New results in the variational approach to turbulent Boussinesq convection

Abstract

The new variational formulation introduced by Doering and Constantin for bounding the heat transport is related to the classical mean-fluctuation approach. These methods are seen to be dual principles. The Doering-Constantin approach seeks to estimate a saddle point value of a functional strictly from above as part of a minimization process. The best bounds on the Nusselt number available in each approach coincide. The optimizing solution is shown to possess no mean flow.