On the uniqueness of steady flow past a rotating cylinder with suction

The subject of this study is a steady two-dimensional incompressible flow p ast a rapidly rotating cylinder with suction. The rotation velocity is assu med to be large enough compared with the cross-how velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysi s of incompressible Navier-Stokes equations is performed. Prandtl's classic al approach of subdividing the flow field into two regions, the outer invis cid region and the boundary layer, was used earlier by Glauert (1957) for a nalysis of a similar flow without suction. Glauert found that the periodici ty of the boundary layer allows the velocity circulation around the cylinde r to be found uniquely. In the present study it is shown that the periodici ty condition does not give a unique solution for suction velocity much grea ter than 1/Re. It is found that these non-unique solutions correspond to di fferent exponentially small upstream vorticity levels, which cannot be dist inguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/root Re. In the last case an explicit a nalysis of the distribution of exponentially small vorticity outside the bo undary layer was carried out.