Possible Implications of a Vortex Gas Model and Self-Similarity for   Tornadogenesis and Maintenance
  We describe tornadogenesis and maintenance using the 3-dimensional vortex gas model presented in Chorin (1994) and developed further in Flandoli and Gubinelli (2002). We suggest that high-energy, super-critical vortices in the sense of Benjamin (1962), that have been studied by Fiedler and Rotunno (1986), have negative temperature in the sense of Onsager (1949) play an important role in the model. We speculate that the formation of high-temperature vortices is related to the helicity inherited as they form or tilt into the vertical and their interaction with the surface and boundary layer. We also exploit the notion of self-similarity to justify power laws derived from observations of weak and strong tornadoes presented in Cai (2005); Wurman and Gill (2000); Wurman and Alexander (2005). Analysis of a Bryan Cloud Model (CM1) simulation of a tornadic supercell reveals scaling consistent with the observational studies. 
Douglas P. Dokken, Kurt Scholz, Mikhail M. Shvartsman, Pavel   B\v{e}l\'ik, Corey Potvin, Brittany Dahl and Amy McGovern
math.DS physics.ao-ph physics.flu-dyn