A nonlinear analysis of the stabilizing effect of rotation in the Benard problem

A phenomenon of major importance in Benard convection is the inhibiting effect which rotation has on the instability of a fluid layer heated from below. In the present investigation, nonlinear energy stability theory is employed to study the stabilizing effect of rotation. The investigation is partly motivated by the failure of previous theoretical analyses to agree with experimental results. Attention is given to a paper published by Rossby (1969). In the present investigation, use is made of an 'energy' which is generalized from the kinetic energy of the motion. The nonlinear stability boundary obtained behaves very much like the experimental boundary reported by Rossby. The obtained data show excellent agreement with Rossby's results for Taylor numbers in the range from 100,000 to 10 to the 8th.