Sandstrom's theorem and the energetics of horizontal convection

Considerable controversy surrounds recent implications drawn from Sandstrom's 'theorem' that: "a closed steady circulation can only be maintained in the ocean if a heat source is situated at a lower level than a cold source". I show that a rigorous version of Sandstrom's 'theorem' is that non-uniform buoyancy imposed at the surface of the ocean cannot supply significant mechanical energy. Thus invocations of Sandstrom's 'theorem' as implying that diapycnal mixing is powered exclusively by winds and tides are indeed on a firm basis. However there is no direct connection between mechanical energy supply and the strength (that is, mass overturning and heat flux) of the large-scale ocean circulation. Thus popular corollaries of Sandstrom's theorem, such as the conclusion that without winds and tides the mass overturning of the thermohaline circulation would be feeble, have no basis. I'll review recent experiments, simulations and theories, all showing that in fact significant mass-overturning circulations are produced by heating and cooling at a horizontal surface.