Transition to Turbulence in 1-D Rayleigh-Bénard Convection

Abstract

The study of one-dimensional -1D- hydrodynamical systems has recently received much interest. In these systems, a steady periodic cellular state, which depends on one space variable, may destabilize and become turbulent when a control parameter is varied. The spatio-temporal chaos observed thus stands between the deterministic chaos of confined systems and the developped turbulence of extended ones. Much theoretical and numerical work was devoted to the study of 1D phase equations[1], coupled map lattices [2,3] and cellular automata [3]. The results show that the transition to turbulence can occur via Spatio-Temporal Intermittency (STI), a fluctuating mixture of organized laminar domains and incoherent turbulent regions. Many experimental work was also devoted to 1D periodic systems. This is the case of Rayleigh-Bénard convection [4,5], directional solidification [6,7], parametric instability [8] and in the periodic front of the meniscus of a fluid between two rotating cylinders[9]. We present in this paper experimental results on the transition to turbulence in thermal convection and compare them with some numerical ones.