A coalescence model for freely decaying two-dimensional turbulence

TL;DR

This paper introduces a ballistic coalescence model to simulate vortex fusion in 2D turbulence, revealing a decay exponent consistent with experimental and numerical data, and providing analytical insights into vortex density decay.

Contribution

The paper presents a novel coalescence model for 2D turbulence that accurately predicts vortex decay behavior and aligns with experimental and simulation results.

Findings

Vortex density decays as t^{-0.71} in simulations.

Analytical approximation predicts a decay exponent near 0.8.

Model aligns with laboratory experiments and Navier-Stokes simulations.

Abstract

We propose a ballistic coalescence model (punctuated-Hamiltonian approach) mimicking the fusion of vortices in freely decaying two-dimensional turbulence. A temporal scaling behaviour is reached where the vortex density evolves like $t^{-\xi}$. A mean-field analytical argument yielding the approximation $\xi=4/5$ is shown to slightly overestimate the decay exponent $\xi$ whereas Molecular Dynamics simulations give $\xi =0.71\pm 0.01$, in agreement with recent laboratory experiments and simulations of Navier-Stokes equation.