Dynamic and Double-Diffusive Instabilities in a Weak Pycnocline. Part II: Direct Numerical Simulations and Flux Laws

Abstract

Abstract This study examines the interaction of diffusive convection and shear through a series of 2D and 3D direct numerical simulations (DNS). The model employed is based on the Boussinesq equations of motion with oscillating shear represented by a forcing term in the momentum equation. This study calculates thermal diffusivities for a wide range of Froude numbers and density ratios and compares the results with those from the analysis of observational data gathered during a 2005 expedition to the eastern Weddell Sea. The patterns of layering and the strong dependence of thermal diffusivity on the density ratio described here are in agreement with observations. Additionally, the authors evaluate salinity fluxes that are inaccessible from field data and formulate a parameterization of buoyancy transport. The relative significance of double diffusion and shear is quantified through comparison of density fluxes, efficiency factor, and dissipation ratio for the regimes with/without diffusive convection. This study assesses the accuracy of the thermal production dissipation and turbulent kinetic energy balances, commonly used in microstructure-based observational studies, and quantifies the length of the averaging period required for reliable statistics and the spatial variability of heat flux.