Small Reynolds number instabilities in two-layer Couette flow
type: Item
instance of: scholarly article
title: Small Reynolds number instabilities in two-layer Couette flow
zbMATH Open document ID: 0978.76022
DOI: 10.1016/S0997-7546(00)00109-6
author: Fabrice Albert
author: F. Charru
published in: European Journal of Mechanics. B. Fluids
publication date: 2002-01-31T00:00:00Z
review text: The authors investigate instabilities in a two-layer Couette flow by using a small-Reynolds-number expansion of the eigenvalue problem governing the linear stability. The wave velocity and growth rate are given explicitly, and previous results for long waves and short waves are retrieved as special cases. In addition to the inertial instability due to viscosity stratification, the flow can also be subject to Rayleigh-Taylor instability. As a result of the competition between these two instabilities, inertia may completely stabilize a gravity-unstable flow above some critical Froude number, or conversely, for a gravity-stable flow, inertia may give rise to finite wave number instability above some finite critical Weber number. Here, the authors give general conditions for these phenomena, as well as calculate exact or approximate the values of critical numbers. The validity of asymptotic solutions is then investigated through comparison with numerical solutions.
reviewed by: Walter Wuest
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 76E17
Mathematics Subject Classification ID: 76M45
zbMATH DE Number: 1462578
zbMATH Keywords: two-layer Couette flow
zbMATH Keywords: small-Reynolds-number expansion
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: linear stability
zbMATH Keywords: wave velocity
zbMATH Keywords: inertial instability
zbMATH Keywords: viscosity stratification
zbMATH Keywords: Rayleigh-Taylor instability
zbMATH Keywords: gravity-unstable flow
zbMATH Keywords: gravity-stable flow
zbMATH Keywords: finite wave number instability
zbMATH Keywords: critical Froude number
zbMATH Keywords: critical Weber number
zbMATH Keywords: asymptotic solution
MaRDI profile type: Publication
full work available at URL: s0997-7546(00)00109-6
OpenAlex ID: W1992228116
description: scientific article; zbMATH DE number 1462578