Relaxation in two dimensions and the ‘‘sinh-Poisson’’ equation

Abstract

Long-time states of a turbulent, decaying, two-dimensional, Navier–Stokes flow are shown numerically to relax toward maximum-entropy configurations, as defined by the ‘‘sinh-Poisson’’ equation. The large-scale Reynolds number is about 14 000, the spatial resolution is (512)2, the boundary conditions are spatially periodic, and the evolution takes place over nearly 400 large-scale eddy-turnover times.