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Double-diffusive interleaving due to horizontal gradients

Published online by Cambridge University Press:  20 April 2006

Judith Y. Holyer
Judith Y. Holyer
Affiliation:
School of Mathematics, University of Bristol, England
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Abstract

In this paper we present a linear stability analysis for an unbounded, vertically stratified fluid which has compensating horizontal temperature and salinity gradients, so there is no horizontal density gradient. We obtain the most unstable perturbation for given linear horizontal and vertical gradients and calculate the growth rates, the vertical lengthscale of the intrusion and the slope of the intrusion to the horizontal. We show that the system is most unstable to two-dimensional disturbances and that, except for a small region in which the temperature stratification is unstable and the salinity stratification is stable, the most-unstable disturbance is non-oscillatory. We also obtain a solution to the fully nonlinear equations and calculate the fluxes of heat and salt. The nonlinear solution shows that alternating interfaces of salt-finger and diffusive interfaces will eventually appear on the intrusion when the vertical stratifications are both stable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 137 , December 1983 , pp. 347 - 362
Copyright
© 1983 Cambridge University Press

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