Concerning closed-streamline flows with discontinuous boundary conditions

High-Reynolds-number (Re) flow containing closed streamlines (Prandtl-Batchelor flows), within a region enclosed by a smooth boundary at which the boundary conditions are discontinuous, is considered. In spite of the need for local analysis to account fully for flow at points of discontinuity, asymptotic analysis for Re ≪ 1 indicates that the resulting mathematical problem for determining the uniform vorticity (ω₀) in these situations, requiring the solution of periodic boundary-layer equations, is in essence the same as that for a flow with continuous boundary data. Extensions are proposed to earlier work [3] to enable ω₀ to be computed numerically; these require coordinate transformations for the boundary-layer variables at singularities, as well as a two-zone numerical integration scheme. The ideas are demonstrated numerically for the classical circular sleeve.