Necessary and sufficient conditions for the stability of flows of incompressible viscous fluids
type: Item
instance of: scholarly article
title: Necessary and sufficient conditions for the stability of flows of incompressible viscous fluids
zbMATH Open document ID: 0809.76029
DOI: 10.1007/BF00391555
author: Wolf von Wahl
published in: Archive for Rational Mechanics and Analysis
publication date: 1994-11-14T00:00:00Z
review text: We perturb a steady flow of an incompressible viscous fluid and derive a necessary and sufficient condition for the marginal cases for monotonic energy stability and stability against small (infinitesimal) disturbances to coincide. Evaluation of this condition in two examples singles out, in terms of the parameters of the problem, the cases where necessary and sufficient conditions for stability coincide and thus the steady flow first becomes unstable, together with the class of perturbations responsible for the instability. The examples we treat are plane parallel shear flow with a non-symmetric profile in an infinite rotating layer and the effect of rotation on convection.
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 687662
zbMATH Keywords: stability against small disturbances
zbMATH Keywords: monotonic energy stability
zbMATH Keywords: plane parallel shear flow
zbMATH Keywords: infinite rotating layer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 687662