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Convective stability of gravity-modulated doubly cross-diffusive fluid layers

Published online by Cambridge University Press:  26 April 2006

Guillermo Terrones  and
C. F. Chen
Guillermo Terrones
Affiliation:
Analytic Sciences Department, Battelle Pacific Northwest Laboratories, Richland, WA 99352, USA
C. F. Chen
Affiliation:
Department of Aerospace and Mechanical Engineering The University of Arizona, Tucson, AZ 85721, USA
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Abstract

A stability analysis is undertaken to theoretically study the effects of gravity modulation and cross-diffusion on the onset of convection in horizontally unbounded doubly diffusive fluid layers. We investigate the stability of doubly stratified incompressible Boussinesq fluid layers with stress-free and rigid boundaries when the stratification is either imposed or induced by Soret separation. The stability criteria are established by way of Floquet multipliers of the amplitude equations. The topology of neutral curves and stability boundaries exhibits features not found in modulated singly diffusive or unmodulated multiply diffusive fluid layers. A striking feature in gravity-modulated doubly cross-diffusive layers is the existence of bifurcating neutral curves with double minima, one of which corresponds to a quasi-periodic asymptotically stable branch and the other to a subharmonic neutral solution. As a consequence, a temporally and spatially quasi-periodic bifurcation from the basic state is possible, in which case there are two incommensurate critical wavenumbers at two incommensurate onset frequencies at the same Rayleigh number. In some instances, the minimum of the subharmonic branch is more sensitive to small parameter variations than that of the quasi-periodic branch, thus affecting the stability criteria in a way that differs substantially from that of unmodulated layers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 255 , October 1993 , pp. 301 - 321
Copyright
© 1993 Cambridge University Press

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