  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, the difference being the appearance of complex instead of real valued
wave numbers. The solution reverts to well-known classical solutions in special
limits: the potential flow solution in the thin boundary layer limit, the
oscillatory flat plate solution in the limit of large sphere radius and the
Stokes flow solutions in the incompressible limit of infinite sound speed. As a
companion analytical result, the steady second order acoustic streaming flow is
obtained. This streaming flow is driven by the Reynolds stress tensor that
arises from the axisymmetric first order primary flow around such a rigid
sphere. These results are obtained with a linearization of the non-linear
Navier-Stokes equations valid for small amplitude oscillations of the sphere.
The streaming flow obeys a time-averaged Stokes equation with a body force
given by the Nyborg model in which the above mentioned primary flow in a
compressible Newtonian fluid is used to estimate the time-averaged body force.
Numerical results are presented to explore different regimes of the complex
transverse and longitudinal wave numbers that characterize the primary flow.
