The wake region in the steady low-Reynolds-number flow past a cylinder

Abstract

Evidently the flow field defined in the title contains three rather than two discernable regimes. The first is the vicinity of the cylinder where the flow is viscosity dominated. The second is known as the outer field. There space variations are milder, viscosity is much less effective and the influence of the uniform parallel stream is dominant. In this regime the stream function representing the obstacle's disturbance is governed by the fourth-order Oseen equation. However, evidently its recorded solution fails over the half-plane downstream of the cylinder's axis. It is the author's contention that this failure reflects the existence of a third regime-the wake-where space variations are sharp but only in the transverse direction. To obtain a solution for the entire flow field an additional low-Reynolds-number expansion is constructed. It is matched with the well-known ones prevailing in the inner and outer regimes.