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

Abstract : Rayleigh-Benard 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 A. The first time-dependent behaviors are given by the appearance of coupled oscillators. At larger A values, the spatial breakdown appears through the propagation of spatial defects, which appear to be solitary waves. This spatiotemporal destabilization is followed at higher % by a spatiotem-poral 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 annu-lar 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.
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F. Daviaud, M. Bonetti, M. Dubois. Transition to turbulence via spatiotemporal intermittency in one-dimensional Rayleigh-Bénard convection. Physical Review A, American Physical Society, 1990, 42 (6), pp.3388 - 3399. ⟨10.1103/PhysRevA.42.3388⟩. ⟨cea-01374027⟩

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