Non-Equilibrium Thermodynamics And Statistical Mechanics of Vortex Gases in Tornado Theory

This work addresses the statistical mechanics of vortex gases and the thermodynamics of the initial formation (genesis) of tornado-like vortices. In particular, it discusses how the thermodynamics of discrete vortices in a quasi-two-dimensional (thin three-dimensional) boundary layer drives the creation of ``hairpins'' and ``cusp'' vortices, their two-dimensional rearrangement, and stretching of vorticity in the vertical direction that originates inside a turbulent boundary layer that leads to a tornado-like flow. Turbulence of that process is analyzed with the help of the vortex filament model and its connection to the fluid flow equations via the Hasimoto and Madelung transforms of the cubic nonlinear Schr\"{o}dinger and Gross--Pitaevskii equations. Finally, a formula for the local non-equilibrium entropy density flux associated with the development of quasi-two-dimensional turbulence in the boundary layer is provided.