NAVIER-STOKES RELAXATION TO SINH POISSON STATES AT FINITE REYNOLDS-NUMBERS

A mathematical framework is proposed in which it seems possible to jus tify the computationally-observed relaxation of a two-dimensional Navi er-Stokes fluid to a ''most probable,'' or maximum entropy, state. The relaxation occurs at large but finite Reynolds numbers, and involves substantial decay of higher-order ideal invariants such as enstrophy. A two-fluid formulation, involving interpenetrating positive and negat ive vorticity fluxes (continuous and square integrable) is developed, and is shown to be intimately related to the passive scalar decay prob lem. Increasing interpenetration of the two fluids corresponds to the decay of vorticity flux due to viscosity. It is demonstrated numerical ly that, in two dimensions, passive scalars decay rapidly, relative to mean-square vorticity (enstrophy). This observation provides a basis for assigning initial data to the two-fluid field variables.