TITLE:
Equilibrium Energy and Entropy of Vortex Filaments in the Context of Tornadogenesis and Tornadic Flows
AUTHORS:
Pavel Bělík, Douglas P. Dokken, Mikhail M. Shvartsman, Eric Bibelnieks, Robert Laskowski, Alek Lukanen
KEYWORDS:
Tornadogenesis, Supercritical Vortices, Vortex Filaments, Negative Temperature, Kinetic Energy, Entropy, Statistical Mechanics, Equilibrium Statistics, Self-Avoiding Walks, Cubic Lattice, Monte-Carlo Techniques, Pivot Algorithm
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.13 No.3,
June
27,
2023
ABSTRACT: 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.