Scott A. Wymer
Renata S. Engel
Dept. Eng. Sci. and Mech., The Pennsylvania State Univ., 227 Hammond Bldg., University Park, PA 16802-1401
In solving for velocity and pressure fields in a slow, viscous, incompressible fluid, frequency-domain scattering techniques can be brought into action by taking the Fourier transform of the equations describing Stokesian flows. This is exemplified by considering the scattering of a transverse plane wave by an impenetrable axisymmetric body immersed in a fluid modeled by the unsteady Stoke's equation, the wave number in the ambient Stoke's fluid being necessarily complex. The pressure and velocity phasors satisfy the Laplace and the Helmholtz equations, respectively, and are written as sums of incident and scattered components. These components are then expanded in terms of spherical harmonic functions. The point-matching technique is used to satisfy boundary conditions on a discrete set of points on the surface of the scattering body. Convergence of the resulting series solutions is studied for spheroids of different aspect ratios and for varying wave numbers.