Date of Award
Doctor of Philosophy in Oceanography
A model is developed to examine the growthrates of salt fingers under supercritical conditions. Solutions valid in a linearly stratified Boussinesq fluid are derived which include complete dependence on the Prandtl number and diffussivity ratio, to allow comparison with data in both the heat-salt arid sugar-salt experiments. It is found that the finger amplitudes cane-fold within one local Brunt-Vaisala period in much of the main thermo-halo-cline of the world ocean, with significantly faster growth rates realized in waters with higher salinity gradients. It is also found that the ratio of the density flux of heat to the density flux of salt (flux ratio = γ) of the fastest growing fingers agrees with the experimental data of Turner (1967) for heat-salt fingers (γ = 0.56) and the data of Lambert and Demenkow (1972) for sugar-salt fingers (γ =0.9). This is the first model to successfully explain the variation of the flux ratio in these two systems, where the Prandtl number and diffusivity ratio differ by two orders of magnitude.
A discrepancy exists, however, in the heat-salt case, between Turner and Linden (1971), who estimates γ = 0.12, Also, Stern (1976) has developed a theory which maximized the buoyancy flux, finding γ = 0.25. In order to resolve these differences, a series of two layer heat-salt experiments were performed in a one meter deep insulated tank. The flux measurements reveal variations in the flux ratio which suggest that the fingers may realize different regimes, depending primarily on the stability ratio, αΔT/βΔS = R. The flux ratio is about 0.6 for R<4 and decreases to 0.3 for R>6. This may help explain the differences between Turner’s and Linden’s results.
Additional data reveals that the ratio of the salt flux to the product of viscosity and local density gradient due to temperature is about one. This result supports the collective instability model of Stern (1969), which provided a mechanism for the breakdown of the fingers and the limitation of the finger interface thickness. Also, the dependence of the salt flux on the 4/3 power of the salinity difference across the interface is confirmed. The coefficient pf the power law as a function of R is determined, allowing the calculation of the salt flux to within 15%. This should be useful in assessing the role of salt fingers in the vertical mixing of the ocean.
As a further test of the collective instability model of Stern, experiments were done on sugar-salt fingers in a rotating reference frame. It is found that the rotating finger interface is slightly thicker than the interface in the equivalent non-rotating experiment. A calculation of the neutral stability conditions in the rotating case is made by including the Coriolis acceleration in the collective instability model. Rotation is found to stabilize the fingers, a result consistent with the observation of a thicker interface in the rotating frame.
Schmitt, Raymond W. Jr., "Time Dependent and Rotational Effects in Salt Finger Convection" (1978). Open Access Dissertations. Paper 1347.