A coalescence model for freely decaying two-dimensional turbulence

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 $t^{-ξ}$. A mean-field analytical argument yielding the approximation $ξ=4/5$ is shown to slightly overestimate the decay exponent $ξ$ whereas Molecular Dynamics simulations give $ξ=0.71\pm 0.01$, in agreement with recent laboratory experiments and simulations of Navier-Stokes equation.