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The onset of convective instability in a triply diffusive fluid layer

Published online by Cambridge University Press:  26 April 2006

Arne J. Pearlstein ,
Rodney M. Harris  and
Guillermo Terrones
Arne J. Pearlstein
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
Rodney M. Harris
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA Present address: BDM International, Albuquerque, NM 87106, USA.
Guillermo Terrones
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
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Abstract

The onset of instability is investigated in a triply diffusive fluid layer in which the density depends on three stratifying agencies having different diffusivities. It is found that, in some cases, three critical values of the Rayleigh number are required to specify the linear stability criteria. As in the case of another problem requiring three Rayleigh numbers for the specification of linear stability criteria (the rotating doubly diffusive case studied by Pearlstein 1981), the cause is traceable to the existence of disconnected oscillatory neutral curves. The multivalued nature of the stability boundaries is considerably more interesting and complicated than in the previous case, however, owing to the existence of heart-shaped oscillatory neutral curves. An interesting consequence of the heart shape is the possibility of ‘quasi-periodic bifurcation’ to convection from the motionless state when the twin maxima of the heart-shaped oscillatory neutral curve lie below the minimum of the stationary neutral curve. In this case, there are two distinct disturbances, with (generally) incommensurable values of the frequency and wavenumber, that simultaneously become unstable at the same Rayleigh number. This work complements the earlier efforts of Griffiths (1979a), who found none of the interesting results obtained herein.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 202 , May 1989 , pp. 443 - 465
Copyright
© 1989 Cambridge University Press

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