Transition to Turbulence in the Rayleigh-Benard Convection

Time evolution of convection appearing in a fluid contained in a rectangular box heated from below is investigated using a 48·mode system of equations. For the case where the Prandtl number (J = 2.5 and the box aspect ratio ry = 3.5, with the increase of the vertical thermal gradient across the system, the fluid motion undergoes successive transitions as follows: periodic motion .... quasi·periodic motion with two fundamental frequencies .... quasi· periodic motion with three frequencies .... turbulence. In particular, the transition to turbulence occurs when the fundamental frequencies of the above quasi·periodicity satisfy the resonance condition.