Thermal convection under external modulation of the driving: I. The Lorenz model.

Thermal convection between horizontal plates is considered for a situation in which the driving force varies periodically in time. This variation may come from changes in the temperature of the plates or from a vertical oscillation of the cell, causing variation of the gravitational force. Truncation of the Boussinesq equations leads to a three-mode model which is a generalization of the Lorenz model to the case of external modulation. The threshold behavior is that of a parametrically driven damped oscillator, whose bifurcations are studied numerically, as well as analytically in certain limits.