Numerical experiments with a fluid heated non-uniformly from below

Convection in a square container driven by non-uniform heating from below is investigated. Itis shown that the normalized heat transport, the Nusselt number (Nu), obeys an Ra^1/5 powerlaw 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 > 10⁶), the stream function increasesrapidly while Nu decreases. For a given Ra, Nu is a strong function of the shape of the imposedtemperature 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 orrapid depending upon whether or not the interior temperature field is affected. These experimentsre-emphasize what is sometimes overlooked, namely that the thermohaline circulationis driven by the imposed horizontal (meridional density) contrast and not by the deep convectionper se.