Effect of the Prandtl number on the onset of turbulence in liquid 4He

We have performed experiments on the onset of turbulence in liquid 4He, as a function of the Prandtl number (0.4 < Pr < 0.8), for a series of cells of confined geometry with two convective rolls. For a low value of Pr the dynamic behaviour is similar to our previous studies, i.e. two frequencies followed by lock-in and subharmonic bifurcations of the lowest frequency, before the onset of turbulence. For high values of Pr a new frequency appears before onset of the Busse oscillatory instability. We associate this new regime with a change of the convective roll structure, perhaps due to the skewed varicose instability predicted by Busse, which gives a three dimensional character to the roll geometry. Various approaches to turbulence are then observed. In some cases the onset of turbulence is intermittent in time; in some others a regime with three frequencies exists before the onset of turbulence. All the results are strongly dependent on the roll wavenumber, in qualitative agreement with the Busse theory.