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

Two-dimensional steady states of plane Poiseuille flow are found by following the evolution of a two-dimensional Navier-Stokes fluid numerically 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 characterized by an array of alternating-sign vortices. The states are accurately time independent in a frame moving with the vortices. In this frame of reference the stream function and the vorticity display an interesting correlation, showing that the flow is divided into three spatially distinct regions. Theoretical understanding of the state is sought in terms of the statistical mechanics of large numbers of discrete line vortices in the mean field limit, but without great success. Attention is devoted to characterizing the relaxed state.