Transition to turbulence via spatiotemporal intermittency in one-dimensional Rayleigh-Bénard convection

Abstract

Rayleigh-Bénard convection is studied in quasi-one-dimensional geometries. Fixed and periodic boundary conditions are imposed using a rectangular and an annular cell, respectively. The destabilization process of the homogeneous convective pattern is studied for increasing Rayleigh number scrR. The first time-dependent behaviors are given by the appearance of coupled oscillators. At larger scrR values, the spatial breakdown appears through the propagation of spatial defects, which appear to be solitary waves. This spatiotemporal destabilization is followed at higher scrR by a spatiotemporal intermittent regime, which corresponds to a dramatic decrease of the spatial coherence and to a mixing of turbulent patches within laminar domains. This last regime is studied within the frame of phase transitions. The statistical analysis evidences a second-order phase transition at least in the rectangular geometry (fixed boundary conditions), while this transition looks imperfect in the annular geometry (periodic boundary conditions). Nevertheless, the essential qualitative features shown by theoretical and numerical models are observed in both geometries. Comparison with a simple model of directed percolation shows that the imperfect nature of the transition in the annulus could be the consequence of some mechanism of self-generation of the turbulent domains. This mechanism is, however, unknown but is probably related to the influence of the boundaries.