Stability of stratified compressible shear flows
type: Item
instance of: scholarly article
title: Stability of stratified compressible shear flows
zbMATH Open document ID: 0663.76030
DOI: 10.1016/0022-247X(89)90328-4
author: S. H. Smith
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: For stratified compressible shear flows, it is shown that the instability region for subsonic disturbances is a semiellipse type region, which depends on the Richardson number, wave number, and depth of the fluid layer. If U(y) is the basic velocity, \(c=c_ r+ic_ i\) is the complex phase velocity, and \(J_ 0\) the minimum of the local Richardson number, then this region reduces to the line \(c_ i=0\) when \(U'_{\min}\neq 0\) and \(J_ 0\to 1/4^-\) in accord with Miles's theorem. Under an approximation, the role of curvature of the basic velocity profile on the stability of the flow is also studied.
Mathematics Subject Classification ID: 76E17
Mathematics Subject Classification ID: 76E99
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4085231
zbMATH Keywords: stratified compressible shear flows
zbMATH Keywords: instability region
zbMATH Keywords: semiellipse type region
MaRDI profile type: Publication
cites work: The extension of the Miles-Howard theorem to compressible fluids
cites work: Note on a paper of John W. Miles
cites work: Stability of stratified shear flows
cites work: Note on Howard's semicircle theorem
cites work: Note on the paper of Kochar & Jain on Howard's semicircle theorem
cites work: On the stability of heterogeneous shear flows
cites work: Q4136791
cites work: Q3908713
full work available at URL: 0022-247x(89)90328-4
OpenAlex ID: W2084794498
description: scientific article; zbMATH DE number 4085231