The convective approximations
Résumé
Convection can occur in a shallow layer of fluid with a small temperature contrast across the layer. Thus, it is natural to hope for a simpler description of buoyantly driven flows via an expansion of the fully compressible equations. The Boussinesq approximation performs well in modeling convection in laboratory experiments, but it is however unsatisfactory for large stratified systems, the lower part of which is compressed by the overlying material. More general approximations are then required to describe convection in natural systems like oceans, stars or planetary cores.
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