%0 Journal Article
%T Equilibrium Energy and Entropy of Vortex Filaments in the Context of Tornadogenesis and Tornadic Flows
%A Pavel B¨§l¨ªk
%A Douglas P. Dokken
%A Mikhail M. Shvartsman
%A Eric Bibelnieks
%A Robert Laskowski
%A Alek Lukanen
%J Open Journal of Fluid Dynamics
%P 144-176
%@ 2165-3860
%D 2023
%I Scientific Research Publishing
%R 10.4236/ojfd.2023.133012
%X In this work, we study approximations of supercritical or suction vortices in tornadic flows and their contribution to tornadogenesis and tornado maintenance using self-avoiding walks on a cubic lattice. We extend the previous work on turbulence by A. Chorin and collaborators to approximate the statistical equilibrium quantities of vortex filaments on a cubic lattice when both an energy and a statistical temperature are involved. Our results confirm that supercritical (smooth, ¡°straight¡±) vortices have the highest average energy and correspond to negative temperatures in this model. The lowest-energy configurations are folded up and ¡°balled up¡± to a great extent. The results support A. Chorin¡¯s findings that, in the context of supercritical vortices in a tornadic flow, when such high-energy vortices stretch, they need to fold and transfer energy to the surrounding flow, contributing to tornado maintenance or leading to its genesis. The computations are performed using a Markov Chain Monte Carlo approach with a simple sampling algorithm using local transformations that allow the results to be reliable over a wide range of statistical temperatures, unlike the originally used pivot algorithm that only performs well near infinite temperatures. Efficient ways to compute entropy are discussed and show that a system with supercritical vortices will increase entropy by having these vortices fold and transfer their energy to the surrounding flow.
%K Tornadogenesis
%K Supercritical Vortices
%K Vortex Filaments
%K Negative Temperature
%K Kinetic Energy
%K Entropy
%K Statistical Mechanics
%K Equilibrium Statistics
%K Self-Avoiding Walks
%K Cubic Lattice
%K Monte-Carlo Techniques
%K Pivot  Algorithm
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=125828