Compressible convection with different levels of approximation

Abstract:

Most studies on convection in the Earth's mantle and core employ the Boussinesq approximation, which assumes an incompressible mantle. However, convection in the Earth's interior is subjected to compressible effects due to increase of density with depth. They are the cause of the so-called Adiabatic (or isentropic) gradient, which plays an important role in the core where conduction along the adiabat can transfer a large fraction of the total heat extracted, and may even potentially generate stagnant layers of pure conduction. We developed a numerical method for a fully compressible convection model, which may later be reduced to the different simplifications such as the anelastic approximation and the anelastic liquid approximation. The tests of our numerical schemes against selfconsistent criteria show that the numerical simulations are fully consistent from the point of view of energy dissipation, heat transfer and entropy budget. We analyze the solutions of this thermal convection problem with different equations of state in a wide range of dimensionless parameters and determine the domain of validity of each approximation.