A numerical study of the time-dependent viscous flow between two rotating spheres

Abstract

An extension of numerical methods described in previous papers is used to analyse the time-dependent rotationally-symmetric motion of an incompressible viscous fluid contained between two concentric spheres having a common axis of rotation. The motion is governed by a pair of coupled non-linear partial differential equations in three independent variables, with singular end conditions. The computational process is described, and numerical solutions are presented for cases in which one (or both) of the spheres is given an impulsive change in angular velocity-starting from a state of either rest or uniform rotation. Reynolds numbers lie in the range 10-1500.