Analytical solution for an acoustic boundary layer around an oscillating rigid sphere

Abstract

Analytical solutions in fluid dynamics can be used to elucidate the physics of complex flows and to serve as test cases for numerical models. In this work, we present the analytical solution for the acoustic boundary layer that develops around a rigid sphere executing small amplitude harmonic rectilinear motion in a compressible fluid. The mathematical framework that describes the primary flow is identical to that of wave propagation in linearly elastic solids, with the difference being the appearance of complex instead of real valued wave numbers. The solution reverts to the well-known classical solutions in special limits: the potential flow solution in the thin boundary layer limit, the o..