Nonlinear Equilibration of Thermohaline Intrusions

Abstract

The nonlinear behavior of thermohaline intrusions on a wide front is investigated using a one-dimensional numerical model. The model is used to follow the evolution of a field of intrusions from infinitesimal amplitude to a large-amplitude state characterized by inversions in temperature and salinity. It is thus possible to extend the analytical studies of Toole and Georgi and others to large amplitude, allowing for the effects of amplitude-dependent diffusivities, and for the appearance of stably stratified, diffusively stratified, and statically unstable regions in the water column as the intrusions grow. The model runs are initialized with infinitesimal disturbances that grow exponentially in time until inversions in temperature and salinity occur. After inversions appear, the intrusions evolve toward an equilibrium state in which friction balances buoyancy forces, for both finger- and diffusive-sense basic-state stratifications. These equilibrium states are characterized by statically unstable ?convecting? layers between layers of finger- and diffusively stratified fluid?the convecting layers appear when intrusions reach large amplitude and help to slow their growth. Equilibration seems to be insensitive to the specific functional forms chosen for the double-diffusive diffusivities and viscosities. The necessary condition for equilibration is that the T?S flux ratio adjusts as the intrusions grow, and (within the context of the present model) turbulent mixing provides the mechanism for this adjustment.