This page under construction.
Work performed with Shan-fu Shen. This work was made possible by support of the Air Force Office of Scientific Research.
This document describes how the nature of unsteady boundary layer separation was discovered.
One of the questions that has been bothering fluid dynamicist is why the boundary layers that form at the surfaces of moving vehicles sometimes separate from it. Separation is undesirable, and understanding why it occurs is helpful in devising new ways to prevent it. The numerical discovery of the initial separation process is described on another page; but knowing that it occurs is not the same as knowing why it occurs.
It turned out that the initial separation is due to the deformation of a small region of air (or water, for ships) inside the boundary layer. Since Shan-fu Shen and I happened to be using a computational method that tracked the deformation of fluid regions, it made it easy to discover the structure of the separation process.
The following sketch shows schematically the distortion of the
small region:
What happens is that the point P' in the picture
moves faster than the point P and caches up with it.
Since the small region around the points is compressed in one direction,
it bulges out in the other direction.
The thickening of the boundary layer eventually destroys it.
That's it? That is it.
Well, except for a few details. The surprise was not so much that the points P' and P would move closer, but that nothing stopped them from getting very close. Or passing below or above each other. By analysing the process mathematically, we found that P and P' must be located at a at a special location within the boundary layer. It is the location at which the sense of rotation of the fluid around its axis reverses sign.
That the collision process had to occur at this location had been argued before in 1958 by Frank Moore and in 1975 more generally by Bill Sears and Dimitri Telionis from Cornell University. Sears and Telionis called it the Moore-Rott-Sears (MRS) condition.
Our analysis also predicted the approximate shape and other features
of the thickening boundary layer until it becomes too thick
to analyze. We obtained the following graph for the local boundary
layer thickness:
The lines connect points at which the fluid rotates at the same
speed. Mathematically, the fuction that describes our solution is
called an elliptic integral.
Numerical results, such as the ones below, do approach our theoretical
curve as long as the thickness remains limited.
Van Dommelen, L. L. & Shen, S. F. (1982) The genesis of separation. In Symposium on Numerical and Physical Aspects of Aerodynamic Flows, (T. Cebeci, Ed.) 293-311. Springer-Verlag. Return
Return to my home page.