Rotating convection driven by differential bottom heating and its application

Abstract

A convection experiment was done with a rotating rectangular tank as a model of oceanic meridional overturning circulation. Heat flux was fixed at one bottom end of the tank using an electrical heater. Temperature was fixed at the other end using a cooling plate. All other boundaries were insulated. The cross sections of temperature field were made at several locations. In equilibrium, the heat input to the fluid H was the same as the meridional heat flux (heat flux from the source to the sink), so it was possible to find a scaling law relating H to the temperature difference across the tank ΔT and rotation rate f. The experimental result suggests that the meridional heat transport in the experiment was mostly due to geostrophic flows with a minor correction caused by the bottom friction. If there was no friction, the scaling law from the experiment resembles the one verified in part in the numerical model by Bryan and Cox (1967). Flow visualization and temperature sections showed that there were meridional geostrophic currents that transported heat. When the typical values of the North Atlantic are introduced, the geostrophic scaling law predicts meridional heat flux comparable to that estimated in the North Atlantic when the vertical eddy diffusivity of heat is about 1cm2s-1. Naturally, this experiment is a only crude model of the oceanic convective circulation. We do not claim that the geostrophic scaling applies in detail to the oceans, however, it may have some important use in climate modeling. For example, almost all existing box models and two-dimensional numerical models of ocean circulation use a frictional scaling law for buoyancy transport. A box model with the geostrophic scaling law is shown to be more robust to a change in the boundary forcing so that it is less likely to have a thermohaline catastrophic transition under the present conditions. It is also shown that a restoring boundary condition for salinity introduces stability to a thermal mode circulation, unless the restoring time for salinity is several orders of magnitude larger than that for temperature.