The onset of convection and turbulence in rectangular layers of normal liquid 4He

Abstract

We have carried out high-precision measurements of the heat transport in intermediate-size rectangular layers of convecting normal liquid 4He with Prandtl numbers of 0.52 and 0.70. The containers used for these experiments had horizontal dimensions, in units of the height d, of 13.4 × 5.95 (cell I) and 18.2 × 8.12 (cell II). The slopes N1 of the Nusselt curves were 0.56 and 0.70 respectively for cell I and cell II. These values are significantly lower than predictions for N1 for horizontally unbound layers, but comparable with results obtained in cylindrical containers of liquid helium with roughly the same number of convection rolls. For the two containers, the onset of the first instability after the onset of convection occurred at Rayleigh numbers R1 that were in reasonable quantitative agreement with the predictions of Busse and Clever for the skewed-varicose instability. For both containers, the transition at R1 was characterized by long transients ranging from ∼ 102 to ∼ 103 vertical-thermal-diffusion times. A decrease in the Nusselt number was also observed. As the Rayleigh number was increased above R1, a new steady state evolved and then additional transitions were observed. These transitions occurred at Rayleigh numbers labelled R2, R3,…, with a total of five transitions seen in cell I and a total of three transitions seen for cell II. The transition for each cell at R2 can be related quantitatively to the skewed-varicose instability, and the transition at R3 is associated with an oscillatory instability. For cell II, the time-dependence beginning at R3 persisted to the highest Rayleigh number studied, R = 11.7Rc. However, for container I, two more regimes of time-independent flow were observed; the last of these was at an unexpectedly high Rayleigh number of 6.7Rc. This work extends to lower Prandtl number recent studies made on moderate-size rectangular layers of convecting water and alcohol.