The base-flow and near-wake problem at very low Reynolds numbers - Part 1. The Stokes approximation

Abstract

The general solutions of the Stokes approximate equations of motion are derived for two-dimensional and axisymmetric flows in the half-space x > 0, for an arbitrarily given velocity field in the plane x = 0. There is assumed to be no solid surface in the half-space. According to whether the velocity at infinity is zero or not, the solutions can be said to describe either jet-type or wake-type flows. Only the latter category is considered; numerical examples are worked out and properties of the base flow at very low Reynolds numbers are investigated. A recirculating flow region may exist, but the flow properties are not sensitive to this feature.