Brands H, Maassen S R, Clercx H J
KNMI (Netherlands Meteorological Institute), P.O. Box 201, 3730 AE De Bilt, The Netherlands.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Sep;60(3):2864-74. doi: 10.1103/physreve.60.2864.
In this paper the applicability of a statistical-mechanical theory to freely decaying two-dimensional (2D) turbulence on a bounded domain is investigated. We consider an ensemble of direct numerical simulations in a square box with stress-free boundaries, with a Reynolds number that is of the same order as in experiments on 2D decaying Navier-Stokes turbulence. The results of these simulations are compared with the corresponding statistical equilibria, 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 best, the global topological structure is correctly predicted from a relatively late time in the Navier-Stokes evolution, when the quasistationary state has almost been reached. This failure of the (basically inviscid) statistical-mechanical theory is related to viscous dissipation and net leakage of vorticity in the Navier-Stokes dynamics at moderate values of the Reynolds number.
