On spectral energy transfer in convective turbulence

The specific features of cascade processes in fully developed turbulence that exists against the background of a density (temperature) gradient are investigated. The gradient is either parallel (turbulence in a stably stratified medium) or anti-parallel (convective turbulence) to the gravitational force. We mainly address the question of realizability of the Obukhov-Boldgiano regime (OB), which implies a balance between buoyancy forces and nonlinear interactions in an extended part of the inertial range. There are no foolproof evidences that prove the existence of OB, although the fragments of spectra with slopes, similar to “-11/5” and “-7/5”, have been observed in some numerical simulations of convective turbulence. This paper presents a critical comparison of these results with the results obtained using a shell model, which allows us to perform simulations in a wide range of governing parameters. The shell model is introduced by generalizing a class of helical shell models to the case of buoyancy driven turbulence. It is shown that, in fully developed turbulence that is characterized by a range of scales with a constant spectral energy flux, the buoyancy forces cannot compete with nonlinear interactions and, therefore, have no impact on the inertial range dynamics. In convective turbulence, exactly these forces provide turbulence with energy, but only at the largest scales. Under conditions of stable stratification, the buoyancy forces reduce the energy of turbulent pulsations. In both cases the OB regime does not appear in the inertial range, where the Kolmogorov's “-5/3” law is established, and the temperature behaves like a passive scalar. Our simulations indicate that the previous interpretations of the observed deviations from the “-5/3” spectrum as the OB regime are wrong because they appear in the case of an insufficient separation between the buoyancy and dissipation scales.