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The salt-finger zone

  • L. N. Howard (a1) and G. Veronis (a2)

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.

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References

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Carleman, T. 1922 Über die Abelsche Integralgleichung mit konstanten Integrationsgrenzen. Math. Z. 15, 111.
Holyer, J. Y. 1984 The stability of long, steady, two-dimensional salt fingers. J. Fluid Mech. 147, 169.
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.
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.
Schmitt, R. W. 1979b Flux measurements on salt fingers at an interface. J. Mar. Res. 37, 419.
Stern, M. E. 1960 The ‘salt-fountain’ and thermohaline convection. Tellus 12, 172.
Stern, M. E. 1969 Collective instability of salt fingers. J. Fluid Mech. 35, 209.
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.
Taylor, J. & Veronis, G. 1985 Experiments in salt fingers in a Hele-Shaw cell. Science 231, 39.
Turner, J. S. 1967 Salt fingers across a density interface. Deep-Sea Res. 14, 599.
Turner, J. S. 1973 Buoyancy effects in fluids. Cambridge University Press.
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The salt-finger zone

  • L. N. Howard (a1) and G. Veronis (a2)

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