Low-Reynolds-number flow past an elliptic cylinder

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Abstract
The primary objective of this paper is to obtain the detailed description of the flow field near an elliptic cylinder that is placed perpendicularly in a uniform stream at low Reynolds number. Attention is paid to the shape effects due to the flattening of the cylinder and to the inertial effects of the fluid. The analysis resorts to the method of matched asymptotic expansions. The main part of the inner expansion describes the near flow field as a Stokes flow, which is characterized by the singularities arranged at the two foci of the ellipse. The first three terms = Reynolds number) in the inner expansion are developed, and the flow aspects under the influence of the fluid inertia are investigated. The streamline patterns with one or two vortices round a finite flat plate of zero thickness, which is a special case of the elliptic cylinder, are presented.