Uniform Asymptotic Solutions for the Potential Field Around a Thin Oblate Body of Revolutions

Abstract

The potential field about an arbitrary oblate body of revolution which satisfies either a Dirichlet or Neumann boundary condition on the body is studied. The first three terms of the uniform asymptotic expansion of the potential field (with respect to the thinness ratio a of the body) are obtained. The potential due to the presence of the body is represented as a superposition of potentials of point singularities distributed along a disk inside the body. The singularity distributions satisfy a sequence of integral equations; the first terms in asymptotic solutions of these equations are obtained. Our method is an extension of the method given by Handelsman and Kelley [J. Fluid Mech. 28 (1967), pp.131–142], [SIAM J. Appl. Math., 15 (1967), pp. 824–841] for solving potential problems for slender bodies of revolution to the case of the oblate bodies of revolution.