Rayleigh-Bénard experiment in liquid helium ; frequency locking and the onset of turbulence

In a Rayleigh-Bénard experiment in liquid helium, we study the time-dependent regimes, above the onset of convection, in a parallelepipedic cell with two convective rolls of oblate cross-section α = 1.90, where α is the rolls wave number. A first frequency f 1, associated to oscillating rolls, appears for a Rayleigh number R ∼ 2 x 104, then for R ∼ 2.7 × 10 4 a second frequency f2, much smaller, is observed. Two frequency locking regimes are present, with hysteresis, for the frequency ratios f1/f2 = 6.5 and f1 /f2 = 7. The onset of turbulence germinates from the last frequency locking state for R ∼ 3.4 × 104. This transition to turbulence is triggered by the generation of the frequencies f2/2, f2/4, ... and in real time is defined by a phase-chaotic behaviour rather than by an amplitude behaviour.