Rayleigh-Marangoni convection in a critical fluid: a tale of two crossovers

We show that if we take a thin layer of fluid where surface tension effects are supposed to dominate and gradually bring the mean temperature of the layer closer and closer to the liquid vapor critical point, then first there is a crossover from Marangoni to Rayleigh-Benard convection and thence to a convection whose onset is determined by the Schwarzchild criterion.