Boundary-layer flow at a saddle point of attachment

Abstract

This paper is a study of the flow of a viscous incompressible fluid in the immediate neighbourhood of a saddle point of attachment, near which the external flow is irrotational with components { ax, by, −(a + b)z }, where a > 0 > b. It is shown that the flow is of a boundary-layer character, and that part of the boundary-layer flow is reversed when b / a < − 0·4294. On the assumption that such flows are physically plausible, the problem may be solved for all values of b / a [ges ] −1. Even in the limiting case b / a = −1, an effect of the boundary layer is everywhere to draw fluid towards the wall, so that vorticity is still convected towards the wall. Numerical solutions have been computed, and some of the results are presented in the tables and diagrams.