Compressible convection in planets and stars, why bother ?
In the study of thermal convection, Oberbeck then Boussinesq devised a simplified model, valid in many practical cases, whereby density is assumed to depend - in a small proportion - on temperature only. The Oberbeck-Boussinesq model has been the starting point for important theoretical advances, like the study of stability by Rayleigh or the study of chaotic dynamical systems by Lorenz. However, in planetary and stellar interiors, pressure effects become dominant. The full equation of states must be considered. A first consequence of the pressure increase with depth is the appearance of a temperature increase, under sufficient mixing by convection. This is the so-called adiabatic gradient, first elucidated by Carnot 200 years ago. In addition, the most striking effect is the distribution of viscous dissipation and expansion work within the fluid. They can even exceed the thermal energy transferred by convection. In our group in Lyon, we have been interested in the numerical, theoretical, and experimental modelling of such effects with a particular focus on planetary interiors. For rocky mantles, we can make predictions on the vertical profile of viscous dissipation and investigate the consequences in terms of rheology. I will review some of these studies and indicate questions to address in the future.
Contact Nathanaël Machicoane for more information or to schedule a discussion with the seminar speaker.