Reynolds Stresses in a Salt-Finger Layer

Oceanic flows are often dominated by buoyant forces. While within the incompressible regime, the fluid density varies significantly due to variations in temperature (T) and salinity (S). A peculiar class of instabilities arise from the fact that temperature and salinity have inverse effects on the density, and diffuse at significantly different rates. The difference in diffusivity can give rise to water columns which are ``heavy on the bottom'', but nonetheless unstable. The associated processes are termed "double-diffusive". Exemplary of these double-diffusive instabilities are salt-fingers, which share many aspects with small scale turbulence: the typical length scale is quite small (~1 cm), and the formations are essentially randomly distributed and highly three-dimensional. Additionally, like turbulence, the small-scale formations have large-scale implications. Salt-fingers are problematic for the computational fluid dynamicist; resolving the small features and the non-trivial impact on the transport of salinity, heat, and momentum can be computationally expensive. Existing work to account for these effects largely focuses on deriving eddy diffusivities for heat and salt using numerical, experimental, or theoretical means. In this study, additional clarity concerning other flow properties associated with salt-fingers is sought, with the ultimate goal of establishing the background turbulent kinetic energy (TKE), TKE dissipation, and ocean small-scale (~1-100 m) flow behaviour associated with salt-fingers and their secondary effects. Millimetre-scale finite-volume simulations using OpenFOAM are employed. These simulations can be used to determine the Reynolds stresses associated with the bouyancy-driven flow, and conduct observations of the time-averaged velocity behaviour for 2D and 3D cases. We will ultimately present the Reynolds stresses derived from direct numerical simulations of salt-fingers, and compare the results to the eddy-diffusivity models commonly used for oceanographic simulations.