Weakly nonlinear stability theory of stratified shear flows

✍ Scribed by S. A. Maslowe; Dr P. G. Drazin

• Publisher: John Wiley and Sons
• Year: 1977
• Tongue: English
• Weight: 948 KB
• Volume: 103
• Category: Article
• ISSN: 0035-9009
• DOI: 10.1002/qj.49710343817

✦ Synopsis

Abstract

A derivation is given of the first‐order, nonlinear amplitude equation governing the temporal evolution of finite‐amplitude waves in stratified shear flows. the theory has been developed on an essentially inviscid basis by perturbing away from the linear neutral stability curve in Richardson number‐wavenumber space. However, viscosity and heat conduction are still required in order to eliminate the singularities that occur in the inviscid limit. Holmboe's mixing layer model has been studied by applying the present theory and the results show, surprisingly, that subcritical instability can occur, i.e. modes that would be stable on a linear basis (e.g. when the Richardson number is greater than 1/4) become unstable when the initial perturbation amplitude is greater than some critical value. an instability due to resonance which occurs at a Richardson number of 0·22 is also revealed by the analysis. These results have interesting implications in connection with clear air turbulence which are discussed herein.