Bénard convection with time-periodic heating

Abstract

A thin liquid layer, which is heated from below, has its lower boundary modulated sinusoidally in time with amplitude δ. Weakly‐nonlinear stability theory shows that the modulation produces a range of stable hexagons near the critical Rayleigh number. For small δ the range is O(δ⁴) in size and decreases with modulation frequency. These hexagons bifurcate subcritically and correspond to downflow at cell centers.