Toward an asymptotic description of Prandtl–Batchelor flows with corners

The Prandtl–Batchelor theorem states that the vorticity in a steady laminar high Reynolds ( Re) number flow containing closed streamlines should be constant; however, apart from simple case of circular streamlines, very little is known about how to determine this constant ω 0 ). This paper revisits earlier work for driven by surrounding smooth moving boundary, with view extending it where enclosing boundary has corners; purpose, benchmark example literature inside semi-circle considered. However, subsequent asymptotic analysis [Formula: see text] and numerical experimentation lead an inconsistency: approach predicts boundary-layer separation, whereas linearized theory computations full Navier–Stokes equations do not. Nevertheless, considering slightly modified problem instead, which does not suffer inconsistency, found that, when extrapolating results such high- Re infinite Re, agreement around 5%, roughly line previous comparisons type. Possible future improvements method are also discussed.