The evolution of a quasi-steady 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 quasi-steady. 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 quasi-steady 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