To decipher the turbulence phenomenology of turbulent thermal convection, we perform numerical simulation of RBC for Rayleigh number Ra = 1.1 x 10^11 and Prandtl number Pr = 1 on a 4096^3 grid. We observe that in the inertial range, the energy spectrum E(k) ~ k^{-5/3} and energy flux Pi(k) is a constant, consistent with the Kolmogorov's theory of fluid turbulence. We rule out the Bolgiano-Obukhov's spectrum E(k) ~ k^{-11/5} for convective turbulence due to the positive energy feed by buoyancy;this is in contrast to the negative energy feed by buoyancy in the stably stratified flows for which the Bolgiano-Obukhov theory is valid [1].
We also compute the rms values of various terms of the momentum equation of turbulent convection, and show that the acceleration of a fluid parcel is provided mainly by the pressure gradient, and the buoyancy and dissipation term are quite close to each other. In addition, we also show that the flow in convective turbulence is quite close to isotropy, consistent with the Kolmogorov's spectrum for the flow.
[1] A. Kumar, A. G. Chatterjee, and M. K. Verma, Energy spectrum of buoyancy-driven turbulence, Phys. Rev. E, 90, 023016 (2014).