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Linearized buoyant motion in a closed container

Published online by Cambridge University Press:  29 March 2006

M. C. Jischke  and
R. T. Doty
M. C. Jischke
Affiliation:
School of Aerospace, Mechanical and Nuclear Engineering, University of Oklahoma
R. T. Doty
Affiliation:
School of Engineering and Technology, McNeese State University
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Abstract

An arbitrarily-shaped, closed container completely filled with fluid is considered. It is assumed that the fluid is originally in a stably-stratified state of rest, and that at an initial instant the temperature of the container walls is impulsively changed. The ensuing unsteady laminar motion is found by solving the linearized Boussinesq equations governing buoyancy-driven flows. A ‘boundarylayer/inviscid-interior’ decomposition leads to a modified asymptotic expansion scheme of analysis. The boundary-layer concept is valid only for large values of the Rayleigh number, and, in addition, we limit the Prandtl number to order unity. It is found that the inviscid interior region heats up by means of a convection process that is driven by suction induced by the boundary layer. The inviscid, adiabatic interior responds to a special horizontal ‘average’ value of the container temperature perturbation. The boundary layer smears out, or averages, any circumferential variation in this perturbation, so that the interior, in effect, responds to an isothermal boundary in each horizontal plane. The interior temperature and vertical velocity component are expressed simply in terms of this horizontal ‘average’ container temperature. The horizontal velocity potential is governed by a Poisson equation, whose solution is developed for several specific geometries to illustrate the nature of the flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 4 , 28 October 1975 , pp. 729 - 754
Copyright
© 1975 Cambridge University Press

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