Axial and transverse Stokes flow past slender axisymmetric bodies

Abstract

This paper deals with Stokes flow due to a stationary axially symmetric slender body in a uniform stream, which may be either parallel or perpendicular to the axis of the body. The effect of the body is represented by distributions of singularities along a segment of its axis of symmetry. Systems of linear integral equations for these distributions are obtained, and the first few terms of uniformly valid (in the Stokes region) asymptotic expansions in the slenderness ratio are discussed. The leading terms yield the expected result that the drag on the body in a transverse stream is double that in an axial stream. The second approximation to the ratio of these two drags is also independent of the body shape.