Instabilities and bifurcations due to buoyancy in a cylindrical container heated from below with and without a free surface

Three-dimensional simulations of the buoyant convection in a cylindrical container heated from below are presented. Both the thresholds for the onset of the convection and the nonlinear evolution of this convection are calculated. The simulations concern two configurations: a cavity with a rigid upper surface (Rigid-Rigid case) and a cavity with a non-constrained free surface (Rigid-Free case). The results show a similar variation of the primary thresholds with the aspect ratio for the two configurations. In contrast, the nonlinear evolution of the convection is much changed between the two configurations. In particular, subcritical secondary branches with a very large subcriticity are obtained in the R-F case. To cite this article: A. El Gallaf et al., C. R. Mecanique 337 (2009).