Asymptotic analysis of Low Reynolds number flow with a linear shear past a circular cylinder
Abstract
Two-dimensional steady flow of an incompressible viscous fluid around a circular cylinder in the case where the velocity field at large distances is the combination of a simple shear and a uniform stream is described in terms of matched asymptotic expansions valid at a low Reynolds number. The main purpose of the present paper is (1) to examine the validity of the assumptions used by Bretherton (1961) and (2) to construct an alternative approach without using such assumptions. In the present paper is constructed a system of governing integral equations for vorticity and stream function based on an Oseen-type equation. Local solutions, inner and outer solutions, are obtained from these equations by using the method proposed by Kida (1991), which is so systematic that we do not need the detailed physical consideration. Finally aerodynamic forces are compared with those obtained by Bretherton. The present paper shows that Bretherton's assumptions are correct within the first approximation. One cycle higher order solutions are obtained in this paper.