  Motivated by the need for energetically consistent climate models, the
Boussinessq-Coriolis (BC) equations are studied with a focus on the Nusselt
number, defined as the averaged vertical heat transport. The
Howard-Krishnamurthy-Coriolis (HKC) hierarchy is defined by explicitly
computing the Galerkin truncations and selecting the Fourier modes in a
particular way, such that this hierarchy can be shown to energy relations
consistent with the PDE. Well-posedness and the existence of an attractor are
then proven for the BC model, and an explicit upper bound on the attractor
dimension is given. By studying the local bifurcations at the origin, a lower
bound on the attractor dimension is provided. Finally, a series of numerical
studies are performed by implementing the HKC hierarchy in MATLAB, which
investigate convergence of the Nusselt number as one ascends HKC hierarchy as
well as other issues related to heat transport parameterization.
