Linear stability analysis of salt fingers with surface evaporation or warming

Abstract

Oceanic observations [Atmos. Ocean 29, 340 (1991)] have revealed small-scale thermohaline plumes near the surface of a calm sea under warming conditions. The stratification was favorable for the double-diffusive salt finger instability, though a previously unreported up–down asymmetry was found in which narrow downward cells are balanced by a broader, weaker upwelling. The scales of the thermal structures are consistent with asymmetric hexagonal salt-finger modes [J. Phys. Oceanogr. 24, 855 (1994)], but no selection mechanism for the asymmetry has previously been identified. This paper explores the influence of nonlinear profiles of temperature and salinity, as might arise due to surface evaporation or warming, on the linear stability problem in a salt-fingering regime. Three models are considered. In the first, a sharp, nonlinear solute-concentration gradient is applied at the upper boundary, as might arise by surface evaporation. A Bénard mode appears, driven by the destabilizing density gradient in the thin boundary layer and influencing motion only within the boundary-layer thickness. In the second model, a weak salinity gradient is introduced below the boundary layer; double-diffusive bulk modes influence the motion across the entire fluid. Nonlinear interaction of the boundary layer and bulk modes provides a mechanism for maintaining salt fingers with up–down asymmetry. The third model contains a large temperature gradient at the surface, as might arise from warming by solar radiation, overlying a quasi-isothermal region above a region of moderate gradient. The largest-growth modes are found to be salt fingers that extend throughout the middle region and disappear in the top and bottom regions. This vertical structure is close to that of the asymmetric salt fingers described in Osborn [Atmos. Ocean 29, 340 (1991)]. The differing length scales of the regions impress an up–down asymmetry on plumes; this is expected to yield a hexagonal pattern at the onset.