TABLE OF CONTENTS Exact singularity representations are known only for a limited class of flows that are bounded by spherical and spheroidal surfaces. Certain examples were presented in Section 6.6, and further representations are collected and discussed by Chwang and Wu (1974, 1975) and Kim and Karrila (1991). To derive approximate representations for more general flows and arbitrary boundary shapes, we resort to asymptotic and numerical methods. The general strategy is to express the flow in terms of discrete or continuous singularity distributions, and then compute the coefficients of the singularities or densities of the distributions, and possibly their location, so as to satisfy the required boundary conditions in some approximate sense.
Burgers (1938, p. 120) represented the disturbance flow due to a sphere that is held stationary in an incident uniform flow in terms of a point force situated at the center. Computing the strength of the point force by requiring that the mean velocity over the surface of the sphere vanish, he observed that the approximate solution reproduces Stokes's law in its exact form. This perfect agreement is explained by noting that the disturbance flow may be represented exactly in terms of a Stokeslet and a potential dipole, and the average velocity of the dipole over the surface of a sphere is equal to zero. Burgers performed a similar computation for the disturbance flow due to a sphere that is held still in a paraboloidal flow and found that the drag force is also in perfect agreement...
