Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-21T08:19:55.187Z Has data issue: false hasContentIssue false
  • English
  • Français

On the stability of vertical double-diffusive interfaces. Part 2. Two parallel interfaces

Published online by Cambridge University Press:  26 April 2006

I. A. Eltayeb  and
D. E. Loper
I. A. Eltayeb
Affiliation:
Department of Mathematics and Computing, Sultan Qaboos University, Muscat, Sultanate of Oman
D. E. Loper
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

This is the second part of a three-part study of the stability of vertically oriented double-diffusive interfaces having an imposed vertical stable temperature gradient. In this study, flow is forced within a fluid of infinite extent by a prescribed excess of compositionally buoyant material between two parallel interfaces. Compositional diffusivity is ignored while thermal diffusivity and viscosity are finite. The stability of the interfaces is analysed first in the limit that they are close together (compared with the salt-finger lengthscale), then for general spacing. Attention is focused on whether the preferred mode of instability is varicose or sinuous and whether its wavevector is vertical or oblique.

The interfaces are found to be unstable for some wavenumber for all values of the Prandtl number and interface spacing. The preferred mode of instability for closely spaced interfaces is varicose and vertical for Prandtl number less than about 9, sinuous oblique for Prandtl number between 9 and 15 and sinuous vertical for larger Prandtl number. For general spacing each of the four possible modes of instability is preferred for some range of Prandtl number and interface separation, with no clear pattern of preference, except that the sinuous oblique mode is preferred for widely separated interfaces. The growth rate of the preferred mode is largest for interfaces having separations of from 1 to 3 salt-finger lengths.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 267 , 25 May 1994 , pp. 251 - 273
Copyright
© 1994 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Dudis, J. J. & Davis, S. H. 1971 Energy stability of the buoyancy boundary layer. J. Fluid Mech. 47, 381–403.Google Scholar
Eltayeb, I. A. & Loper, D. E. 1991 On the stability of vertically oriented double-diffusive interfaces. Part 1. A single plane interface. J. Fluid Mech. 228, 149–181.Google Scholar
Gill, A. E. 1966 The boundary-layer regime for convection in a rectangular cavity. J. Fluid Mech. 26, 515–536.Google Scholar
Gill, A. E. & Davey, A. 1969 Instabilities of a buoyancy-driven system. J. Fluid Mech. 35, 775–798.Google Scholar
Hinch, E. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463–465.Google Scholar
Holyer, J. Y. 1983 Double-diffusive interleaving due to horizontal gradients. J. Fluid Mech. 137, 347–362.Google Scholar
Lister, J. R. 1987 Long-wavelength instability of a line plume. J. Fluid Mech. 175, 413–428.Google Scholar
Schneider, W. 1981 Flow induced by jets and plumes. J. Fluid Mech. 108, 55–65.Google Scholar