Expressions for the dissipation driven by convection in the Earth’s core

Four previously published expressions for the dissipation driven by convection in the Earth’s core are compared to clarify the relationship between them. Three are shown to be exactly equivalent, with the fourth a good approximation. Though two expressions were originally derived by considerations of mechanical energy, all four can be viewed as linear combinations of the energy and entropy budgets. Since they are solved in conjunction with the energy budget, the three equivalent expressions give the same dissipation for a given parameterization. Finally, a highly simplified parameterization of the evolving adiabatic, well-mixed, hydrostatic mean state is proposed to aid analytical examination of the constraints on the core’s cooling history.