cross sections (geometric self-similarity).

The remainder of this paper is organized as follows. In Section \[sec:wurman\] we discuss both observed and studied power laws in the tangential velocity of tornadoes as a function of the radial distance from the axis of the vortex. In Section \[sec:pseudovorticity\] we briefly review the work in [@cai05] and discuss power laws in the vertical vorticity and pseudovorticity as a function of scale for some tornadic and nontornadic mesocyclone data obtained from Doppler and dual Doppler data. In Section \[sec:cm1\] we discuss the results of a supercell thunderstorm simulation using the Bryan Cloud Model 1 and observe an agreement between the work in [@cai05] and a resulting power law for vorticity over multiple scales. In Section \[sec:energy\_spectrum\] we use the vortex gas model developed in our related paper [@vortexgas17], and use a modified argument due to Chorin to show that an increase in fractal dimension of the cross section of a negative temperature vortex corresponds to an increase in energy at large scales. Finally, Section \[sec:conclusions\] offers conclusions and describes future work.

Power laws in the tangential velocity of tornadoes {#sec:wurman}
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While it has been known since at least the 1950s that in tropical 