New experimental results on haline convection show a surprising preference for narrow fingers over large-scale convection when even a small stabilizing temperature gradient is present (Hage and Tilgner, 2010). This regime has heat/salt density ratios below one, a parameter range that has not been explored in traditional salt finger theory. Here the properties of the exact (long finger) solutions of Schmitt (1979, 1983) are explored at low density ratios. It is found that narrow finger solutions are indeed obtained and remain the fastest growing in some circumstances, though the selective advantage of the “Stern scale” can disappear as the density ratio decreases. The variation of solutions with Prandtl number and the relation to the Stern (1975) approximate solution are examined and discussed.
Schmitt, Raymond W.. 2011. "Thermohaline convection at density ratios below one: A new regime for salt fingers." Journal of Marine Research 69, (4). https://elischolar.library.yale.edu/journal_of_marine_research/327