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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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References

Baines, P. G. & Gill, A. E. 1969 On thermohaline convection with linear gradients J. Fluid Mech. 37, 289.Google Scholar
Fedorov, K. N. 1978 The Thermohaline Finestructure of the Ocean. Pergamon.
Gregg, M. C. 1975 Microstructure and intrusions in the California current J. Phys. Oceanogr. 5, 253.Google Scholar
Gregg, M. C. 1979 Thermohaline intrusions lie across isopycnals Nature 280, 310.Google Scholar
Holyer, J. Y. 1981 On the collective stability of salt fingers J. Fluid Mech. 110, 195.Google Scholar
Horne, E. p. W. 1978 Interleaving at the subsurface front in the slope water off Nova Scotia J. Geophys. Res. 83, 3659.Google Scholar
Huppert, H. E. & Manins, P. C. 1973 Limiting conditions for salt fingering Deep-Sea Res. 20, 315.Google Scholar
Ruddick, B. R. & Turner, J. S. 1979 The vertical length scale of double-diffusive intrusions Deep-Sea Res. 26, 903.Google Scholar
Schmitt, R. W. 1979 The growth rate of super-critical salt fingers Deep-Sea Res. 26, 23.Google Scholar
Schmitt, R. W. & Georgi, D. T. 1982 Finestructure and microstructure in the North Atlantic J. Mar. Res. 40, 659.Google Scholar
Stern, M. E. 1967 Lateral mixing of water masses Deep Sea Res. 14, 747.Google Scholar
Stommel, H. & Fedorov, K. N. 19?? Small scale structure in temperature and salinity near Timor and Mindanao. Tellus 19, 306.Google Scholar
Thorpe, S. A., Hutt, P. K. & Soulsby, R. 1969 The effects of horizontal gradients on thermohaline convection J. Fluid Mech. 38, 375.Google Scholar
Toole, J. M. & Georgi, D. T. 1981 On the dynamics and effects of double-diffusively driven intrusions Prog. Oceanogr. 10, 123.Google Scholar
Walin, G. 1964 Note on the stability of water stratified by salt and heat Tellus 16, 389.Google Scholar
Wirtz, R. A., Briggs, D. G. & Chen, C. F. 1972 Physical and numerical experiments on layered convection in a density-stratified fluid Geophys. Fluid Dyn. 3, 265.Google Scholar