The subject of this study is a steady two-dimensional incompressible flow past a
rapidly rotating cylinder with suction. The rotation velocity is assumed to be large
enough compared with the cross-flow velocity at infinity to ensure that there is no
separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes
equations is performed. Prandtl's classical approach of subdividing the flow
field into two regions, the outer inviscid region and the boundary layer, was used
earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found
that the periodicity of the boundary layer allows the velocity circulation around the
cylinder to be found uniquely. In the present study it is shown that the periodicity
condition does not give a unique solution for suction velocity much greater than 1/Re.
It is found that these non-unique solutions correspond to different exponentially small
upstream vorticity levels, which cannot be distinguished 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/√Re. In the last
case an explicit analysis of the distribution of exponentially small vorticity outside
the boundary layer was carried out.