The effect of tilt on turbulent thermal convection for a heated soap bubble

Abstract

We use DNS to explore the effect of tilt on two-dimensional turbulent thermal convection on a half-soap bubble that is heated at its equator. In the DNS, the bubble is tilted by an angle δ∈[0o,90o], the Rayleigh number is varied between Ra∈[3*106, 3*109]. The DNS reveals two qualitatively different flow regimes: the dynamic plume regime (DPR) and the stable plume regime (SPR). In the DPR, small dynamic plumes constantly emerge from random locations on the equator and dissipate on the bubble. In the SPR, the flow is dominated by a single large and stable plume rising from the lower edge of the bubble. The scaling behaviour of the Nusselt number and Reynolds number are different in these two regimes, with Nu∝Ra0.3 for the DPR and Nu∝Ra0.24 for the SPR. Concerning Re, the scaling in the DPR lies between Re∝Ra0.48 and Re∝Ra0.53 depending on Ra and δ, while in the SPR, the scaling lies between Re∝Ra0.44 and Re∝Ra0.45 depending on δ. The turbulent thermal and kinetic energy dissipation rates (εT' and εu', respectively) are also very different in the DPR and SPR. The PDFs of the normalized logεT' and logεu' are close to a Gaussian PDF for small fluctuations, but deviate considerably from a Gaussian at large fluctuations in the DPR. In the SPR, the PDFs of normalized logεT' and logεu' deviate considerably from a Gaussian PDF even for small values. The globally averaged thermal energy dissipation rate due to the mean temperature field was shown to exhibit different scaling.