The time-dependent Stokes paradox

Abstract

When a uniform stream starts to flow impulsively at time t = 0 t = 0 past a two-dimensional body, the solution of the Stokes equation indicates that the velocity grows without bound as t → ∞ t \to \infty . It is seen that this is a natural extension of the Stokes paradox to unsteady flows. Two resolutions of this result are presented: firstly, through an analysis of the Oseen equation on the basis of singular perturbation theory and, secondly, through considering the two-dimensional body as the limit of a three-dimensional body when the length increases without bound.