The evolution of a quasisteady critical layer in a stratified viscous shear layer
Abstract
The paper examines the evolution of the critical layer of a slightly viscous stratified shear flow with a hyperbolic tangent velocity profile for which there exists a marginally unstable free oscillation at J = 1/4 of wavenumber 1/2 when R is infinite. For J less than 1/4, the flow is unstable; for J greater than 1/4, there are no free oscillations with critical layers. The development of this layer is studied on a time scale of t much greater than R to the 1/3, which is sufficiently long for it to become quasisteady. The leading terms of a rational asymptotic approximation are presented for the viscous critical layer. The nonlinear equation for the amplitude of the oscillation is determined analytically for a quasisteady critical layer when Pr is unity and the order of magnitude of R bears a certain relation to epsilon, the small parameter characterizing the oscillation.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 March 1981
 DOI:
 10.1098/rspa.1981.0051
 Bibcode:
 1981RSPSA.375..271B
 Keywords:

 Oscillating Flow;
 Shear Layers;
 Stratified Flow;
 Viscous Fluids;
 Flow Distortion;
 Flow Equations;
 Nonlinear Equations;
 Prandtl Number;
 Fluid Mechanics and Heat Transfer