Self-Sustained Oscillations In 2D Thermohaline Convection

Abstract:

The last glacial period was punctuated by a series of abrupt climate changes. These “Dansgaard-Oeschger” (DO) events may have been at least hemispheric in extent and are generally thought to be associated with changes in the poleward heat flux by the meridional circulation in the Atlantic Ocean. Among the agents influencing this circulation are the equator-to-pole differences in the temperature and salinity of ocean surface waters. Temperature (T) and salinity (S) exert a competing influence on seawater density and meridional circulation: when the equator-to-pole density difference is dominated by T, cold and fresh water would sink at high latitudes and upwell at low latitudes, leading to a T mode of circulation akin to the meridional circulation in the modern Atlantic. In contrast, when the equator-to-pole density difference is dominated by S, warm and salty water would sink at low latitudes and upwell at high latitudes, leading to a S mode. The oscillations between different modes of meridional circulation has long been proposed as a cause of the DO events, but the physical mechanism responsible for these oscillations remains largely unknown.

Here a numerical model is constructed to study the competing effects of T and S on the thermohaline convection in a two-dimensional chamber. Emphasis is placed on the possibility that the flow exhibits self-sustained oscillations, i.e., oscillations that arise from a constant source of energy, here provided by the time-invariant differences of T and S specified along the fluid surface. The flow is governed by 5 dimensionless numbers: the Rayleigh numbers for T and S set the thermal and haline forcing, respectively, the Lewis number (Le) is the ratio of thermal diffusivity to salt diffusivity, the Prandtl number (Pr) is the ratio of viscosity to thermal diffusivity, and the aspect ratio of the chamber (d). We find that, for Pr = d = 1 and Le > 1, the model exhibits a rich array of flows, ranging from a steady T-driven cell, to unsteady flows with multiple cells, and to a steady S-driven cell. Self-sustained oscillations are found that are characterized by T-driven and S-driven cells that alternately contract and expand. Attention will be paid on the parameter regime(s) that are conducive to these oscillations as well as on their possible implications for our understanding of paleoclimates.