TABLE OF CONTENTS Because the velocity of a viscous fluid over a stationary solid boundary is required to vanish, the Reynolds number of the flow in the vicinity of the boundary is necessarily small, and the structure of the local flow is governed by the equations of Stokes flow. The role of the outer flow is to determine the asymptotic behavior of the flow far from the boundary.
There are other circumstances where the flow is due to the motion of a boundary, but the Reynolds number of the flow in a certain neighborhood of the boundary is small. In these cases, the structure of the Stokes flow in the vicinity of the boundary is determined by the local geometry of the boundary and nature of the required boundary conditions.
In the present section, we examine the structure of a family of two-dimensional flows in wedge-shaped domains that are bounded by intersecting stationary, translating, or rotating walls, as depicted in Figures 6.2.1 6.2.5 and 6.2.7. To bypass the computation of the pressure, and thus reduce the number of unknowns, we describe the flow in terms of the stream function ?. Noting that the boundary conditions are to be applied at intersecting planes, we introduce plane polar coordinates with the origin at the vertex, and separate the radial from the angular dependence writing
Furthermore, we stipulate the power-law functional dependence
where A and ? are two complex constants; the magnitude of the former is a measure of...
