On finite amplitude Bénard convection in a cylindrical container

Abstract

A study analogous to that of Daniels (1977) is undertaken for finite amplitude Benard convection in a shallow cylindrical container with an imperfectly insulated sidewall. A novel feature of the investigation is the singularity which develops in the amplitude function as the centre of the cylinder is approached. This singularity results in an unexpectedly large cell amplitude at the origin, and a slight increase in the value of the Rayleigh number at which the convection cells spread throughout the fluid from that predicted by linear theory.