law, whether this occurs uniformly around the tornado or inhomogeneously as in the case of the Mulhall tornado. Additional comments about inhomogeneous properties of such flows will be provided in section \[sec:energy\_spectrum\].

Power laws in vorticity and pseudovorticity {#sec:pseudovorticity}
===========================================

The evidence of power laws for tangential velocity discussed in the previous section suggests that similar power laws should also exist for vertical vorticity. Several tornadic and nontornadic mesocyclones have been studied in [@cai05] from the point of view of vertical vorticity and pseudovorticity, and power laws have been discovered to hold over several magnitudes of the length scale.

Specifically, in [@cai05] the vertical vorticity was obtained from dual-Doppler radar data. The velocity data were interpolated in a standard way [@wakimotoliucai98; @wakimotocai00; @dowell02a; @dowell02b] to grids with horizontal spacing ranging from $\varepsilon=300$ m to $\varepsilon=9600$ m and maximum vertical vorticities, $\zeta_{\text{max}}$, were computed. A strong linear correlation with a linear correlation coefficient close to $1$ was found between $\log{\zeta_{\text{max}}}$ and $\log{\varepsilon}$ and the best fit lines were termed [*vorticity lines*]{}. If we denote the (negative) slopes of the vorticity lines by $-\beta$, then this means that $$\label{eq:zeta_power_law}
  \zeta_{\text{max}}
  \propto
  \varepsilon^{-\beta},$$ and this, in turn, is implied by a power law 