Low Reynolds number oscillatory flow through a hole in a wall

Abstract

For a viscous incompressible fluid the low Reynolds number description of the flow generated by a three-dimensional point source of oscillating strength situated on a wall is approximately quasi-steady in the neighbourhood of the singularity. This quasi-steady solution contains a number of unacceptable features, the principal one being that it is not a uniformly valid approximation within a small region surrounding the source point. In addition to this the vorticity in this region is predicted to be zero everywhere on the wall except at the singular point where it is infinite, which does not seem to be a physically reasonable distribution. When account is taken of the finite radius of the hole through which the fluid is driven and the finite width of the wall, the above difficulties are resolved yielding results that are quite realistic and informative.