Matched-asymptotic analysis of low-Reynolds-number flow past two equal circular cylinders

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Abstract
Jeffery's solution in bi-polar co-ordinates of the two-dimensional Stokes equations cannot be applied to the low-Reynolds-number flow past two parallel circular cylinders because of severe mathematical difficulties. These difficulties can be overcome by considering the flow field far from the cylinders and then modifying the solution near the cylinders so that it becomes the inner expansion for an application of the method of matched asymptotic expansions. After the calculation of the drag, lift and moment coefficients of two adjacent equal circular cylinders to O(1) in the Reynolds number R, the analysis is extended to incorporate partially the effects of fluid inertia of order R. The results show fairly good agreement with Taneda's experimental data.