TY - JOUR

T1 - Statistical-mechanical predictions and Navier-Stokes dynamics of two-dimensional flows in a bounded domain.

AU - Brands, H.

AU - Maassen, S.R.

AU - Clercx, H.J.H.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

U2 - 10.1103/PhysRevE.60.2864

DO - 10.1103/PhysRevE.60.2864

M3 - Article

SN - 1063-651X

VL - 60

SP - 2864

EP - 2874

JO - Physical Review E: Statistical, Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E: Statistical, Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 3

ER -