Energetic consistency and heat transport in rotating Rayleigh Benard convection

Parameterization is an essential tool for modeling turbulent convection in general circulation models, yet parameterizations may fail to obey physically consistent principles such as energy conservation.  In this presentation, I will present recent analytical and numerical results regarding the importance of energetic consistency in rotating Rayleigh-Benard convection. Specifically, spectral discretizations of the Boussinesq-Oberbeck equations are considered, and we are able to pinpoint the exact criteria under which a spectral discretization will obey energy balance laws consistent with the PDE.  The energy balance laws are then shown to imply a compact global attractor.  We are also able to show that almost any spectral model which does not satisfy such criteria will exhibit unbounded solutions, which are wildly unphysical.  The dynamics of the energetically consistent models are studied, and particular attention is given to stable values of heat transport, as well as the convergence across models where the models accurately represent the PDE.  Implications for energetically consistent parameterization of convective heat transport will then be discussed.