suggest streamlines following the upward slope of the surface. The profiles of streamwise turbulence intensity show that the turbulence reaches a high peak just below the crest line, which is also the location of maximum value of mean shear, shown in Figure 5d. A second peak at all the stations in the vicinity of *y*/*d* = 0.2, leads to the conclusion that there is a distance from the bed beyond which the turbulence is little affected by the dune shape. The peak exists at *X*/*h* = 12 and -2, and suggests the presence of remnant of the turbulence generated in the shear layer of the upstream dune. Figure 5e indicates that large values of vertical components of the turbulent intensities occur in recirculation zone and in the shear layer above it. Quite large values of shear stress (Figure

Balachandar et al., 2007, copyright permission of NRC Research Press).

**3.2 Time averaged flow along the dune**

case of a fixed dune.

flux as dunes grow and the overall form of the velocity profiles display an approximately linear distribution below roughness tops and a potentially logarithmic distribution above roughness tops; (d) peak Reynolds stresses occur in the shear layer associated with the separation zone consistent with shear layer instabilities and vortex shedding off this layer.

### **3. Temporal and spatial flow over dunes**

This section presents a discussion of results related to temporal and spatial velocity characteristics and flow resistance of open channels with bed forms

### **3.1 Temporal and spatial flow over dunes**

Compared to flow over a hydrodynamically smooth channel boundary, the interactions of flow with the bed formation are considerably harder to predict. Dunes disrupt the boundary layer type flow and generate turbulence. Extensive research regarding fluid flow over dunes has been undertaken in the past forty years (Engelund and Fredsøe 1982; Lyn 1993; McLean et al. 1994; Nelson et al. 1993; Raudkivi 1966). To summarize, five zones (Figure 3) have been recognized within the dune-flow interaction region (Balachandar et al., 2007; Balachandar et al. 2008; Bennett and Best, 1995; Best 2003).

Fig. 3. Schematic diagram of the principal regions of flow over asymmetrical angle-of-repose dunes (from Best 2005, Reproduced by permission of AGU)

A typical dune and the flow over the dune are indicated in Figure 4 (Balachandar et al., 2007). The flow ahead of the crest (indicated by C in Figure 4) resembles a typical near-wall, boundary-layer like flow. Following separation at C, a typical recirculation pattern is formed. Above this separation zone lies a decelerating flow with wake-like characteristics that extends downstream beyond the reattachment point (denoted as R in Figure 4). Experimental and field investigations have documented the formation of kolks or boils, which are tilting vortices emanating from the reattachment region and rising to the free surface. Near the bottom, following reattachment, an internal boundary layer develops and interacts with the overlying wake zone. Close to the free surface and over the dune wavelength, there is an outer zone that is generally modeled as a quasi-inviscid region. Along the separating shear layer, regions of high Reynolds stresses have been observed. Many previous studies have suggested that the macroturbulence associated with dunes is

flux as dunes grow and the overall form of the velocity profiles display an approximately linear distribution below roughness tops and a potentially logarithmic distribution above roughness tops; (d) peak Reynolds stresses occur in the shear layer associated with the separation zone consistent with shear layer instabilities and vortex shedding off this layer.

This section presents a discussion of results related to temporal and spatial velocity

Compared to flow over a hydrodynamically smooth channel boundary, the interactions of flow with the bed formation are considerably harder to predict. Dunes disrupt the boundary layer type flow and generate turbulence. Extensive research regarding fluid flow over dunes has been undertaken in the past forty years (Engelund and Fredsøe 1982; Lyn 1993; McLean et al. 1994; Nelson et al. 1993; Raudkivi 1966). To summarize, five zones (Figure 3) have been recognized within the dune-flow interaction region (Balachandar et al., 2007; Balachandar et

Fig. 3. Schematic diagram of the principal regions of flow over asymmetrical angle-of-repose

A typical dune and the flow over the dune are indicated in Figure 4 (Balachandar et al., 2007). The flow ahead of the crest (indicated by C in Figure 4) resembles a typical near-wall, boundary-layer like flow. Following separation at C, a typical recirculation pattern is formed. Above this separation zone lies a decelerating flow with wake-like characteristics that extends downstream beyond the reattachment point (denoted as R in Figure 4). Experimental and field investigations have documented the formation of kolks or boils, which are tilting vortices emanating from the reattachment region and rising to the free surface. Near the bottom, following reattachment, an internal boundary layer develops and interacts with the overlying wake zone. Close to the free surface and over the dune wavelength, there is an outer zone that is generally modeled as a quasi-inviscid region. Along the separating shear layer, regions of high Reynolds stresses have been observed. Many previous studies have suggested that the macroturbulence associated with dunes is

dunes (from Best 2005, Reproduced by permission of AGU)

**3. Temporal and spatial flow over dunes**

**3.1 Temporal and spatial flow over dunes**

al. 2008; Bennett and Best, 1995; Best 2003).

characteristics and flow resistance of open channels with bed forms

important in controlling the stability of the bed forms and the entrainment and transport of the sediments. It has been suggested that this macroturbulence has its origin in Kelvin-Helmoltz instabilities in the separating shear layer (Best 2003; Kostaschuk and Church 1993; Muller and Gyr 1987). In particular, Best (2003) and Hyun et al. (2003) provide whole field quantification using particle image velocimetry. As an important step towards better understanding the flow-dune interaction, researchers have analyzed the flow field for the case of a fixed dune.

Fig. 4. Schematic of the flow field. Not to scale, all dimensions in millimeters (from Balachandar et al., 2007, copyright permission of NRC Research Press).

### **3.2 Time averaged flow along the dune**

Using laser-Doppler measurements, Balachandar et al., (2007) analyzed the velocity data at various axial stations between two dune crests and is shown in Figure 5. In the figure, *d1* = flow depth ahead of the crest at *X*/*h* = -2 or 18; X = horizontal distance from the dune crest; *h* = dune height. It was observed that the flow over the dune train was periodic in space insofar as the flow pattern was the same over successive dunes, but there was a significant variation in flow properties along the wavelength of the dune. The velocity profile at *X*/*h* = -2, just ahead of the crest, indicates a log-region, although of a much reduced extent compared with a plane channel flow (see Figure 5a). A region of reverse flow can be seen at *X*/*h* = 4 and the mean reattachment point is located around *X*/*h* = 4.5. It was also observed that the flow in the outer region was not influenced by the local bed geometry, which is shown in Figure 5b. The average vertical velocity is zero at the dune crest, yet flow expansion and separation cause bed wise movement and thus negative velocities over much of the dune. This indicates downward deflection of streamlines (Figure 5c). The positive vertical velocities at *X*/*h* = 12 suggest streamlines following the upward slope of the surface. The profiles of streamwise turbulence intensity show that the turbulence reaches a high peak just below the crest line, which is also the location of maximum value of mean shear, shown in Figure 5d. A second peak at all the stations in the vicinity of *y*/*d* = 0.2, leads to the conclusion that there is a distance from the bed beyond which the turbulence is little affected by the dune shape. The peak exists at *X*/*h* = 12 and -2, and suggests the presence of remnant of the turbulence generated in the shear layer of the upstream dune. Figure 5e indicates that large values of vertical components of the turbulent intensities occur in recirculation zone and in the shear layer above it. Quite large values of shear stress (Figure

Bed Forms and Flow Mechanisms Associated with Dunes 43

**b**)

(Uo - U)/Uo

0.05

0.000

0.004

0.008

0.012

Fig. 5. Mean velocity and turbulence profiles (*d1*/*h* = 6): (a) streamwise mean velocity profiles; (b) mean velocity profiles plotted in the velocity-defect format; (c) vertical

component, *V*, of the mean velocity; (d) profiles of the streamwise root mean squared (rms) turbulence intensity (*u*/*Uo*); (e) vertical component of the rms turbulence intensity (*v*/*Uo*); (f) Reynolds shear stress profiles (from Balachandar et al., 2007, copyright permission of NRC

o

0.016

0.020

**f**)

0.10

0.15

0.20

**d**)

u/Uo

0.0 0.2 0.4 0.6 0.8 1.0 1.2

= 0.23, U

/Uo = 0.0426

y/d ~ 0.5

100 1000 10000 100000

yUo /

0.0 0.2 0.4 0.6 0.8 1.0

y/d

Crestline

**y/d ~ 0.2**

1000 10000 100000

yUo / **y/d ~ 0.2**

100 1000 10000 100000

yUo /

Smooth open channel

 X/h = -2 X/ = -0.10 X/h = 2 X/ = 0.10 X/h = 4 X/ = 0.20 X/h = 5 X/ = 0.25 X/h = 6 X/ = 0.30 X/h = 12 X/ = 0.60 X/h = 18 X/ = 0.90

1000 10000 100000

yUo /

1000 10000 100000

yUo /

**y/d ~ 0.2**

**U /Uo = 0.0426**

**a**)

U/Uo

0.10

**c**)

0.15

**e**)

v/Uo

0.00

Research Press).

0.05

0.10

0.00

V/Uo

0.05

5f) can be seen measured in the separation zone. Shear stresses decrease to upstream values with increasing distance from the reattachment.

### **3.3 Effect of flow depth**

In studying ripple-dune transition, Bennett and Best (1996) noted important changes in macroturbulence structure due to effect of depth on flow past bed forms. Wiberg and Nelson (1992) studied two flow depths over a train of ripples closely resembling the bed form shape of Nelson and Smith (1989) and noticed a higher value of bed friction at the smaller depth. Figure 6 (Balachandar et al., 2007) shows streamwise mean velocities profiles at six locations along the dune for four depth ratios (*y*/*h*), ranging from 3 to 8. At *X*/*h* = -2, in inner scaling, *U+* versus *y+* (inset of Figure 6a) collapses at all depths but the outer region is different from a simple open channel with a smooth bed. Velocity profiles at *X*/*h* = 2 to 12 show similarity in the near wall region and independent of depth in the outer region (*y*/*d* > 0.35). It is important to note that at X/h =5, the mean velocity in the near-wall region is positive for *d1*/*h* ≥ 4 and is negative at *d1*/*h* = 3. This indicates the depth of flow influences the near-bed region and the length of the separation region is longer at the shallower depth. The profiles of the vertical component of turbulence reveal a systematic dependence on flow depth near the crestline and at the larger depths indicate lower values of turbulent intensity. In the recirculation region, the shear stresses are very high and increase with decreasing flow depth.

### **3.4 Effect of bed roughness on the flow over dunes**

Balachandar and Patel (2008) studied the effect of bed roughness superimposed on a train of well-formed dunes by conducting laser-Doppler measurements at several stations between two dune crests. In these studies, rough surfaces were generated using (a) stainless steel wire mesh made of 0.72 mm wires with 6.35 mm centerline spacing and (ii) sand grain roughness created from sand grains of 1.8 mm nominal mean diameter carefully glued onto a double-sided tape to ensure a uniform distribution. Their results showed that the wire mesh provided for a higher degree of roughness as compared to sand grain roughness. It was found that with increasing streamwise distance from the crest, the dependence of the near-bed part of the profiles on the roughness becomes apparent. In the outer region (*y*/*d* > 0.2), the profiles are independent of the bed roughness (Figure 7). It is also found that outer region was clearly different from that in the simple open channel flow over a smooth surface, indicating that the entire depth of flow has been affected by the dune geometry. The effect of the near-bed roughness is more dominant in the recirculation zone. The peak value of turbulence at any station is influenced by the bed roughness and the location of the peak is farther extended into the flow away from the wall with increasing roughness. It is found that the length of the separation region is longer for the flow with larger bed roughness. The results indicate that the shape of the dunes have a major influence on the flow features, where as the effect of dune roughness is limited to the near wall region extending to a distance of about 80% of the dune height about the crest.

#### **3.5 Relation between suspended sediment and dune characteristics**

Bennett and Best, (1996), Best (2005 a, b), Lopez et al., (2000), Robert and Uhlman (2001) and Schindler and Robert (2004) have shown that suspended sediment concentration increases with increase in scale and magnitude of turbulent structures. Schindler and Robert (2005)

5f) can be seen measured in the separation zone. Shear stresses decrease to upstream values

In studying ripple-dune transition, Bennett and Best (1996) noted important changes in macroturbulence structure due to effect of depth on flow past bed forms. Wiberg and Nelson (1992) studied two flow depths over a train of ripples closely resembling the bed form shape of Nelson and Smith (1989) and noticed a higher value of bed friction at the smaller depth. Figure 6 (Balachandar et al., 2007) shows streamwise mean velocities profiles at six locations along the dune for four depth ratios (*y*/*h*), ranging from 3 to 8. At *X*/*h* = -2, in inner scaling, *U+* versus *y+* (inset of Figure 6a) collapses at all depths but the outer region is different from a simple open channel with a smooth bed. Velocity profiles at *X*/*h* = 2 to 12 show similarity in the near wall region and independent of depth in the outer region (*y*/*d* > 0.35). It is important to note that at X/h =5, the mean velocity in the near-wall region is positive for *d1*/*h* ≥ 4 and is negative at *d1*/*h* = 3. This indicates the depth of flow influences the near-bed region and the length of the separation region is longer at the shallower depth. The profiles of the vertical component of turbulence reveal a systematic dependence on flow depth near the crestline and at the larger depths indicate lower values of turbulent intensity. In the recirculation region, the shear stresses are very high and increase with decreasing

Balachandar and Patel (2008) studied the effect of bed roughness superimposed on a train of well-formed dunes by conducting laser-Doppler measurements at several stations between two dune crests. In these studies, rough surfaces were generated using (a) stainless steel wire mesh made of 0.72 mm wires with 6.35 mm centerline spacing and (ii) sand grain roughness created from sand grains of 1.8 mm nominal mean diameter carefully glued onto a double-sided tape to ensure a uniform distribution. Their results showed that the wire mesh provided for a higher degree of roughness as compared to sand grain roughness. It was found that with increasing streamwise distance from the crest, the dependence of the near-bed part of the profiles on the roughness becomes apparent. In the outer region (*y*/*d* > 0.2), the profiles are independent of the bed roughness (Figure 7). It is also found that outer region was clearly different from that in the simple open channel flow over a smooth surface, indicating that the entire depth of flow has been affected by the dune geometry. The effect of the near-bed roughness is more dominant in the recirculation zone. The peak value of turbulence at any station is influenced by the bed roughness and the location of the peak is farther extended into the flow away from the wall with increasing roughness. It is found that the length of the separation region is longer for the flow with larger bed roughness. The results indicate that the shape of the dunes have a major influence on the flow features, where as the effect of dune roughness is limited to the near wall region extending to a

with increasing distance from the reattachment.

**3.4 Effect of bed roughness on the flow over dunes**

distance of about 80% of the dune height about the crest.

**3.5 Relation between suspended sediment and dune characteristics**

Bennett and Best, (1996), Best (2005 a, b), Lopez et al., (2000), Robert and Uhlman (2001) and Schindler and Robert (2004) have shown that suspended sediment concentration increases with increase in scale and magnitude of turbulent structures. Schindler and Robert (2005)

**3.3 Effect of flow depth**

flow depth.

Fig. 5. Mean velocity and turbulence profiles (*d1*/*h* = 6): (a) streamwise mean velocity profiles; (b) mean velocity profiles plotted in the velocity-defect format; (c) vertical component, *V*, of the mean velocity; (d) profiles of the streamwise root mean squared (rms) turbulence intensity (*u*/*Uo*); (e) vertical component of the rms turbulence intensity (*v*/*Uo*); (f) Reynolds shear stress profiles (from Balachandar et al., 2007, copyright permission of NRC Research Press).

Bed Forms and Flow Mechanisms Associated with Dunes 45

0.05

x/h = 2.0

0.05

x/h = 5.0

y/d **<sup>e</sup>**)

0.05

x/h = 12.0

0.10

u

Fig. 7. Variation of streamwise turbulence intensity.  Effect of depth on mean velocity profiles at various axial stations (-2≤*X*/*h*≤12) using the depth of flow, d, as the normalizing length scale (from Balachandar et al., 2007, copyright permission of NRC Research Press).

have concluded that the transition from 2-D to 3-D bed forms, result in increased sediment transport, increased turbulence and increased bed form migration rate. Venditti and Bennett (2000) found that suspended sediment concentration is highest over the dune crest and at flow reattachment. Further research is needed to spatially analyze both the fluid dynamics and the sediment transport processes over mobile bed forms.

Tevez et al. (1999) reported that spatially averaged mean velocity profiles over dunes consist of upper and lower semi log-linear segments. The upper segment reflects the total shear stress of the flow. The lower segment on symmetric dunes reflects the skin friction from sand particles, but for asymmetric dunes it is the skin friction plus the effect of form roughness from the superimposed dunes. Villard and Kostaschuk (1998) found that predictions of the Rouse equation indicated that sediment suspension is controlled by total stress for symmetric dunes, whereas for asymmetric dunes sediment suspension is related to stress associated with skin friction plus form roughness. It is reported that dunes in bed load-dominated environments are often asymmetric having low-sloping upstream side (stoss) and steep lee faces (Guy et al. 1966; Kostaschuk et al. 2004), while those in suspended load dominated environments are often more symmetric with relatively low angle lee faces (Best and Kostaschuk 2002; Kostaschuk and Villard 1996).

Fig. 6. Effect of depth on mean velocity profiles at various axial stations (-2≤*X*/*h*≤12) using

have concluded that the transition from 2-D to 3-D bed forms, result in increased sediment transport, increased turbulence and increased bed form migration rate. Venditti and Bennett (2000) found that suspended sediment concentration is highest over the dune crest and at flow reattachment. Further research is needed to spatially analyze both the fluid dynamics

Tevez et al. (1999) reported that spatially averaged mean velocity profiles over dunes consist of upper and lower semi log-linear segments. The upper segment reflects the total shear stress of the flow. The lower segment on symmetric dunes reflects the skin friction from sand particles, but for asymmetric dunes it is the skin friction plus the effect of form roughness from the superimposed dunes. Villard and Kostaschuk (1998) found that predictions of the Rouse equation indicated that sediment suspension is controlled by total stress for symmetric dunes, whereas for asymmetric dunes sediment suspension is related to stress associated with skin friction plus form roughness. It is reported that dunes in bed load-dominated environments are often asymmetric having low-sloping upstream side (stoss) and steep lee faces (Guy et al. 1966; Kostaschuk et al. 2004), while those in suspended load dominated environments are often more symmetric with relatively low angle lee faces

the depth of flow, d, as the normalizing length scale (from Balachandar et al., 2007,

copyright permission of NRC Research Press).

and the sediment transport processes over mobile bed forms.

(Best and Kostaschuk 2002; Kostaschuk and Villard 1996).

Fig. 7. Variation of streamwise turbulence intensity. SM - experiments conducted with a train of smooth bed dunes manufactured from Plexiglas, SG sand grain pasted on smooth dune; WM, wire mesh glued to dune. (from Balachandar et al., 2007, copyright permission of NRC Research Press)

Bed Forms and Flow Mechanisms Associated with Dunes 47

Fig. 8. Vertical sorting measured in experiments. The dune or bar top is on the left-hand side

Kleinhans (2002), Blom and Kleinhans (1999), experiments T5, T7 and T9. The sediment here is divided into two grain size fractions (sand and gravel), coarser and finer than 2.0 mm. The level of the dune troughs agrees with the level of the armour layer in T5 and T7, whereas in T9 the armour layer of T7 can still be observed. (From Kleinhans, 2004, copyright permission

Schmeeckle et al., (1999) presented a method for the 3-D simulation of turbulence over 2-D dunes and compared the accuracy of PIV measurements and numerical simulations using a dense grid of two-dimensional laser Doppler velocimetry measurements. Balachandar et al. (2002) carried out LDV and PIV measurements and complementary LES simulation over a fixed dune. LDV and PIV provide complementary data on time-averaged and instantaneous flow structure over the dune. The time-averaged results reveal, in considerable detail, flow features such as separation and reattachment, and associated large variations in velocity and turbulence profiles. The instantaneous PIV results reveal a complex pattern of near-random but well-defined vortices. Vortices form downstream of flow separation and grow in size as they are convected along the dune. Balachandar and Patel (2008) studied the turbulent flow over a long train of fixed two-dimensional dunes, identical in size and shape by combining the complementary capabilities of LDV and PIV over a range of flow depths in a fully developed region. In this study, the points of interest were the instantaneous and mean velocity fields, the Reynolds stresses, triple-correlations, vorticity maps and analysis of

of the graphs, and the base is on the right-hand side. Vertical sorting in the dunes in

**4.1 Combined use of PIV and LDV to measure turbulence and flow over a dune**

information that reveals the true complexity of the flow over dunes.

Hyun et al. (2003) assessed the relative merits of LDV and PIV to measure mean velocity and turbulence in water flow over a train of fixed two-dimensional dunes. Figure 10 shows the LDV measurement stations and PIV field-of-views. The flow field over the dune was divided into five different fields-of-view with a 20 mm overlap between the images. Though PIV is limited in the field-of-view normal to the bed, it provides instantaneous flow-field

of Science Direct)

events in the four quadrants.

### **3.6 Sediment heterogeneity**

Existing literature mostly points to studies that focus on the case of uniform sediment while dealing with laboratory dune studies. However, sediment heterogeneity may be of practical interest because formation and development of bed forms in natural rivers happens distinctively with non-uniform sediment. It is quite challenging to study flow over dunes with sediment mixtures in a laboratory. A few studies have been conducted in this area (Parker et al., 1982, Wilcock and Southard, 1988 and Wilcock, 1992). Wilcock and Southard (1989), Klaassen et al., (1987), Ribberink, (1987) and Klaassen (1990) investigated the mutual influence of sediment gradation on ripples and dunes, on fractional transport rates and on vertical sorting. ASCE Task Committee on Flow and Transport over Dunes (2002) reported that fully developed dunes composed of highly heterogeneous sediment exhibit different geometric, flow, and transport characteristics than the more intensively studied homogenous-sediment counterparts. Klaassen (1991), Blom and Kleinhans (1999), Kleinhans (2002) and Blom and Ribberink (1999) have reported that, in the vertically sorted bimodal gravel bed streams the coarser material tends to accumulate at the base of the dunes, creating a partial barrier between the coarser substrate below and finer material in the migrating dunes above (see Figure 8). A clear armour layer was also observed at the level of the dune troughs.

Lanzoni (2000), Lanzoni and Tubino (1999), Lanzoni et al., (1994) and Lisle et al., (1991) studied the sand bar formation with bimodal mixtures of fine and coarse sediment and suggested that grain sorting associated with selective transport of graded sediment may induce a overall stabilizing effect on bottom development with appreciable reduction of bar amplitude and a shortening of bar wave lengths (see Figure 9). In the caption of Figure 9, the term FC70 is a sediment mixture of poorly sorted with strongly bimodal character, *is* is the water surface slope and MUNI is near uniform sand. In addition, these studies are designed to get a better insight on longitudinal and vertical sorting. Lanzoni (2000) opined that a suitable model for vertical sorting is required to study the presence of heterogeneous sediments.

### **4. Experimental studies, limitations of some of the studies, recent PIV studies**

Turbulence studies in water flows over dunes were commenced with the development of hot-film anemometers and flow visualization techniques. Muller and Gyr (1982) used fluorescent dye, a light sheet and video to visualize the flow. Nezu et al. (1994) used both dye and hydrogen bubbles in conjunction with video to study turbulent structures over dunes, and Bennett and Best (1995) took long exposure photographs of small neutrally buoyant particles to view the paths of fluid particles. These studies provide valuable information about features such as point of separation, point of reattachment, shear layer development, and generation and shedding of transverse vortices. Since three decades, much more accurate measurements of water flows became feasible with the increased use of laser-Doppler anemometer or laser Doppler velocimeter (LDA or LDV).

In the last decade, quantitative flow visualization techniques such as particle tracking velocimetry (PTV) and particle image velocimetry (PIV) have become popular to study coherent eddies in space and time. The ability of PIV to yield flow-field information ensures its usage to extend further. Hyun et al. (2003) provide a discussion of the factors that determine the accuracy of PIV data, and a discussion of the physics of the flow over a dune is given in Balachandar et al., (2003).

Existing literature mostly points to studies that focus on the case of uniform sediment while dealing with laboratory dune studies. However, sediment heterogeneity may be of practical interest because formation and development of bed forms in natural rivers happens distinctively with non-uniform sediment. It is quite challenging to study flow over dunes with sediment mixtures in a laboratory. A few studies have been conducted in this area (Parker et al., 1982, Wilcock and Southard, 1988 and Wilcock, 1992). Wilcock and Southard (1989), Klaassen et al., (1987), Ribberink, (1987) and Klaassen (1990) investigated the mutual influence of sediment gradation on ripples and dunes, on fractional transport rates and on vertical sorting. ASCE Task Committee on Flow and Transport over Dunes (2002) reported that fully developed dunes composed of highly heterogeneous sediment exhibit different geometric, flow, and transport characteristics than the more intensively studied homogenous-sediment counterparts. Klaassen (1991), Blom and Kleinhans (1999), Kleinhans (2002) and Blom and Ribberink (1999) have reported that, in the vertically sorted bimodal gravel bed streams the coarser material tends to accumulate at the base of the dunes, creating a partial barrier between the coarser substrate below and finer material in the migrating dunes above (see Figure 8). A clear armour layer was also observed at the level of

Lanzoni (2000), Lanzoni and Tubino (1999), Lanzoni et al., (1994) and Lisle et al., (1991) studied the sand bar formation with bimodal mixtures of fine and coarse sediment and suggested that grain sorting associated with selective transport of graded sediment may induce a overall stabilizing effect on bottom development with appreciable reduction of bar amplitude and a shortening of bar wave lengths (see Figure 9). In the caption of Figure 9, the term FC70 is a sediment mixture of poorly sorted with strongly bimodal character, *is* is the water surface slope and MUNI is near uniform sand. In addition, these studies are designed to get a better insight on longitudinal and vertical sorting. Lanzoni (2000) opined that a suitable model for vertical sorting is required to study the presence of heterogeneous

**4. Experimental studies, limitations of some of the studies, recent PIV studies**  Turbulence studies in water flows over dunes were commenced with the development of hot-film anemometers and flow visualization techniques. Muller and Gyr (1982) used fluorescent dye, a light sheet and video to visualize the flow. Nezu et al. (1994) used both dye and hydrogen bubbles in conjunction with video to study turbulent structures over dunes, and Bennett and Best (1995) took long exposure photographs of small neutrally buoyant particles to view the paths of fluid particles. These studies provide valuable information about features such as point of separation, point of reattachment, shear layer development, and generation and shedding of transverse vortices. Since three decades, much more accurate measurements of water flows became feasible with the increased use of

In the last decade, quantitative flow visualization techniques such as particle tracking velocimetry (PTV) and particle image velocimetry (PIV) have become popular to study coherent eddies in space and time. The ability of PIV to yield flow-field information ensures its usage to extend further. Hyun et al. (2003) provide a discussion of the factors that determine the accuracy of PIV data, and a discussion of the physics of the flow over a dune

laser-Doppler anemometer or laser Doppler velocimeter (LDA or LDV).

is given in Balachandar et al., (2003).

**3.6 Sediment heterogeneity**

the dune troughs.

sediments.

Fig. 8. Vertical sorting measured in experiments. The dune or bar top is on the left-hand side of the graphs, and the base is on the right-hand side. Vertical sorting in the dunes in Kleinhans (2002), Blom and Kleinhans (1999), experiments T5, T7 and T9. The sediment here is divided into two grain size fractions (sand and gravel), coarser and finer than 2.0 mm. The level of the dune troughs agrees with the level of the armour layer in T5 and T7, whereas in T9 the armour layer of T7 can still be observed. (From Kleinhans, 2004, copyright permission of Science Direct)

Schmeeckle et al., (1999) presented a method for the 3-D simulation of turbulence over 2-D dunes and compared the accuracy of PIV measurements and numerical simulations using a dense grid of two-dimensional laser Doppler velocimetry measurements. Balachandar et al. (2002) carried out LDV and PIV measurements and complementary LES simulation over a fixed dune. LDV and PIV provide complementary data on time-averaged and instantaneous flow structure over the dune. The time-averaged results reveal, in considerable detail, flow features such as separation and reattachment, and associated large variations in velocity and turbulence profiles. The instantaneous PIV results reveal a complex pattern of near-random but well-defined vortices. Vortices form downstream of flow separation and grow in size as they are convected along the dune. Balachandar and Patel (2008) studied the turbulent flow over a long train of fixed two-dimensional dunes, identical in size and shape by combining the complementary capabilities of LDV and PIV over a range of flow depths in a fully developed region. In this study, the points of interest were the instantaneous and mean velocity fields, the Reynolds stresses, triple-correlations, vorticity maps and analysis of events in the four quadrants.

### **4.1 Combined use of PIV and LDV to measure turbulence and flow over a dune**

Hyun et al. (2003) assessed the relative merits of LDV and PIV to measure mean velocity and turbulence in water flow over a train of fixed two-dimensional dunes. Figure 10 shows the LDV measurement stations and PIV field-of-views. The flow field over the dune was divided into five different fields-of-view with a 20 mm overlap between the images. Though PIV is limited in the field-of-view normal to the bed, it provides instantaneous flow-field information that reveals the true complexity of the flow over dunes.

Bed Forms and Flow Mechanisms Associated with Dunes 49

Figure 11 (Hyun et al. 2003) shows the profiles of the x-component of mean velocity (U), the rms turbulence intensities in the x- and y-directions ( 2 2 *u v* ', ' ), and the Reynolds shear stress **(** *u v*' ' **)** at one streamwise station (*X/h* = 5). All variables are made dimensionless by the maximum velocity Uo, held constant at 0.48 m/s in the experiments. The figure provides a direct comparison between PIV and LDV data at a station that is located close to the mean reattachment point. The limitation of the PIV field-of-view (and quality of light sheet) is clear from the extent of the data in the vertical direction. Also seen is the limitation of the two-component LDV in the near-wall region due to blockage of the beams by the dune. These limitations of the two systems are obvious, and present in most arrangements although their criticality will depend on the flow, or flow region of interest. In general, the PIV and LDV data show agreement within the expected uncertainties of the two systems in

Hyun et al. (2003) opined that principal advantage of PIV is its capability to provide information about the instantaneous flow field. The flow is well illustrated by the two sets of successive instantaneous images shown in Figure 12. They correspond to two overlapping fields-of-view, taken at different times. In the region of the dune crest (Figure 12a), at time t = to, there appear to be two vortical structures, one just forming below the shear layer emanating from flow separation at the crest, and the other farther downstream. The former is small and nascent while the latter is larger and more diffused. With increasing time, the latter moves out of the field-of-view while the former grows in size and travels downstream at a velocity of about 0.4Uo. In the last frame, this vortex is seen to again decrease in size. The subsequent evolution of this vortex could not be tracked due to limitation of the fieldof-view - a limitation that is set by the PIV configuration. The second sequence of images (Figure 12b) shows the organized motions in a region downstream of the first. Here, strong ejection and sweep-type events are observed along with other flow structures. Further processing of the PIV images using some of the techniques suggested by Adrian et al. (2000) could provide more quantitative information, such as the length and time scales of the observed flow structures. The most obvious flow feature of the instantaneous flow is the formation of vortices just downstream of the crest below the shear layer, and their growth as

The RANS based turbulence models such as the *k*- *ε* model, the algebraic model and the Reynolds stress model (RSM) are based on the statistical theory of turbulence, and therefore these models cannot in principle simulate coherent structures such as bursting phenomenon (Nezu and Nakagawa 1993). Johns et al. (1993) developed a numerical scheme with a oneequation turbulence model in which a transport equation was solved for eddy viscosity and their comparison of mean flow information, such as velocity profiles, Reynolds shear stress, and bed resistance with experiments were encouraging. Yoon and Patel (1996) developed a k-ω model based on the study of Wilcox (1993) that avoids the use of wall functions. Their computed velocity and turbulence fields, as well as the pressure and friction distributions along the dune are in general agreement with existing detailed experimental data in a rectangular channel with two-dimensional dunes of typical but regular shape. Cheong and Xue (1997) developed a three-layer near-wall k- ε model to account for the separated and reattached region by treating the anisotropy between normal stresses with streamline

the mean velocity and turbulence intensities.

they travel downstream.

**5. Modeling and numerical simulation–RANS, LES**

Fig. 9. Comparison between longitudinal bed profiles and differences between right-side and left-side bed elevation (Y) measured under similar hydraulic conditions during experiments with uniform (MUNI) and mixed (FC70) sediments. (a) Equilibrium phase of P2709 (MUNI) with *Q* = 45 L/s and *is* = 0.514%. (b) Initial phase of P1309 (FC70) with *Q* = 45 L/s and *is* = 0.525%. (c) Equilibrium phase of P1309 (FC70) with *Q* = 45 L/s and *is* = 0.525%. The data are plotted every 20 cm. (from Lanzoni, 2000, reproduced by permission of AGU)

Fig. 10. Schematic of flow and notation (from Hyun et al. 2003, copyright permission of Springer)

Fig. 9. Comparison between longitudinal bed profiles and differences between right-side and left-side bed elevation (Y) measured under similar hydraulic conditions during experiments with uniform (MUNI) and mixed (FC70) sediments. (a) Equilibrium phase of P2709 (MUNI) with *Q* = 45 L/s and *is* = 0.514%. (b) Initial phase of P1309 (FC70) with *Q* = 45 L/s and *is* = 0.525%. (c) Equilibrium phase of P1309 (FC70) with *Q* = 45 L/s and *is* = 0.525%. The data are plotted every 20 cm. (from Lanzoni, 2000, reproduced by permission of AGU)

Fig. 10. Schematic of flow and notation (from Hyun et al. 2003, copyright permission of

Springer)

Figure 11 (Hyun et al. 2003) shows the profiles of the x-component of mean velocity (U), the rms turbulence intensities in the x- and y-directions ( 2 2 *u v* ', ' ), and the Reynolds shear stress **(** *u v*' ' **)** at one streamwise station (*X/h* = 5). All variables are made dimensionless by the maximum velocity Uo, held constant at 0.48 m/s in the experiments. The figure provides a direct comparison between PIV and LDV data at a station that is located close to the mean reattachment point. The limitation of the PIV field-of-view (and quality of light sheet) is clear from the extent of the data in the vertical direction. Also seen is the limitation of the two-component LDV in the near-wall region due to blockage of the beams by the dune. These limitations of the two systems are obvious, and present in most arrangements although their criticality will depend on the flow, or flow region of interest. In general, the PIV and LDV data show agreement within the expected uncertainties of the two systems in the mean velocity and turbulence intensities.

Hyun et al. (2003) opined that principal advantage of PIV is its capability to provide information about the instantaneous flow field. The flow is well illustrated by the two sets of successive instantaneous images shown in Figure 12. They correspond to two overlapping fields-of-view, taken at different times. In the region of the dune crest (Figure 12a), at time t = to, there appear to be two vortical structures, one just forming below the shear layer emanating from flow separation at the crest, and the other farther downstream. The former is small and nascent while the latter is larger and more diffused. With increasing time, the latter moves out of the field-of-view while the former grows in size and travels downstream at a velocity of about 0.4Uo. In the last frame, this vortex is seen to again decrease in size. The subsequent evolution of this vortex could not be tracked due to limitation of the fieldof-view - a limitation that is set by the PIV configuration. The second sequence of images (Figure 12b) shows the organized motions in a region downstream of the first. Here, strong ejection and sweep-type events are observed along with other flow structures. Further processing of the PIV images using some of the techniques suggested by Adrian et al. (2000) could provide more quantitative information, such as the length and time scales of the observed flow structures. The most obvious flow feature of the instantaneous flow is the formation of vortices just downstream of the crest below the shear layer, and their growth as they travel downstream.

### **5. Modeling and numerical simulation–RANS, LES**

The RANS based turbulence models such as the *k*- *ε* model, the algebraic model and the Reynolds stress model (RSM) are based on the statistical theory of turbulence, and therefore these models cannot in principle simulate coherent structures such as bursting phenomenon (Nezu and Nakagawa 1993). Johns et al. (1993) developed a numerical scheme with a oneequation turbulence model in which a transport equation was solved for eddy viscosity and their comparison of mean flow information, such as velocity profiles, Reynolds shear stress, and bed resistance with experiments were encouraging. Yoon and Patel (1996) developed a k-ω model based on the study of Wilcox (1993) that avoids the use of wall functions. Their computed velocity and turbulence fields, as well as the pressure and friction distributions along the dune are in general agreement with existing detailed experimental data in a rectangular channel with two-dimensional dunes of typical but regular shape. Cheong and Xue (1997) developed a three-layer near-wall k- ε model to account for the separated and reattached region by treating the anisotropy between normal stresses with streamline

Bed Forms and Flow Mechanisms Associated with Dunes 51

0

0

0

(a) Field-of-view #2 in Figure 11 (b) Field-of-view #3 in Figure 11

Fig. 12. Instantaneous velocity field obtained by PIV (from Hyun et al. 2003, copyright

<sup>0</sup> t

<sup>0</sup> t

<sup>0</sup> t

t <sup>o</sup> sec

<sup>o</sup> +(1/15) sec

<sup>o</sup> +(2/15) sec

<sup>o</sup> +(1/5) sec

<sup>o</sup> +(4/15) sec

<sup>o</sup> +(1/3) sec

t

t

0 t <sup>o</sup> sec

0 t

> 0 t

0 t

> 0 t

0 t

<sup>o</sup> +(2/15) sec

<sup>o</sup> +(1/15) sec

<sup>o</sup> +(1/5) sec

<sup>o</sup> +(4/15) sec

<sup>o</sup> +(1/3) sec

permission of Springer)

curvature correction. They opined that standard wall function treatment appears to be inadequate in the separating-reattachment region but computations are fairly satisfactory in other regions.

Fig. 11. Comparison between PIV and LDV data (from Hyun et al. 2003, copyright permission of Springer)

curvature correction. They opined that standard wall function treatment appears to be inadequate in the separating-reattachment region but computations are fairly satisfactory in

s

**y/h**

**y/h**

a) X/h = 5, X/λ = 0.25

Fig. 11. Comparison between PIV and LDV data (from Hyun et al. 2003, copyright

**v' / Uo**

**\_\_\_**

0.04 0.08 0.12 0.16 0.2 0.24 <sup>0</sup>

**U/Uo**

LDV PIV

**x/h = 5**

1

2

3

4

5

1

2

3

4

5

**u'/Uo**

**u'v' / Uo 2**

**\_\_\_\_**

0.004 0.008 0.012 0.016 0.02 0.024 <sup>0</sup>

**\_\_\_**

0 0.04 0.08 0.12 0.16 0.2 0.24 <sup>0</sup>

other regions.

**y/h**

1

permission of Springer)

2

3

4

5

0

1

2

3

4

5

**y/h**

Fig. 12. Instantaneous velocity field obtained by PIV (from Hyun et al. 2003, copyright permission of Springer)

Bed Forms and Flow Mechanisms Associated with Dunes 53

**xxxxxxxxxxxxxxxxxxxxxxxxxxx <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> xxxxxx**

**xx <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> xxxxxxxxxx**

point of reattachment.

**xxxxxx xx xx xx <sup>x</sup> <sup>x</sup> xx xx x x x x x x x x x x x x x x x x x x x x x x**

> **v'2 /Uo**

**\_\_\_\_ \_\_\_\_\_\_**

<sup>0</sup> 0.06 0.12 0.18 0.24 <sup>0</sup>

d/h=6 (LDV) d/h=7 (PIV) **<sup>x</sup>** d/h=6 (LES)

**y/h**

**y/h**

2

4

6

8

2

4

6

8

**U/Uo**

**x x x x x x x x x x x x x x x x x x x x x x**

**y/h**

**y/h**

Fig. 13. Comparison of LDV, PIV and LES results at *x*/*h*=4 (from Balachandar et al., 2002)

(*Re* = 3300) and presented mean flow and turbulent structures of the open channel flow over bed forms. Hayashi et al. (2003) also found the presence of hairpin-shaped vortices, vortex patterns that showed both a normal and reverse hairpin shapes. Yue et al. (2006) used LES to study high-Reynolds number open-channel flow (*Re* = 5.7x104) over an idealized, two-dimensional laboratory-scale dune to investigate the unsteady flow structures as well as the mean-flow details and turbulence statistics. In a qualitative manner, they detected sweeps and ejections as well as formation of near-bed streaks and free surface structures and movement. They found that LES predicts the secondary peaks lying farther out from the bed, as observed in the experiments, their magnitudes are substantially under predicted. As the secondary peaks are remnants of the primary ones on the previous dunes, the discrepancy leads to the conclusion that the present LES does not adequately account for the upstream history. Williams (2007) carried out large eddy simulation of flow over a 2-D dune by using a surface adaptive curvilinear finite volume method to solve free-surface flows. The computed mean velocity profiles and normalized RMS plots of stream wise velocities were in good agreement with available experimental data of Balachandar et al. (2002) and PIV and LES offer a very graphic view of the instantaneous structures in the flow, as shown in Figure 14. Stoesser et al., (2008) investigated large eddy simulations of instantaneous flow over 2-D dunes (the geometry of the dunes is identical to that used previously by Balachandar et al. 2002) and found splats and evolution of hairpin vortices from kolk-boil vortexes around and beyond the

2

4

6

8

2

4

6

8

**<sup>x</sup> <sup>x</sup> <sup>x</sup> xxxxxxxxxxxxxxxxxxxxxxxxx xxx <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> xxx**

<sup>0</sup> 0.06 0.12 0.18 0.24 <sup>0</sup>

**u'2 /Uo**

**\_\_\_\_ \_\_\_\_\_**

**x x x x x x x x x x x x x x x x x x x**

**xx <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> xx xxx <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> <sup>x</sup> xxx**

> **-u'v'/Uo 2**

**\_\_\_\_\_\_**

<sup>0</sup> 0.006 0.012 0.018 0.024 <sup>0</sup>

**x x x x x x x x x x x x x x x x x x x x**

Cokljat and Kralj (1997) used a *k*- *ε* model and RSM to investigate the better turbulence model for prediction of flows over river bed forms. Cokljat and Kralj (1997) used Lyn's (1993) data for validation of their numerical model and found that *k*- *ε* model of turbulence is capable of modeling the main features of the flow to acceptable level of accuracy. Mendoza and Shen (1990) used a k-ε model with wall functions but with an algebraic stress model in place of the more commonly used eddy viscosity assumption. The model was validated using experimental data obtained by Raudkivi (1966) and concluded that model satisfactorily predicted *U*-velocity, *uv* , and turbulent kinetic-energy profiles, pressure and shear stress distributions of the steady turbulent flow over two-dimensional dune-like artificial bed forms. The above-mentioned models used the rigid lid assumption. Bravo and Zheng (1999) studied the standard *k*- *ε* model, RNG (Renormalization Group) *k*- *ε* model and differential RSM (Reynolds stress model) model for their applicability to predict turbulent flow over artificial bed forms. They implemented both free surface and rigid lid models to study the effects of sand grain roughness, near wall modeling, free surface, body forces and grid resolution. They found that free surface flow models gave better flow predictions and take fewer iterations to convergence than the rigid lid models. Patel and Lyn (2004) illustrated the results of both RANS computations and large eddy simulations (LES), compared the mean velocities and turbulent statistics to those measured by Hyun et al. (2003). The above-mentioned numerical models with RANS based turbulence closures provide mean flow information, such as velocity profiles, Reynolds shear stress, and bed resistance, but do not give any information about the unsteady flow structures that are important features of such flows. Lyn (2002) mentioned coherent turbulent flow structures can only be predicted either by direct numerical simulation (DNS) or large-eddy simulation (LES).

Balachandar et al. (2002) carried out experimental investigations (PIV and LDV) and complemented them with numerical simulations (LES). The LES computations used the assumption of space periodicity and approximate treatment of the free surface by simulating the flow over a single dune in a closed channel formed by the mirror reflection of the open channel on the free surface. The finite-volume LES numerical code of Cui et al. (2000) was used in the study. No-slip conditions were applied at the top and bottom walls, periodic conditions were applied at the inlet and outlet, and also along the sides of the solution domain at each instant. Convergence was claimed at each time step when the sum of the pressure and viscous resistance was in balance with the imposed pressure difference between the duct inlet and outlet. After the flow reached "steady-state", the solution was continued for about five large-eddy turnover times (2*d*/*u\**, where *u\** is the friction velocity) to accumulate the statistics. Measurements were compared with simulations for time averaged flow and instantaneous flow. The normalized measurements mean velocity in the x-direction, the RMS velocity fluctuations in the (*x*, *y*) directions, and the Reynolds shear stress ( *u v*' ' ) by LDV and PIV are in agreement but the LES results for the longitudinal fluctuations and the shear stress are lower than the experiments (shown in Figure 13). In the case of the instantaneous flow field, the PIV shows better-defined vortices just downstream of the crest below the shear layer.

A recent DNS on an artificial dune-type wavy bed was carried out by Hayashi et al. (2003) to examine coherent structures and "boil of the first kind" in a low Reynolds number flow

Cokljat and Kralj (1997) used a *k*- *ε* model and RSM to investigate the better turbulence model for prediction of flows over river bed forms. Cokljat and Kralj (1997) used Lyn's (1993) data for validation of their numerical model and found that *k*- *ε* model of turbulence is capable of modeling the main features of the flow to acceptable level of accuracy. Mendoza and Shen (1990) used a k-ε model with wall functions but with an algebraic stress model in place of the more commonly used eddy viscosity assumption. The model was validated using experimental data obtained by Raudkivi (1966) and concluded that model satisfactorily predicted *U*-velocity, *uv* , and turbulent kinetic-energy profiles, pressure and shear stress distributions of the steady turbulent flow over two-dimensional dune-like artificial bed forms. The above-mentioned models used the rigid lid assumption. Bravo and Zheng (1999) studied the standard *k*- *ε* model, RNG (Renormalization Group) *k*- *ε* model and differential RSM (Reynolds stress model) model for their applicability to predict turbulent flow over artificial bed forms. They implemented both free surface and rigid lid models to study the effects of sand grain roughness, near wall modeling, free surface, body forces and grid resolution. They found that free surface flow models gave better flow predictions and take fewer iterations to convergence than the rigid lid models. Patel and Lyn (2004) illustrated the results of both RANS computations and large eddy simulations (LES), compared the mean velocities and turbulent statistics to those measured by Hyun et al. (2003). The above-mentioned numerical models with RANS based turbulence closures provide mean flow information, such as velocity profiles, Reynolds shear stress, and bed resistance, but do not give any information about the unsteady flow structures that are important features of such flows. Lyn (2002) mentioned coherent turbulent flow structures can only be predicted either by direct numerical simulation (DNS) or large-eddy simulation

Balachandar et al. (2002) carried out experimental investigations (PIV and LDV) and complemented them with numerical simulations (LES). The LES computations used the assumption of space periodicity and approximate treatment of the free surface by simulating the flow over a single dune in a closed channel formed by the mirror reflection of the open channel on the free surface. The finite-volume LES numerical code of Cui et al. (2000) was used in the study. No-slip conditions were applied at the top and bottom walls, periodic conditions were applied at the inlet and outlet, and also along the sides of the solution domain at each instant. Convergence was claimed at each time step when the sum of the pressure and viscous resistance was in balance with the imposed pressure difference between the duct inlet and outlet. After the flow reached "steady-state", the solution was continued for about five large-eddy turnover times (2*d*/*u\**, where *u\** is the friction velocity) to accumulate the statistics. Measurements were compared with simulations for time averaged flow and instantaneous flow. The normalized measurements mean velocity in the x-direction, the RMS velocity fluctuations in the (*x*, *y*) directions, and the Reynolds shear stress ( *u v*' ' ) by LDV and PIV are in agreement but the LES results for the longitudinal fluctuations and the shear stress are lower than the experiments (shown in Figure 13). In the case of the instantaneous flow field, the PIV shows better-defined vortices just downstream

A recent DNS on an artificial dune-type wavy bed was carried out by Hayashi et al. (2003) to examine coherent structures and "boil of the first kind" in a low Reynolds number flow

(LES).

of the crest below the shear layer.

Fig. 13. Comparison of LDV, PIV and LES results at *x*/*h*=4 (from Balachandar et al., 2002)

(*Re* = 3300) and presented mean flow and turbulent structures of the open channel flow over bed forms. Hayashi et al. (2003) also found the presence of hairpin-shaped vortices, vortex patterns that showed both a normal and reverse hairpin shapes. Yue et al. (2006) used LES to study high-Reynolds number open-channel flow (*Re* = 5.7x104) over an idealized, two-dimensional laboratory-scale dune to investigate the unsteady flow structures as well as the mean-flow details and turbulence statistics. In a qualitative manner, they detected sweeps and ejections as well as formation of near-bed streaks and free surface structures and movement. They found that LES predicts the secondary peaks lying farther out from the bed, as observed in the experiments, their magnitudes are substantially under predicted. As the secondary peaks are remnants of the primary ones on the previous dunes, the discrepancy leads to the conclusion that the present LES does not adequately account for the upstream history. Williams (2007) carried out large eddy simulation of flow over a 2-D dune by using a surface adaptive curvilinear finite volume method to solve free-surface flows. The computed mean velocity profiles and normalized RMS plots of stream wise velocities were in good agreement with available experimental data of Balachandar et al. (2002) and PIV and LES offer a very graphic view of the instantaneous structures in the flow, as shown in Figure 14. Stoesser et al., (2008) investigated large eddy simulations of instantaneous flow over 2-D dunes (the geometry of the dunes is identical to that used previously by Balachandar et al. 2002) and found splats and evolution of hairpin vortices from kolk-boil vortexes around and beyond the point of reattachment.

Bed Forms and Flow Mechanisms Associated with Dunes 55

contributions from *Q1* and *Q*3 are small, and the fact that the contributions are negative indicates the presence of flow structures that transfer energy from the turbulence to the mean flow. All along the dune, the contributions by *Q1* events are more or less similar. With increasing distance from the dune crest, there is a very slight increase in the contributions from *Q1* events, especially along the separating shear layer, and immediately upstream and downstream of reattachment. As pointed out by Bennett and Best (1995), these events are probably associated with structures brought towards the bed along the separating shear layer. These events provide one possible mechanism by which

> 0 **t**

> 0 **t**

0 **t**

0 **t**

0

0 **t**

**t**

**<sup>o</sup> + (6/30) sec**

**<sup>o</sup> + (7/30) sec**

**<sup>o</sup> + (8/30) sec**

**<sup>o</sup> + (9/30) sec**

**<sup>o</sup> + (10/30) sec**

**<sup>o</sup> + (11/30) sec**

a) PIV

sediment can be eroded.

0 **t <sup>o</sup> sec**

0 **t**

0 **t**

0 **t**

0 **t**

0 **t**

**<sup>o</sup> + (1/30) sec**

**<sup>o</sup> + (2/30) sec**

**<sup>o</sup> + (3/30) sec**

**<sup>o</sup> + (4/30) sec**

**<sup>o</sup> + (5/30) sec**

### **6. Formation of coherent structures**

Experimental and field investigations have documented the macro-turbulent characteristics of spatially varied flow over the bed forms and the formation of "kolks" and "boils" proposed by Matthes (1947). The "kolks" and "boils" are the upward tilting vortices of both fluid and sediment originating downstream of dune crests and at the point of reattachment. Bennett and Best (1995) suggested that the bursting events due to turbulent flow are associated with zone of Kelvin-Helmholtz instabilities developed at the zone of flow separation in front of ripple lee.

### **6.1 Turbulent structures by quadrant analysis**

To evaluate the role of coherent structures, it is a common practise to divide the *u-v* sample space of the fluctuating velocities into four quadrants. Such representation has potential to reveal the relative contribution of the turbulent structures (events) from different quadrants to the total Reynolds shear stress. Flow visualization studies on rough wall bounded flows by Grass (1971) documented a streak that migrates slowly away from the wall and at some point detaches from it completely. This process of upward lifting of low-speed fluid away from the solid wall is commonly referred to as *ejection*. During the ejection process, the instantaneous local velocity (*Ui*) is lower than the time-averaged local velocity (*U*). Whenever ejection occurs, in order to satisfy continuity, high speed fluid moves towards the wall (*Ui > 0*) from outer flow regions and this event is called a *sweep*. It is only possible to detect ejection events when *u < 0* and *v > 0* are observed simultaneously. In the same way, sweep events can be detected by simultaneously observing a high-speed fluid parcel (*u > 0*), moving towards the bed (*v < 0)*. There are two other events that also contribute to the total Reynolds shear stress. They are known as outward interactions (*u > 0, v > 0*) and inward interactions (*u < 0, v < 0*).

At every measurement location, the Reynolds shear stress is calculated and further decomposed as a sum of different events according to the procedure described by Lu and Willmarth (1973). By using the concept of a hyperbolic hole of size *H*, defined by *uv Hu v rms rms* , the contribution from a particular quadrant can be written as

$$\overline{I(\mu v)}\_{Q\_i, H} = \lim\_{T \to \infty} \frac{1}{T} \int\_0^T \mu(t)v(t)I(t)dt\tag{1}$$

Here, *I(t)* is a detection function defined as:

$$I(t) = \begin{cases} 1 & \text{when} \quad \left\| \boldsymbol{w} \right\|\_{\boldsymbol{Q}} \ge \boldsymbol{H} \boldsymbol{u}\_{rms} \boldsymbol{v}\_{rms} \\ 0 & \text{otherwise} \end{cases} \tag{2}$$

It is assumed that the velocity used to compute ( )*Q,H uv* is a function of time only. The parameter *H* defines a threshold value, which separates the extreme events from the random background turbulence. By increasing the value of *H* more extreme/strong events are identified. In the present study, quadrant decomposition yields Reynolds stress contribution to each quadrant for a given value of H denoted as ( ) () *Qi uv y* and is represented as *Qi* (i = 1 to 4) for convenience.

Figure 15 shows the contributions by the four quadrants events (Balachandar et al., 2007) for the flow past the dune shown in Figure 4. At each station, the local maximum value of the mean shear stress is used as the normalizing scale. As expected, at *X*/*h* = -2, the

Experimental and field investigations have documented the macro-turbulent characteristics of spatially varied flow over the bed forms and the formation of "kolks" and "boils" proposed by Matthes (1947). The "kolks" and "boils" are the upward tilting vortices of both fluid and sediment originating downstream of dune crests and at the point of reattachment. Bennett and Best (1995) suggested that the bursting events due to turbulent flow are associated with zone of Kelvin-Helmholtz instabilities developed at the zone of flow

To evaluate the role of coherent structures, it is a common practise to divide the *u-v* sample space of the fluctuating velocities into four quadrants. Such representation has potential to reveal the relative contribution of the turbulent structures (events) from different quadrants to the total Reynolds shear stress. Flow visualization studies on rough wall bounded flows by Grass (1971) documented a streak that migrates slowly away from the wall and at some point detaches from it completely. This process of upward lifting of low-speed fluid away from the solid wall is commonly referred to as *ejection*. During the ejection process, the instantaneous local velocity (*Ui*) is lower than the time-averaged local velocity (*U*). Whenever ejection occurs, in order to satisfy continuity, high speed fluid moves towards the wall (*Ui > 0*) from outer flow regions and this event is called a *sweep*. It is only possible to detect ejection events when *u < 0* and *v > 0* are observed simultaneously. In the same way, sweep events can be detected by simultaneously observing a high-speed fluid parcel (*u > 0*), moving towards the bed (*v < 0)*. There are two other events that also contribute to the total Reynolds shear stress. They are known as outward interactions (*u > 0, v > 0*) and inward

At every measurement location, the Reynolds shear stress is calculated and further decomposed as a sum of different events according to the procedure described by Lu and Willmarth (1973). By using the concept of a hyperbolic hole of size *H*, defined

> 0 <sup>1</sup> ( ) lim ( ) ( ) ( ) *<sup>i</sup> T*

*when uv Hu v <sup>Q</sup> rms rms I t otherwise*

It is assumed that the velocity used to compute ( )*Q,H uv* is a function of time only. The parameter *H* defines a threshold value, which separates the extreme events from the random background turbulence. By increasing the value of *H* more extreme/strong events are identified. In the present study, quadrant decomposition yields Reynolds stress contribution to each quadrant for a given value of H denoted as ( ) () *Qi uv y* and is represented as *Qi* (i = 1

Figure 15 shows the contributions by the four quadrants events (Balachandar et al., 2007) for the flow past the dune shown in Figure 4. At each station, the local maximum value of the mean shear stress is used as the normalizing scale. As expected, at *X*/*h* = -2, the

*uv u t v t I t dt <sup>T</sup>* (1)

(2)

by *uv Hu v rms rms* , the contribution from a particular quadrant can be written as

*Q ,H <sup>T</sup>*

1 ( ) <sup>0</sup>

**6.

Here, *I(t)* is a detection function defined as:

contributions from *Q1* and *Q*3 are small, and the fact that the contributions are negative indicates the presence of flow structures that transfer energy from the turbulence to the mean flow. All along the dune, the contributions by *Q1* events are more or less similar. With increasing distance from the dune crest, there is a very slight increase in the contributions from *Q1* events, especially along the separating shear layer, and immediately upstream and downstream of reattachment. As pointed out by Bennett and Best (1995), these events are probably associated with structures brought towards the bed along the separating shear layer. These events provide one possible mechanism by which sediment can be eroded.

Bed Forms and Flow Mechanisms Associated with Dunes 57

contributions of quadrant 2 events are dominant at all *X*/*h* locations as shown in Figure 15. In the figure, *F* represents the fractional contribution to the total shear stress by each quadrant. With increasing distance from the crest, the *Q2* profiles indicate large gradients, especially near the crest line. These high-magnitude events correspond to the source of the dune-related bursting phenomena reported previously (Jackson 1976). Similar to *Q2* events, the *Q4* events show large changes in the vicinity of the shear layer. In Figure 15a, for *y*/*d* < 0.3, the *Q4* profiles show a trend that is opposite to that of the *Q2* profiles. Ahead of reattachment (*X*/*h* = 2 and 4), and slightly above the crestline, the magnitude of the *Q4*

Studying several results such as that in Figure 15, differences due to flow depth were noticeable in the contributions of all four quadrants. However, as noted with respect to Figure 15, the contributions of *Q2* events are very important and most likely associated with much of the entrainment and transport of sediment. Therefore, the effect of depth on *Q2* events is presented in Figure 16 over the wavelength of the dune. The results are shown in a two-column format with *h* as the normalizing scale in the left column and *d* as the normalizing scale in the right column. Ahead of separation (Figures 16a,c and e), the *Q2* profiles show a similar trend at all flow depths, each showing a near-wall peak in the vicinity of *y*/*h* = 1. This is identified with the remnants of the turbulence activity carried over from the previous dune. This trend continues well after reattachment, indicating the persistence of the *Q2* events on the stoss side of the dune. At stations ahead of the dune crest, a peak in the *Q2* profiles (Figures 16 d and f) around y/d = 0.2 indicates the sustenance of turbulence generated by the previous dune, carried over to the next dune. This value is not influenced by the bed roughness. Overall it is concluded that the characteristics of the shear layer, the length of the reattachment zone and the *Q2* events control the turbulence

Balachandar and Patel (2008) carried out LDV measurements to obtain more detailed information on the effect of bed roughness superimposed on a train of well-formed dunes. The fractional contribution to the mean Reynolds shear stress by quadrant 2 (*Q2*: *u* < 0, *v* > 0) events are shown in Figure 17. The figure is presented in three-column format with one type of wall condition being represented in each column. In all the graphs, with increasing distance from the dune surface, the *Q2* values gradually increase towards the free surface. The profiles show large gradients, especially near the crest line. In all the graphs shown in Figure 17, the tendency is to have two local peaks (indicated as A and B, see, middle column of Figure 17). Except for the first row of graphs (*X*/*h* = -2), peak A, closer to the bed (0.16 < *y*/*d* < 0.23), corresponds to the location of the separating streamline; whereas peak B, away from the bed (0.5 < *y*/*d* < 0.62) is an indicator of a large-scale event in the outer region. The peaks at *X*/*h* = -2 (first row) correspond to the turbulence activities carried over from the previous dunes. Comparing the three columns of graphs, the peaks are located farther away from the bed with increasing bed roughness. As seen in the middle column of graphs, the high magnitude *Q2* events correspond to the source of the dune-related bursting phenomenon reported previously (Jackson 1976; Yalin 1972). It is also possible that the separating shear layer is associated with streamwise vortices generated along the braids between the Kelvin-Helmhotz instabilities (Lasheras and Choi 1988; Metcalfe et al. 1987). The *Q2* events influence the vertical convection of sediment and can be responsible for much

events tends to be close to the *Q2* events.

structure over the dunes.

of the vertical mixing in the rivers.

Fig. 14. Time sequence of instantaneous velocity field (from Balachandar et al., 2002)

Detailed experimental observations (Balachandar et al., 2007; Best, 2005a, b; Kostachuck and Church, 1993; Rood and Hickin, 1989) revealed that *Q2* events are most likely associated with much of the entrainment and transport of sediment. The variation of *Q2* events over the wavelength of the dune was studied by Balachandar et al., (2007). It was found that the

**<sup>0</sup> + (6/30) sec**

**<sup>0</sup> + (7/30) sec**

**<sup>0</sup> + (8/30) sec**

**<sup>0</sup> + (9/30) sec**

**<sup>0</sup> + (10/30) sec**

**<sup>0</sup> + (11/30) sec**

b) LES

Detailed experimental observations (Balachandar et al., 2007; Best, 2005a, b; Kostachuck and Church, 1993; Rood and Hickin, 1989) revealed that *Q2* events are most likely associated with much of the entrainment and transport of sediment. The variation of *Q2* events over the wavelength of the dune was studied by Balachandar et al., (2007). It was found that the

Fig. 14. Time sequence of instantaneous velocity field (from Balachandar et al., 2002)

**t**

**t**

**t**

**t**

**t**

**t**

**<sup>0</sup> sec t**

**<sup>0</sup> + (1/30) sec t**

**<sup>0</sup> + (2/30) sec t**

**<sup>0</sup> + (3/30) sec t**

**<sup>0</sup> + (4/30) sec t**

**<sup>0</sup> + (5/30) sec t**

contributions of quadrant 2 events are dominant at all *X*/*h* locations as shown in Figure 15. In the figure, *F* represents the fractional contribution to the total shear stress by each quadrant. With increasing distance from the crest, the *Q2* profiles indicate large gradients, especially near the crest line. These high-magnitude events correspond to the source of the dune-related bursting phenomena reported previously (Jackson 1976). Similar to *Q2* events, the *Q4* events show large changes in the vicinity of the shear layer. In Figure 15a, for *y*/*d* < 0.3, the *Q4* profiles show a trend that is opposite to that of the *Q2* profiles. Ahead of reattachment (*X*/*h* = 2 and 4), and slightly above the crestline, the magnitude of the *Q4* events tends to be close to the *Q2* events.

Studying several results such as that in Figure 15, differences due to flow depth were noticeable in the contributions of all four quadrants. However, as noted with respect to Figure 15, the contributions of *Q2* events are very important and most likely associated with much of the entrainment and transport of sediment. Therefore, the effect of depth on *Q2* events is presented in Figure 16 over the wavelength of the dune. The results are shown in a two-column format with *h* as the normalizing scale in the left column and *d* as the normalizing scale in the right column. Ahead of separation (Figures 16a,c and e), the *Q2* profiles show a similar trend at all flow depths, each showing a near-wall peak in the vicinity of *y*/*h* = 1. This is identified with the remnants of the turbulence activity carried over from the previous dune. This trend continues well after reattachment, indicating the persistence of the *Q2* events on the stoss side of the dune. At stations ahead of the dune crest, a peak in the *Q2* profiles (Figures 16 d and f) around y/d = 0.2 indicates the sustenance of turbulence generated by the previous dune, carried over to the next dune. This value is not influenced by the bed roughness. Overall it is concluded that the characteristics of the shear layer, the length of the reattachment zone and the *Q2* events control the turbulence structure over the dunes.

Balachandar and Patel (2008) carried out LDV measurements to obtain more detailed information on the effect of bed roughness superimposed on a train of well-formed dunes. The fractional contribution to the mean Reynolds shear stress by quadrant 2 (*Q2*: *u* < 0, *v* > 0) events are shown in Figure 17. The figure is presented in three-column format with one type of wall condition being represented in each column. In all the graphs, with increasing distance from the dune surface, the *Q2* values gradually increase towards the free surface. The profiles show large gradients, especially near the crest line. In all the graphs shown in Figure 17, the tendency is to have two local peaks (indicated as A and B, see, middle column of Figure 17). Except for the first row of graphs (*X*/*h* = -2), peak A, closer to the bed (0.16 < *y*/*d* < 0.23), corresponds to the location of the separating streamline; whereas peak B, away from the bed (0.5 < *y*/*d* < 0.62) is an indicator of a large-scale event in the outer region. The peaks at *X*/*h* = -2 (first row) correspond to the turbulence activities carried over from the previous dunes. Comparing the three columns of graphs, the peaks are located farther away from the bed with increasing bed roughness. As seen in the middle column of graphs, the high magnitude *Q2* events correspond to the source of the dune-related bursting phenomenon reported previously (Jackson 1976; Yalin 1972). It is also possible that the separating shear layer is associated with streamwise vortices generated along the braids between the Kelvin-Helmhotz instabilities (Lasheras and Choi 1988; Metcalfe et al. 1987). The *Q2* events influence the vertical convection of sediment and can be responsible for much of the vertical mixing in the rivers.

Bed Forms and Flow Mechanisms Associated with Dunes 59

0.0

X/h = -2.0

0.6

**d**)

0.0

X/h = 4.0

0.6

0.0

Fig. 16. Effect of depth on fractional contribution to quadrant 2: (a, c, e) using the dune height, h, as the normalizing length scale and (b, d, f) using the depth of flow d as the normalizing length scale. (from Balachandar and Patel 2008, copyright permission of NRC

X/h = 6.0

0.1

0.2

0.3

F

0.4

0.5

0.1

0.2

0.3

F

0.4

0.5

0.1

0.2

0.3

F

0.4

0.5

0.6

 d1 /h = 3 d1 /h = 4 d1 /h = 6 d1 /h = 8

0.0 0.2 0.4 0.6 0.8 1.0

y/d

0.0 0.2 0.4 0.6 0.8 1.0

y/d

0.0 0.2 0.4 0.6 0.8 1.0

y/d

0123456789

y/h

**<sup>a</sup>**) **<sup>b</sup>**) F = -<uv>Q/uvmax

0123456789

y/h

**e**) **f**)

0123456789

y/h

0.0

X/h = -2.0

0.6

**c**)

0.0

X/h = 4.0

0.6

0.0

research press)

X/h = 6.0

0.1

0.2

0.3

F

0.4

0.5

0.1

0.2

0.3

F

0.4

0.5

0.1

0.2

0.3

F

0.4

0.5

0.6

Fig. 15. Fractional contribution by the four quadrants (*d1*/*h* = 6). (a) *X*/*h* = -2.0; (b) *X*/*h* = 4.0; (c) *X*/*h* = 4.0; (d) *X*/*h* = 5.0; (e) *X*/*h* = 6.0; (f) *X*/*h* = 12.0. (from Balachandar and Patel 2008, copyright permission of NRC research press)

0.0

0.0

0.0

Fig. 15. Fractional contribution by the four quadrants (*d1*/*h* = 6).  Effect of depth on fractional contribution to quadrant 2: (a, c, e) using the dune height, h, as the normalizing length scale and (b, d, f) using the depth of flow d as the normalizing length scale. (from Balachandar and Patel 2008, copyright permission of NRC research press)

Bed Forms and Flow Mechanisms Associated with Dunes 61

The ASCE taskforce subcommittee (2002) and Best (2005 a) have suggested several important research directions to further understand, quantify and model the dynamics of flow over dunes. The taskforce opined the need to synthesize the knowledge gained with the advances in measurement techniques and simulation technologies to quantify the development of dunes, amount of sediment transport and bed changes. Efficiency of the available theoretical models to simulate the formation of the bed forms with uniform and heterogeneous sediment needs to be ascertained for laboratory and field data. Presently, 2-D dunes are modeled in laboratory and simulations but changes in the transverse direction should be included in the simulations (Parsons et al. 2005). Most of the dune studies are concentrated on flow separation and flow field on lee side of dunes, however near-bed turbulence characteristics on the stoss side are not fully understood. Carling et al. (2000) found that evidence of large-scale, coherent low frequency flow structures and separated boundary layers above the stoss side of the large dunes. The knowledge gained in understanding of coherent structures should be utilized in future research (Stoesser et al. 2008 and Yue et al. 2005) on modeling of sediment transport and evolution of bed in open channels. Another important research direction is to study the scaling effects between laboratory and field studies of flow over dunes (Best and Kostaschuk 2002). Measurements and simulations of formation of bed forms should be studied during varying discharge regimes because most of the sediment transport and bed form changes takes place during the floods (Ten Brinke et al. 1999). Low angle dunes are common in big rivers such as Jamuna river in Bangladesh (Kostaschuk et al., 2004) therefore modeling and laboratory studies on low angle dunes are required. Venditti et al. (2005) concluded that movement of the entire bed form is controlled by superimposed bed forms therefore morphodynamics of super imposed bed forms over migrating dunes needs to be studied theoretically and experimentally. Yue et al. (2005) opined that more realistic simulations of the interaction of the free surface with the bed is needed to understand the coherent structures and sediment transport. Kostaschuk et al. (2008) suggested to carry out further research with respect to amount of suspended sediment on formation and as well as migration of dunes. The future research may also include simulation of 2-D and 3-D flow over dunes using DES (detached eddy simulation) which is computationally more efficient (Xu et al., 2007) than LES

Adrian, R. J., Meinhart, C. D. and Tomkins, C. D. (2000). "Vortex organization in the outer

Balachandar, R. and Patel, V.C. (2002). "Rough Wall Boundary Layer on a Plate in an Open

region of the turbulent boundary layer." J. Fluid. Mech., 422, 1-54. ASCE Task Force (2002), Flow and transport over dunes, *J. Hydraul. Eng.*, 127, 726– 728. Balachandar, R., Hyun, B. S., and Patel, V. C. (2007). Effect of depth on flow over a fixed

dune, *Canadian Journal of Civil Engineering*, 34, pp. 1587-1599.

Channel". *J. Hydr. Engrg.*, ASCE 128(10), 947–951.

**7. Future research topics**

modeling.

**8. References**

Fig. 17. Contribution to shear stress by quadrant 2. SM - train of smooth bed dunes manufactured from Plexiglas; SG - sand grain test; WM - wire mesh test. (from Balachandar and Patel 2008, copyright permission of NRC research press)

### **7. Future research topics**

60 Sediment Transport – Flow Processes and Morphology

**0.1 y/d 1**

**0.1 y/d 1**

A B

**0.1 y/d 1**

<sup>A</sup> <sup>B</sup>

**0.1 y/d 1**

A B

**0.1 y/d 1**

**0.1 y/d 1**

manufactured from Plexiglas; SG - sand grain test; WM - wire mesh test. (from Balachandar

B

<sup>A</sup> <sup>B</sup>

**X/h = 2.0**

**X/h = 4.0**

**X/h = 5.0**

**X/h = 6.0**

**X/h = 12.0**

A

Fig. 17. Contribution to shear stress by quadrant 2. SM - train of smooth bed dunes

A B

**SG X/h = -2.0**

**0.1 y/d 1**

**0.1 y/d 1**

**0.1 y/d 1**

**0.1 y/d 1**

B

**0.1 y/d 1**

A B

**0.1 y/d 1**

A B

A B

<sup>A</sup> <sup>B</sup>

**X/h = 2.0**

**X/h = 4.0**

**X/h = 5.0**

**X/h = 6.0**

**X/h = 12.0**

A

A B

**WM**

**X/h = -2.0**

**X/h = 2.0**

**X/h = 4.0**

**X/h = 5.0**

**X/h = 6.0**

**X/h = 12.0**

**0.1 y/d 1**

A B

**0.1 y/d 1**

<sup>A</sup> <sup>B</sup>

**0.1 y/d 1**

<sup>A</sup> <sup>B</sup>

**0.1 y/d 1**

<sup>A</sup> <sup>B</sup>

**0.1 y/d 1**

A B

**0.1 y/d 1**

A

B

**SM X/h = -2.0**

and Patel 2008, copyright permission of NRC research press)

The ASCE taskforce subcommittee (2002) and Best (2005 a) have suggested several important research directions to further understand, quantify and model the dynamics of flow over dunes. The taskforce opined the need to synthesize the knowledge gained with the advances in measurement techniques and simulation technologies to quantify the development of dunes, amount of sediment transport and bed changes. Efficiency of the available theoretical models to simulate the formation of the bed forms with uniform and heterogeneous sediment needs to be ascertained for laboratory and field data. Presently, 2-D dunes are modeled in laboratory and simulations but changes in the transverse direction should be included in the simulations (Parsons et al. 2005). Most of the dune studies are concentrated on flow separation and flow field on lee side of dunes, however near-bed turbulence characteristics on the stoss side are not fully understood. Carling et al. (2000) found that evidence of large-scale, coherent low frequency flow structures and separated boundary layers above the stoss side of the large dunes. The knowledge gained in understanding of coherent structures should be utilized in future research (Stoesser et al. 2008 and Yue et al. 2005) on modeling of sediment transport and evolution of bed in open channels. Another important research direction is to study the scaling effects between laboratory and field studies of flow over dunes (Best and Kostaschuk 2002). Measurements and simulations of formation of bed forms should be studied during varying discharge regimes because most of the sediment transport and bed form changes takes place during the floods (Ten Brinke et al. 1999). Low angle dunes are common in big rivers such as Jamuna river in Bangladesh (Kostaschuk et al., 2004) therefore modeling and laboratory studies on low angle dunes are required. Venditti et al. (2005) concluded that movement of the entire bed form is controlled by superimposed bed forms therefore morphodynamics of super imposed bed forms over migrating dunes needs to be studied theoretically and experimentally. Yue et al. (2005) opined that more realistic simulations of the interaction of the free surface with the bed is needed to understand the coherent structures and sediment transport. Kostaschuk et al. (2008) suggested to carry out further research with respect to amount of suspended sediment on formation and as well as migration of dunes. The future research may also include simulation of 2-D and 3-D flow over dunes using DES (detached eddy simulation) which is computationally more efficient (Xu et al., 2007) than LES modeling.

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**3**

*1Iran 2Australia*

**Stochastic Nature of Flow Turbulence and**

The formation of bed topography is the result of a complicated interaction between flow and sediment particles along the bed. Bed form and the geometry of ripples are also a function of bed roughness, median diameter of sediment particles and flow characteristics for example shear stress, separation and Froude number (Mogridge et al. 1994). Ripple geometry and its interaction with flow structure has been studied by many investigators; for example, Bagnold (1946), Carstens et al. (1969), Mogridge et al. (1994), Yalin (1977), Khelifa and Ouellet (2000), Miller and Komar (1980), and Nielsen (1992). In these studies, the geometry of bed ripples was found to be a function of turbulent shear stress parameters. Raudkivi (1997) pointed out that the ripples and vortices within the shear layer are affected by the flow depth, velocity distribution and shear stress on the bed. Despite more than three decades of investigation, there is still insufficient information to characterize ripple-flow

One area where this lack of information exists is the application of image processing for particle entrainment and analyze of the turbulence characteristics and flow over ripples. To study the flow structure over the ripples, Sajjadi et al. (1996) found that the vortices that form in the lee of ripples are important for the entrainment of sediment particles. Keshavarzi and Ball (1999) used image processing technique to record entrained and deposited particles over flat bed and found that there is an intermittent nature for particles entrainment and deposition over the bed. Jeremy et al. (2005) used high resolution super-VHS video system to monitor the development of the sand bed over a flat bed and observed that initiation occurs at relatively low flow strengths, where sediment transport is patchy and sporadic. Lajeunesse et al. (2010) used high speed video imaging system to record the trajectories of the moving particles over flat bed and observed that entrained particles exhibit intermittent motion composed of the succession of periods of flight and rest. Bennett and Best (1996) conducted a series of experiment over fixed bed ripples and compared the

interaction in adequate detail and over a range of turbulent flow conditions.

**1. Introduction**

**Sediment Particle Entrainment over the**

**Ripples at the Bed of Open Channel Using Image Processing Technique**

> Alireza Keshavarzi1,2 and James Ball2 *1Water Department, Shiraz University, Shiraz 2School of Civil and Environmental Engineering, University of Technology Sydney, NSW, 2007,*

## **Stochastic Nature of Flow Turbulence and Sediment Particle Entrainment over the Ripples at the Bed of Open Channel Using Image Processing Technique**

Alireza Keshavarzi1,2 and James Ball2

*1Water Department, Shiraz University, Shiraz 2School of Civil and Environmental Engineering, University of Technology Sydney, NSW, 2007, 1Iran 2Australia*

### **1. Introduction**

68 Sediment Transport – Flow Processes and Morphology

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separated flow around a circular cylinder[J], *Journal of Hydrodynamics, Ser. B* 19 (5),

The formation of bed topography is the result of a complicated interaction between flow and sediment particles along the bed. Bed form and the geometry of ripples are also a function of bed roughness, median diameter of sediment particles and flow characteristics for example shear stress, separation and Froude number (Mogridge et al. 1994). Ripple geometry and its interaction with flow structure has been studied by many investigators; for example, Bagnold (1946), Carstens et al. (1969), Mogridge et al. (1994), Yalin (1977), Khelifa and Ouellet (2000), Miller and Komar (1980), and Nielsen (1992). In these studies, the geometry of bed ripples was found to be a function of turbulent shear stress parameters. Raudkivi (1997) pointed out that the ripples and vortices within the shear layer are affected by the flow depth, velocity distribution and shear stress on the bed. Despite more than three decades of investigation, there is still insufficient information to characterize ripple-flow interaction in adequate detail and over a range of turbulent flow conditions.

One area where this lack of information exists is the application of image processing for particle entrainment and analyze of the turbulence characteristics and flow over ripples. To study the flow structure over the ripples, Sajjadi et al. (1996) found that the vortices that form in the lee of ripples are important for the entrainment of sediment particles. Keshavarzi and Ball (1999) used image processing technique to record entrained and deposited particles over flat bed and found that there is an intermittent nature for particles entrainment and deposition over the bed. Jeremy et al. (2005) used high resolution super-VHS video system to monitor the development of the sand bed over a flat bed and observed that initiation occurs at relatively low flow strengths, where sediment transport is patchy and sporadic. Lajeunesse et al. (2010) used high speed video imaging system to record the trajectories of the moving particles over flat bed and observed that entrained particles exhibit intermittent motion composed of the succession of periods of flight and rest. Bennett and Best (1996) conducted a series of experiment over fixed bed ripples and compared the

Stochastic Nature of Flow Turbulence and Sediment Particle Entrainment

**3. Quadrant decomposition of velocity fluctuations**

quadrant of the event. As shown in Figure 1, the events are:

and particle entrainment from the bed.

Outward interaction event *u v* ' 0, ' 0

Inward interaction event *u v* ' 0, ' 0 and

Fig. 1. Quadrant analysis of bursting process

they are defined by

Where;

defined as:

Ejection event *u v* ' 0, ' 0 ,

Sweep event *u v* ' 0, ' 0 .

over the Ripples at the Bed of Open Channel Using Image Processing Technique 71

measure three dimensional velocities, CCD camera to record images of particle motion and image processing technique enables to provide an accurate measurement of flow structure

The bursting process consists of four categories of event; these categories are defined by the

The velocity fluctuations and *u v* are defined as variations from the time-averaged (mean) velocities in the longitudinal and vertical directions, ( *u* and *v* ), respectively. Algebraically,

1

*i i u u n* and

The time-averaged instantaneous shear stress (Reynolds shear stress) at each point of flow is

As shown by Jafari Mianaei and Keshavarzi (2008, 2009), the distribution of the

1 *<sup>n</sup>*

instantaneous velocities is influenced significantly by presence of ripples.

*n* being is the number of instantaneous velocity samples.

*u uu* and *v vv* (1)

(2)

*u v* (3)

1

1 *<sup>n</sup> i i v v n*

spatial structure of flow over fixed symmetrical ripples to reveal the contrasts in the dynamics of the flow separation zone over ripples. Kostachuck and Church (1993), Julien and Klassen (1995), Kostaschuk and Villard (1996), Carling et al. (2000) and Kostachuck (2000) have conducted field studies and concluded that the shear related coherent structures were very important in bed form development and bed stability. Consideration of the results from these studies indicates that the turbulence characteristics have a direct influence on sediment entrainment and the ripple geometry.

### **2. Coherent structure of flow over the bed**

Analysis of the turbulence characteristics is based on the concept of the bursting phenomenon which was initially introduced by Kline et al. (1967) as a means of describing the transfer of momentum between the turbulent and laminar regions near a boundary. They defined bursting process as; Sweep event ( *u v* ' 0, ' 0 ); Ejection event ( ' 0, ' 0 *u v* ); Outward interaction event ( ' 0, ' 0 *u v* ); and Inward interaction event ( ' 0, ' 0 *u v* ) (Figure 1). The four bursting events have been identified having different effects on the mode and rate of sediment transport (Bridge and Bennett 1992). Particle entrainment from the bed is closely correlated to the sweep event (Thorne et al. 1989; Nelson et al. 1995; Drake et al. 1988; Nakagwa and Nezu 1978; Grass 1971 and Keshavarzi and Ball 1997, 1999). Also the contribution of sweep and ejection events has been found to be more important than outward and inward interactions. Furthermore, sweep and ejection events occur more frequently than outward and inward interactions (Nakagwa and Nezu 1978; Thorne et al. 1989; Keshavarzi and Ball 1997). In addition to the above characteristics, the average magnitude of the shear stress during sweep event being much higher than the time averaged shear stress (Keshavarzi and Ball 1997). A number of studies, for example, Offen and Kline (1975) and Papanicolaou et al. (2002) investigated the characteristics of the bursting process and its effect on particle motion. Consideration of this research led Yen (2002) to point out the necessity to incorporate the bursting process into the modelling of turbulent flow and sediment transport. Jafari Mianaei and Keshavarzi (2008, 2009) found that at the stoss side of ripples, ejection and sweep events and at the lee side of the ripple outward interaction and inward interaction events were dominant. The studies by Ojha and Mazumder (2008) showed that the ratio of shear stress for sweep and ejection events along the dunes varied in an oscillatory pattern at the near bed region, whereas such patterns disappear towards the outer flow. Also they found that along the dune length, sweep events contribute to shear stress generation more than other events. Termini and Sammartano (2009) investigated the effects of the variation of bed roughness conditions on the vertical distributions frequency of the occurrence of ejection and sweep events and concluded that the occurrence of sweep events increases as the bed roughness increases.