Probing the energy cascade of convective turbulence

The existence of a buoyancy-dominated scaling range in convective turbulence is a longstanding open question. We investigate this issue by considering the scale-by-scale energy budget in direct numerical simulations of Rayleigh-Bénard convection. We try to minimize the so-called Bolgiano length scale, the length scale at which buoyancy becomes dominant for scaling. Therefore, we deliberately choose modest Rayleigh numbers Ra=2.5×10(6) and 2.5×10(7). The budget reveals that buoyant forcing, turbulent energy transfer, and dissipation are contributing significantly over a wide range of scales. Thereby neither Kolmogorov-like (balance of turbulent transfer and dissipation) nor Bolgiano-Obukhov-like scaling (balance of turbulent transfer and buoyancy) is expected in the structure functions, which indeed reveal inconclusive scaling behavior. Furthermore, we consider the calculation of the Bolgiano length scale. To account for correlations between the dissipation rates of kinetic energy and thermal variance we propose to average the Bolgiano length scale directly. This gives an estimate, which is one order of magnitude larger than the previous estimate, and actually larger than the domain itself. Rather than studying the scaling of structure functions, we propose that the use of scale-by-scale energy budgets resolving anisotropic contributions is appropriate to consider the energy cascade mechanisms in turbulent convection.