Statistical-mechanical predictions and Navier-Stokes dynamics of two-dimensional flows on a bounded domain

In this paper the applicability of a statistical-mechanical theory to freel y decaying two-dimensional (2D) turbulence on a bounded domain is investiga ted. We consider an ensemble of direct numerical simulations in a square bo x with stress-free boundaries, with a Reynolds number that is of the same o rder as in experiments on 2D decaying Navier-Stokes turbulence. The results of these simulations are compared with the corresponding statistical equil ibria, calculated from different stages of the evolution. It is shown that the statistical equilibria calculated from early times of the Navier-Stokes evolution do not correspond to the dynamical quasistationary states. At be st, the global topological structure is correctly predicted from a relative ly late time in the Navier-Stokes evolution, when the quasistationary state has almost been reached. This failure of the (basically inviscid) statisti cal-mechanical theory is related to viscous dissipation and net leakage of vorticity in the Navier-Stokes dynamics at moderate values of the Reynolds number. [S1063-651X(99)00508-5].