Abstract
Two-dimensional slow viscous flow in a partitioned channel is investigated based on the Stokes approximation. The partitioned channel is composed of two infinite parallel planes and a semi-infinite plate located midway between the infinite planes. The flow is allowed to turn around the semi-infinite plate by a proper pressure gradient. By solving a Wiener–Hopf equation, an exact analytic solution for the stream function is obtained. From the streamline patterns shown, it is found that a Moffatt’s infinite sequence of viscous eddies develops in the channel. The pressure and shear stress distribution on the boundaries are illustrated, and a local analysis for the flow near the edge of the plate is performed. By superposing the symmetric and the anti-symmetric flow, general flows in this partitioned channel are obtained and typical flow patterns are shown.
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