Scaling of high Reynolds number weakly separated channel flows

It is shown analytically and verified numerically that weakly separated laminar two-dimensional incompressible channel flows can display a self-similar solution. The numerical method used is the split NOS method, one of a class of semidirect methods which are very efficient for steady-state and slowly-time-varying solutions. Fine-mesh solutions and Richardson extrapolation are used to achieve truncation error convergence. It is found that, if the channel length is increased proportional to the Reynolds number, the solutions become self-similar in the scaled longitudinal variable. This scaling behavior has implications for the interpretation of accuracy limits on high Reynolds number Navier-Stokes calculations.