A laboratory and quantitative model of finite-amplitude thermohaline intrusions

An experiment that models the growth and evolution of double-diffusively dr iven intrusions across an initially sharp thermohaline front is described. A removable barrier was placed in the center of a 2 m long tank that was st ratified with equal density gradients of sugar solution on the left and sal t solution on the right. After the barrier was removed and small lateral de nsity differences had been adjusted, an organized set of laterally intrusiv e layers formed. These consisted of layers of fingers separated by diffusiv e interfaces sloping systematically upwards from the high-S (sugar) side of the front. Each layer consisted of a central, finger-filled region plus "n ose" regions on either side in which fingers do not extend through the comp lete layer depth. The sugar concentration within the layers decreased smoot hly from the high-S side to the low-S and increased with height in the fing er region as required for the existence of sugar fingers. This structure sp read in a self-similar fashion as the layers extended into previously undis turbed fluid. The lateral velocity within each intrusion was Z-shaped, with nearly uniform vertical shear in the finger zones and stronger shear of op posite sign across the diffusive interfaces. The peak layer velocity increa sed from the nose extension velocity U-n at the noses to about 3.7 U-n in t he centre of the front. This implies significant horizontal divergence and consequent vertical motion and recirculation within the layers, with unknow n effects on the finger fluxes. The velocity structure, like the S, has spr ead with the noses and the front in a self-similar manner. The nose velocit y was constant with time and proportional to the S-jump across the front. U sing the results of Ruddick and Turner (1979) [Ruddick, B., Turner, J.S., 1 979. The vertical length scale of double-diffusive intrusions. Deep-Sea Res . 26A, 903-913] for the vertical scale of the layers, the nose velocity was found to be approximately described by a constant, but very small, Froude number of 0.005. The lateral S-flux was measured directly (by re-inserting the barrier after some time had elapsed) as well as from correlations betwe en layer velocity and S, and was well-described by assuming that the front spread with the noses. The S-flux was therefore proportional to the nose ve locity times the lateral S-contrast, or alternatively, to the square of the lateral S-contrast. This flux is independent of the frontal width. The mai n structural features of the laboratory intrusions are consistent with the assumption that the flow is in a state of continuous hydrostatic adjustment close to equilibrium with the ambient stratified density field. The depth difference between the two ends of the layers is shown to be equal to the t otal layer thickness, and the length of the nose beyond the finger-filled r egion on the more-diffusive side is r(S) times the total length of the fing er-filled region, where rs is the ratio of the (top-to-bottom) to (end-Co-e nd) differences in the layer of the less-diffusive solute. Consideration of the advective fluxes provides another relation involving r(S), the (finger ) flux ratio gamma and density differences across the layer which leads to an expression for the layer depth similar to that given by Ruddick and Turn er (1979) but with a little less empiricism. A salt balance equating the fl ux across the vertical centerline to the rate of increase of total salt con tent beyond it connects r(S) to the ratio of the maximum velocity of the me an circulation to the rate of extension of the nose, which was measured. Th is gives r(S) = 0.46 +/- 0.4 and gamma = 0.67 +/- 0.03 for the flux ratio i n these cells. A more complete theory to account for the detailed circulation patterns and flow speeds has not yet been developed. (C) 1999 Published by Elsevier Sci ence B.V. All rights reserved.