Backtracking of a sphere slowing down in a viscous compressible fluid

It is shown on the basis of the linearized Navier-Stokes equations that a sphere set in motion by a sudden impulse, and slowing down in a viscous compressible fluid, can temporarily reverse its velocity at a late stage of the motion before finally slowing down with a positive velocity. For the effect to occur, the fluid needs to be sufficiently compressible, and the bulk viscosity needs to be sufficiently small relative to the shear viscosity. More generally, the velocity decays nonmonotonically, without necessarily passing through zero. The results are derived from the frequency-dependent friction coefficient, and hold for general boundary condition on the surface of the sphere.