Asymmetric Squares as an Attracting Set in Rayleigh-Bénard Convection

Properties of asymmetric square convection in a horizontal fluid layer heated from below are studied numerically with a Galerkin method. Since the Boussinesq approximation is used and symmetric rigid boundaries are assumed, both types of asymmetric square convection---those with rising and those with descending motion in the center---are physically equivalent. It is shown that asymmetric square convection becomes stable with respect to arbitrary three-dimensional infinitesimal disturbances for Rayleigh numbers in excess of 3 to 4 times the critical value.