slope of approximately $-1.6$. The larger (in absolute value) vorticity/velocity power law exponents found in strongly tornadic mesocyclones are consistent with the observation that “parcels that nearly conserve angular momentum penetrate closer to the central axis of the tornadic mesocyclones, resulting in large tangential velocities” [@trapp99].

In both vorticity and pseudovorticity approaches, the calculated regression lines strongly fit the data over scales between that of the mesocyclone core and that of the “edge” of the mesocyclonic tangential flow, indicating that a (pseudo)vorticity vs. scale power law is valid over those scales. The exponent $\beta$ in may be interpreted as a fractal dimension associated with the vortex [@cai05]. The vorticity power law, if valid, may extend to smaller (including tornadic) scales, but this could not be determined given the limited resolution of the radar observations in [@cai05]. As noted in [@cai05] and discussed in the previous section, hurricanes exhibit a similar velocity power law and exponent outside their eyewall [@mallenmontgomerywang2005; @miller67]. Hence roughly the same vorticity power law seems to apply over a range of atmospheric vortex scales.

Vorticity lines computed from a numerical simulation {#sec:cm1}
====================================================

A supercell thunderstorm simulation was investigated to help confirm the conclusions in [@cai05] regarding 