Convective heat transfer in planetary dynamo models

Abstract

The magnetic fields of planets and stars are generated by the motions of electrically conducting fluids within them. These fluid motions are thought to be driven by convective processes, as internal heat is transported outward. The efficiency with which heat is transferred by convection is integral in understanding dynamo processes. Several heat transfer scaling laws have been proposed, but the range of parameter space to which they apply has not been firmly established. Following the plane layer convection study by King et al. (2009), we explore a broad range of buoyancy forcing (Ra) and rotation strength (E−1) to show that heat transfer (Nu) in spherical dynamo simulations occurs in two distinct regimes. We argue that heat transfer scales as Nu ∼ Ra6/5 in the rapidly rotating regime and Nu ∼ Ra2/7 in the weakly rotating regime. The transition between these two regimes is controlled by the competition between the thermal and viscous boundary layers. Boundary layer scaling theory allows us to predict that the transition between the regimes occurs at a transitional Rayleigh number, Rat = E−7/4. Furthermore, boundary layer control of heat transfer is shown to relate to the interior temperature profiles of the models. In the weakly rotating regime, the interior fluid is nearly adiabatic. In the rapidly rotating regime, adverse mean temperature gradients abide, irrespective of the Reynolds number (Re). Extrapolating our results to Earth's core, we estimate that core convection resides in the rapidly rotating regime, with Ra ≈ 2 × 1024 (Ra/Rat ≈ 0.02), corresponding to a superadiabatic density variation of Δρ/ρo ≈ 10−7, which is significantly below the sensitivity of present seismic observations.