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Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle
Darren G Crowdy1, Samuel J Brzezicki1
1Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK.
Abstract:
An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.
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