Journal of Fluid Mechanics



The onset of instability in unsteady boundary-layer separation


K. W.  Cassel a1, F. T.  Smith a2 and J. D. A.  Walker a1
a1 Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015, USA
a2 Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK

Article author query
cassel kw   [Google Scholar] 
smith ft   [Google Scholar] 
walker jd   [Google Scholar] 
 

Abstract

The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous—inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought.

(Published Online April 26 2006)
(Received March 1 1994)
(Revised September 18 1995)



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