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Equilibrium Energy and Entropy of Vortex Filaments in the Context of Tornadogenesis and Tornadic Flows

Open Journal of Fluid Dynamics 2023年第3期13卷 144-176页

作者： Pavel Bělík Douglas P. Dokken Mikhail M. Shvartsman Eric Bibelnieks Robert Laskowski Alek Lukanen Department of Mathematics Statistics and Computer Science Augsburg University Minneapolis USA Department of Mathematics University of St. Thomas St. Paul USA

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.

关键词： Tornadogenesis supercritical vortices Vortex Filaments Negative Temperature Kinetic Energy Entropy Statistical Mechanics Equilibrium Statistics Self-Avoiding Walks Cubic Lattice Monte-Carlo Techniques Pivot Algorithm

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