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

We use direct numerical simulation (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 delta is an element of [0 degrees, 901, the Rayleigh number is varied between Ra is an element of [3 x 10(6), 3 x 10(9)], and the Prandlt number is fixed at Pr = 7. 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 behavior of the Nusselt number Nu and Reynolds number Re is different in these two regimes, with Nu proportional to Re-0.3 for the DPR and Nu proportional to Ra-0.24 for the SPR Concerning Re, the scaling in the DPR lies between Re proportional to Ra-0.48 and Re proportional to Ra-0.53 depending on Ra and delta, while in the SPR, the scaling lies between Re proportional to Ra-0.44 and Re proportional to Ra-0.45 depending on delta. The turbulent thermal and kinetic energy dissipation rates (epsilon(T') and epsilon(u'), respectively) are also very different in the DPR and SPR The probability density functions (PDF) of the normalized log epsilon(T') and log epsilon(u') are close to a Gaussian PDF for small fluctuations but deviate considerably from a Gaussian at large fluctuations in the DPFt. In the SPR, the PDFs of normalized log epsilon(T') and log epsilon(u') 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 the scaling < T >)> (R) proportional to Ra-0.23 in the DPR and < T >)> (R) proportional to Ra-0.28 in the SPR. The globally averaged kinetic energy dissipation rate due to the mean velocity field is shown to exhibit the scaling < u >)> (R) proportional to Ra-0.47 in the DPR (the exponent reduces from 0.47 to 0.43 as delta is increased up to 30 degrees). In the SPR, the behavior changes considerably to < u >)> (R) proportional to Ra-0.27. For the turbulent dissipation rates, the results indicate the scaling (R) proportional to Ra-0.18, and (R) proportional to Ra-0.28 in the DPR. However, the dependencies of (R) and (R) on Ra cannot be described by power-laws in the SPR. Published under an exclusive license by NP Publishing.

Automated summary

This study investigates the effect of tilt on two-dimensional turbulent thermal convection using direct numerical simulation. The results show that the tilt angle and Rayleigh number have significant effects on the flow patterns and characteristics.