The decay of slow viscous flow

Abstract

A weak force acts within a viscous fluid for a finite time leading to a slow flow with negligible viscous effects; the force then ceases so that the fluid returns steadily to a state of the rest under the action of diffusion. In the model developed, the force is equivalent in time to a delta function mathematically, having the form of a pulse physically; singular solutions such as rotlets and skokeslets are introduced to simplify the calculations and their use can be justified as representing solid bodies. Here we solve the transient Stokes flow equations to fins the behaviour in a number of different situations, the rates of decay are computed, and the nature of the final motion described. A number of general conclusions are deduced from these examples.