FINITE-AMPLITUDE STEADY-STATES OF HIGH REYNOLDS-NUMBER 2-D CHANNEL FLOW

Two-dimensional steady states of plane Poiseuille flow are found by fo llowing the evolution of a two-dimensional Navier-Stokes fluid numeric ally for long times. Two runs are presented, one for Reynolds number R = 4000, the other for R = 15000. The Reynolds number is based on the pressure gradient and channel half-width. The final states are charact erized by an array of alternating-sign vortices. The states are accura tely time independent in a frame moving with the vortices. In this fra me of reference the stream function and the vorticity display an inter esting correlation, showing that the flow is divided into three spatia lly distinct regions. Theoretical understanding of the state is sought in terms of the statistical mechanics of large numbers of discrete li ne vortices in the mean field limit, but without great success. Attent ion is devoted to characterizing the relaxed state.