The Onset of Bénard Convection in a Shallow Sloping Container

A study is made of the onset of Bénard convection in a shallow rectangular container of aspect ratio 2L (»1) which slopes at a small angle, α, to the horizontal. The resulting flow-field is a combination of the large scale circulation driven by the misalignment of the thermal gradient with the direction of gravity, and the small scale convective motions driven by the gravitational instability. The sidewalls of the container also play a crucial role in the generation of the convective motion, the amplitude of which increases smoothly with increasing Rayleigh number provided that α≠0.