On upper bounds for infinite Prandtl number convection with or without rotation

Bounds for the bulk heat transport in Rayleigh-Benard convection for an inf inite Prandtl number fluid are derived from the primitive equations. The en hancement of heat transport beyond the minimal conduction value (the Nussel t number Nu) is bounded in terms of the nondimensional temperature differen ce across the layer (the Rayleigh number Ra) according to Nu less than or e qual to cRa(2/5), where c <1 is an absolute constant. This rigorous upper l imit is uniform in the rotation rate when a Coriolis force, corresponding t o the rotating convection problem, is included. (C) 2001 American Institute of Physics.