TIME-DEPENDENT DECAY OF THE MOTION OF A SPHERE TRANSLATING AND ROTATING IN A VISCOUS LIQUID

An exact solution of the Navier-Stokes equations is found for the (axisymmetric) motion (with swirl) representing exponentially time-dependent decay of a solid sphere translating and rotating in a viscous fluid relative to a uniform stream whose speed also decays exponentially with time. A similar solution is also described for the two-dimensional analogue where the sphere is replaced by a circular cylinder of infinite length.