Transition to Turbulence in the Rayleigh-Benard Convection

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Abstract
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 σ = 2.5 and the box aspect ratio Γy = 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.