Boundary-layer relaxation after a separated region

Abstract

With reference particularly to the work of Peter Bradshaw and his associates, some remarks are made about the recovery of previously distorted shear flows. It is emphasized that such recovery is usually extremely slow, and this is further illustrated by new measurements of the velocity field and turbulence structure in the relaxing flow downstream of a separated region. Data have been obtained for downstream distances ( x) up to about 20 times the length of the separated region ( x r), or about 75 times the flow thickness at reattachment. This is a significantly more extensive region than has been previously studied, and the data are more comprehensive than any previously available. It is shown that the recovery is even slower than previously surmized. Furthermore, the measurements demonstrate that the turbulence stresses eventually fall below standard boundary-layer values (at the same Reynolds number), although around reattachment they are very much higher, having values more akin to those in plane mixing layers. This undershoot is apparently a new finding and is argued to be a result of the influence of the outer part of the flow on the growing inner region. The usual log-law only begins to appear beyond x/ x r = 2.5. It effectively “sees” a turbulent outer region that recovers even more slowly than itself, and the response of the inner region therefore has similarities to the response of an ordinary boundary layer to free-stream turbulence. It is concluded that even current second-order (i.e., Reynolds stress) models may not capture the exquisitely slow decay of the strong, large eddy motions in the outer part of the flow and the subtleties of their influence on the inner region.