Steady separated flow in a linearly decelerated free stream

Numerical methods are used to investigate the separated flow over a finite flat plate when the flow at large distances is given by the stream function $a = xy and the plate is situated on the x axis from 1 to 1. The range of nominal Reynolds number is 10-800. Reduced-mesh calculations are used for fine resolution of the flow field in the immediate vicinity of the separation point. Streamlines, equivorticity lines, and shear stress and pressure gradient at the plate surface illustrate the overall structure of the flow. In each case the streamwise pressure gradient is less than that for undisturbed potential flow and the position of separation is consequently downstream of that predicted by classical boundarylayer theory. The boundary-layer structure in the vicinity of the separation point shows a direct transition between the regular upstream behaviour and Dean’s (1950) solution right at separation with no sign whatever of intermediate singular behaviour of the type predicted by Goldstein (1948). The implications of these results for the structure of high Reynolds number, steady, laminar flow are discussed.