Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-18T09:57:16.137Z Has data issue: false hasContentIssue false
  • English
  • Français

The salt-finger zone

Published online by Cambridge University Press:  21 April 2006

L. N. Howard  and
G. Veronis
L. N. Howard
Affiliation:
Mathematics Department, Florida State University, Tallahassee, FL 32306, USA
G. Veronis
Affiliation:
Geology and Geophysics Department, Yale University, New Haven, CT 06511, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In order to investigate the stability of infinitely long fully developed salt fingers Stern (1975) has proposed a model in which the basic configuration is independent of the vertical and is sinusoidal in the horizontal direction, with constant background gradients of temperature and salinity. The present study deals with a model of finite vertical extent where τ, the ratio of the diffusivities of salt and heat, is small, and where the constant background salt gradient is replaced by a salt difference between the reservoirs above and below a salt-finger region of finite depth. Steady-state solutions in two and three dimensions are obtained for the zero-order (τ = 0) state in which rising (sinking) fingers have the salinity of the lower (upper) reservoir. For two-dimensional fingers the horizontal scale corresponding to maximum buoyancy flux turns out to be 1.7 times the buoyancy-layer scale associated with the background stable temperature gradient. Heat, salt and buoyancy fluxes are calculated. A boundary-layer analysis is given for the (salt) diffusive correction to the zero-order solution. The same set of calculations is carried out for salt fingers in a Hele-Shaw cell. An assessment of Schmitt's (1979a) model of a finger zone of finite depth shows that the parametric restrictions required by the model cannot be satisfied when Stern's idealization is used for the final state. The present model appears to be preferable for constructing a Schmitt-like theory for τ [Lt ] 1.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 1 - 23
Copyright
© 1987 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

Carleman, T. 1922 Über die Abelsche Integralgleichung mit konstanten Integrationsgrenzen. Math. Z. 15, 111.Google Scholar
Holyer, J. Y. 1984 The stability of long, steady, two-dimensional salt fingers. J. Fluid Mech. 147, 169.Google Scholar
Linden, P. F. 1971 The effect of turbulence and shear on salt fingers. Ph.D. Thesis, Cambridge University.
Linden, P. F. 1973 On the structure of salt fingers. Deep-Sea Res. 20, 325.Google Scholar
Piascek, S. & Toomre, J. 1980 Nonlinear evolution and structure of salt fingers. In Marine Turbulence (ed. J. C. Nihoul), p. 193. Elsevier.
Prandtl, L. 1952 Essentials of Fluid Dynamics, Hafner.
Schmitt, R. W. 1979a The growth rate of super-critical salt fingers. Deep-Sea Res. 26, 23.Google Scholar
Schmitt, R. W. 1979b Flux measurements on salt fingers at an interface. J. Mar. Res. 37, 419.Google Scholar
Stern, M. E. 1960 The ‘salt-fountain’ and thermohaline convection. Tellus 12, 172.Google Scholar
Stern, M. E. 1969 Collective instability of salt fingers. J. Fluid Mech. 35, 209.Google Scholar
Stern, M. E. 1975 Ocean Circulation Physics. Academic.
Stern, M. E. 1976 Maximum buoyancy flux across a salt finger interface. J. Mar. Res. 34, 95.Google Scholar
Taylor, J. & Veronis, G. 1985 Experiments in salt fingers in a Hele-Shaw cell. Science 231, 39.Google Scholar
Turner, J. S. 1967 Salt fingers across a density interface. Deep-Sea Res. 14, 599.Google Scholar
Turner, J. S. 1973 Buoyancy effects in fluids. Cambridge University Press.