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 $t^{-\xi }$. 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.

6 pages, 1 figure, to appear in Europhysics Letters

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