Abstract
The scattering of a plane compressional wave by an incompressible viscous fluid sphere is studied. After assuming low Reynolds number, the Stokes approximation is used for the description of the fluid. A singular perturbation technique has been adopted, under the assumption of Rayleigh scattering, i.e., long wavelength compared with the radius a of the sphere. Appropriate asymptotic expansions are constructed in the solid region. The matching of the expansions leads to a knowledge of the near and the far field in the solid region, and the motion inside of the fluid sphere. The scattering cross section is shown to obey the familiar Rayleigh’s fourth-power law. It is found that the scattering cross section is independent of the fluid density, but is affected by variations in the viscosity of the fluid.
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