Numerical simulation of two-dimensional salt fingers

Numerical calculations of unperturbed, regularly spaced fingers in the heat-salt system (with a ratio of salt to heat diffusivities of 1/80) were carried out for a configuration in which a reservoir of uniformly salty, warm fluid lies initially above a reservoir of fresh, cold fluid. Cases were calculated in which the stability ratio, R-rho, was 1.5 and 3.0, and they were calculated for different magnitudes of the destabilizing salt increment, Delta S, expressed in terms of a salt Rayleigh number, R-S. Blobs of fluid with a salt anomaly accumulate at the ends of the evolving fingers. The magnitude and size of the anomaly increase with decreasing R-rho and increasing R-S. The density of those blobs is gravitationally unstable to perturbations. In the range of parameters used in these calculations the ratio of the flux of density due to heat to that due ro salt varies from 0.17 to 0.74 for the unperturbed fingers. Essentially, the flux ratio decreases when the vertical velocity in the fingers is small, so that a relatively large amount of heat is diffused laterally from warm, salty descending fingers to cool, fresh ascending ones. A detailed account of the evolution of the perturbed system describes the various stages of the instability, concluding with the formation of larger structures in the reservoirs, which squash the fingers near the interface, so that isotherms and isohaline contours at midlevel are more or less horizontal. There is an indication of three period doublings in the spacing of the unstable blobs as they penetrate into the lower reservoir. The destruction of the regular array of upright, uniformly spaced fingers appears to be the natural evolution of perturbed systems in which R-rho is near unity and R-S is large.