Rayleigh-Bénard convection: The container shape matters

In an effort to achieve very large Rayleigh numbers when studying turbulence on a Rayleigh--Baposenard configuration, one can carry out simulations and experiments in as high convection cells as possible which involves using convection cells with the smallest possible aspect ratio. However, with the increasing height of the cell, the Rayleigh number grows much slower than the critical Rayleigh number for the onset of convection in the same container. This article discusses how to estimate accurately the critical Rayleigh number for the onset of convection in confined geometries and the optimal shape of the container.