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Free Content Salt fingers in an unbounded thermocline

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Numerical solutions for salt fingers in an unbounded thermocline with uniform overall vertical temperature-salinity gradients are obtained from the Navier-Stokes-Boussinesq equations in a finite computational domain with periodic boundary conditions on the velocity. First we extend previous two-dimensional (2D) heat-salt calculations [Prandtl number Pr = /kT = 7 and molecular diffusivity ratio  = kS/kT = 0.01] for density ratio R = 2; as R decreases we show that the average heat and salt fluxes increase rapidly. Then three-dimensional (3D) calculations for R = 2.0, Pr = 7, and the numerically "accessible" values of  = 1/6, 1/12 show that the ratio of these 3D fluxes to the corresponding 2D values [at the same (, R, Pr)] is approximately two. This ratio is then extrapolated to  = 0.01 and multiplied by the directly computed 2D fluxes to obtain a first estimate for the 3D heat-salt fluxes, and for the eddy salt diffusivity (defined in terms of the overall vertical salinity gradient).

Since these calculations are for relatively "small domains" [O (10) finger pairs], we then consider much larger scales, such as will include a slowly varying internal gravity wave. An analytic theory which assumes that the finger flux is given parametrically by the small domain flux laws shows that if a critical number A is exceeded, the wave-strain modulates the finger flux divergence in a way which amplifies the wave. This linear theoretical result is confirmed, and the finite amplitude of the wave is obtained, in a 2D numerical calculation which resolves both waves and fingers. For highly supercritical A (small R) it is shown that the temporally increasing wave shear does not reduce the fluxes until the wave Richardson number drops to ~0.5, whereupon the wave starts to overturn. The onset of density inversions suggests that at later time (not calculated), and in a sufficiently large 3D domain, strong convective turbulence will occur in patches.

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Document Type: Research Article

Publication date: May 1, 2001

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  • The Journal of Marine Research, one of the oldest journals in American marine science, publishes peer-reviewed research articles covering a broad array of topics in physical, biological and chemical oceanography. Articles that deal with processes, as well as those that report significant observations, are welcome. Biological studies involving coupling between ecological and physical processes are preferred over those that report systematics. The editors strive always to serve authors and readers in the academic oceanographic community by publishing papers vital to the marine research in the long and rich tradition of the Sears Foundation for Marine Research. We welcome you to the Journal of Marine Research.
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