Numerical Simulations, Mean Field Theory and Modulational Stability Analysis of Thermohaline Intrusions

Thermohaline intrusions are produced by lateral shear advection across thermal and haline fronts, self-driven via double-diffusion, and cause significant lateral fluxes. The primary goal of this thesis is to understand the mechanisms responsible for their development and equilibration. Previous theories mean-field models were limited by their reliance on the vertical flux laws, which still remain a great source of uncertainty and require modelers to assume that intrusion development is uniquely determined by the background gradients. An alternative approach, based on the multiscale mechanics, views intrusions as modulational instability of the rapidly varying salt fingers. We present an exhaustive study on the effects of background parameters on the vertical and horizontal fluxes of temperature and salinity using two-dimensional numerical simulations. Specific experiments are designed to identify the most promising theoretical techniques for predicting intrusion evolution. Based on numerical results, the assessments of the two theoretical models are made and the mean field theory is found to be superior. Growth rates are calculated as a function of inclination of intrusions, which is used to determine the dominant modes by focusing on the fastest-growing instability. Equilibrium diffusivities are calculated to develop an explicit parameterization for the effects of thermohaline intrusions.