On the separation of a slow linear shear flow from a cylindrical ridge or trough in a plane

Abstract

A slow linear shear flow past a plane with a cylindrical ridge or trough is considered. It is shown that an infinite set of vortices exist in a finite region in the neighbourhood of the line of intersection between a cylindrical ridge and a plane if the angle of intersection is less than about 146.3°, the extent of the eddy region increasing as the angle of intersection decreases. For ridges with larger angles of intersection, separation of the flow from the boundary does not occur. However, with a depression or trough in the plane, separation of the flow from the wall of the trough occurs if the angle of intersection between the trough and the plane is more than about 65.15°. For angles greater than this value, there is a closed addy region consisting of one vortex. In the limit when the trough becomes a half-space, the flow is anti-symmetrical about the plane of the boundary.