Stokes flow past a slender body of revolution

Abstract

The complete uniform asymptotic expansion of the velocity and pressure fields for Stokes flow past a slender body of revolution is obtained with respect to the slenderness ratio ε of the body. A completely general incident Stokes flow is assumed and hence these results extend the special cases treated by Tillett (1970) and Cox (1970). The part of the flow due to the presence of the body is represented as a superposition of the flows produced by three types of singularity distributed with unknown densities along a portion of the axis of the body and lying entirely inside the body. The no-slip boundary condition on the body then leads to a system of three coupled, linear, integral equations for the densities of the singularities. The complete expansion for these densities is then found as a series in powers of ε and ε log ε. It is found that the extent of these distributions of singularities inside the body is the same for all the singular flows and depends only upon the geometry of the body. The total force, drag and torque experienced by the body are computed.