Journal of Fluid Mechanics

Boundary-layer development at a two-dimensional rear stagnation point

A. J.  Robins a1 and J. A.  Howarth a1
a1 School of Mathematics, University of Bristol

Article author query
robins aj   [Google Scholar] 
howarth ja   [Google Scholar] 


This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.

(Published Online March 29 2006)
(Received May 25 1972)