Bounding dissipation in Rayleigh-Benard convection
In session: TUE 5.3 - Convection and Bouyancy-Driven Flows
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Rayleigh-Benard convection is a configuration that has been the subject of many studies. When we have in mind the geophysical context, we are often interested in compressible effects: density in the atmosphere depends a lot on pressure (or altitude), but this is the case also in the Earth's mantle or in the Earth's core. In that case, we must consider the general equations of fluid mechanics and thermodynamics, not just the Boussinesq approximation. We also use intermediate models, anelastic equations. The amount of energy dissipation and its distribution within the fluid is an interesting quantity. If dissipation is due to Joule effects in the core, it provides a constraint on the self-generated dynamo. In the mantle, dissipation may be associated with damage and grain refinement. With the Boussinesq approximation, the total amount of dissipation is directly proportional to the convective heat flux through the layer of fluid. In compressible convection however, there is no such strong link. We have an upper bound for dissipation from the entropy balance (Backus, 1975). I will give conditions when this bound can be improved depending on the relationship between Nusselt and Rayleigh numbers.