Rayleigh-Benard Convection with Time-Dependent Boundary Conditions.

The thirteen-mode Lorenz model previously introduced to describe hexagons and rolls in a Rayleigh-Benard cell with periodic modulation of the lower plate is generalized to arbitrary time dependence of both upper and lower plates. Earlier results of Krishnamurti for the case of a linear ramp with constant temperature difference are recovered. The conditions for observing hexagons are derived analytically for periodic modulation with different frequencies, amplitudes and phases at the two plates.