Thermal instability of a heterogeneous rotating fluid layer with free boundaries
type: Item
instance of: scholarly article
title: Thermal instability of a heterogeneous rotating fluid layer with free boundaries
zbMATH Open document ID: 0549.76066
author: Priti Mohapatra
author: Srimati Misra
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: The authors study the thermal instability of a heterogeneous rotating fluid layer with free boundaries. The model is a viscous, incompressible, rotating and nonhomogeneous fluid layer with free boundaries with density \(\rho_ 0f(z)\), where \(\rho_ 0\) is a positive constant with the dimension of the density, and f is a monotonic function of the vertical coordinate z with \(f(0)=1\). The fluid is rotating with an angular velocity \(\Omega\) about the vertical axis. In this respect, one notes that the principle of exchange of stabilities is not valid for this problem. The present solution is shown to be characterized by a variational principle expressed in terms of certain parameters related to the Rayleigh number. Moreover, for certain values of these parameters, marginal state does not exist and non-oscillatory unstable modes exist. The paper also contains numerical computations with the assumption that the density of the fluid varies exponentially.
reviewed by: Jacob Burbea
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76E30
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 76E17
Mathematics Subject Classification ID: 76E99
zbMATH DE Number: 3876841
zbMATH Keywords: boundary layer
zbMATH Keywords: principle of exchange of stabilities
zbMATH Keywords: Rayleigh number
zbMATH Keywords: non-oscillatory unstable modes
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3876841