Numerical experiments with a fluid heated non-uniformly from below

Convection in a square container driven by non-uniform heating from below is investigated. It is shown that the normalized heat transport, the Nusselt number (Nu), obeys an Ra-1/5 power law where Ra is the Rayleigh number based on the total temperature contrast along the bottom. As the Prandtl number (Pr) is decreased from 10 to 1 (Ra > 10(6)), the stream function increases rapidly while Nu decreases. For a given Ra, Nu is a strong function of the shape of the imposed temperature distribution and increases as the lateral extent of the thermal contrast is reduced. It is also shown that the response of the system to a new temperature distribution is slow or rapid depending upon whether or not the interior temperature field is affected. These experiments re-emphasize what is sometimes overlooked, namely that the thermohaline circulation is driven by the imposed horizontal (meridional density) contrast and not by the deep convection per se.