The nonlinear stability of a free shear layer in the viscous critical layer regime
Abstract
The nonlinear evolution of weakly amplified waves in a hyperbolic tangent free shear layer is described for spatially and temporally growing waves when the shear layer Reynolds number is large and the critical layer viscous. An artificial body force is introduced to keep the mean flow parallel. Jump conditions on the perturbation velocity and mean vorticity are derived across the critical layer by applying the method of matched asymptotic expansions, and it is shown that viscous effects outside the critical layer have to be taken into account in order to obtain a uniformly valid solution. It is also shown that when the mean flow distortion generated by Reynolds stresses is also included, the Landau constant becomes positive. Thus, in both the spatial and temporal case, linearly amplified waves are further destabilized and damped waves are unstable above a threshold amplitude.
 Publication:

Philosophical Transactions of the Royal Society of London Series A
 Pub Date:
 January 1980
 DOI:
 10.1098/rsta.1980.0006
 Bibcode:
 1980RSPTA.293..643H
 Keywords:

 Flow Stability;
 Free Flow;
 Parallel Flow;
 Shear Layers;
 Viscous Flow;
 Wave Amplification;
 Asymptotic Series;
 Critical Flow;
 Flow Distortion;
 Landau Factor;
 Reynolds Number;
 Vorticity;
 Fluid Mechanics and Heat Transfer