Bounds on heat transport in rotating Rayleigh-Bénard convection

Traditional methods providing bounds on the heat transport in convective flows do not account for the influence of rigid body rotation, as these methods typically rely on energy type estimates. We demonstrate these difficulties and show several approaches that do yield insight into the effects of rigid body rotation on the convective heat transport. Most of these bounds are determined first via numerical solution of semi-definite programs, providing insight into rigorous upper bounds via the auxiliary functional method.