ASYMPTOTIC STATES OF DECAYING TURBULENCE IN 2-DIMENSIONAL INCOMPRESSIBLE FLOWS

We investigate the relaxation of a strongly turbulent fluid to metasta ble states, in times much shorter than the dissipation time scale. Sev eral simulations of decaying two-dimensional Navier-Stokes flows were performed, which show the relaxation to organized states dominated by coherent vortex structures of length scales comparable to the size of the system. Ln the case of periodic boundary conditions, the organized state is characterized by a strong correlation between vorticity and stream function, the second of which satisfies a sinh-Poisson equation quite accurately. However, in the case of free-slip boundary conditio ns the relaxed state does not display any significant correlation betw een its vorticity and its stream function. Notwithstanding, in both ca ses the role of nonlinearities is found to be essential even at these late stages of the evolution. However, we show that even severe trunca tions of a few (short wave number) nonlinearly coupled Fourier modes p rovide an accurate description of the long-term dynamics of the fluid. Therefore the dynamics of the flow in these metastable states is some where in between a strong turbulent regime and a (mostly linear) dissi pative relaxation stage.