Large-scale analysis of self-similar unstably stratified homogeneous turbulence

The large-scale properties of self-similar unstably stratified homogeneous (USH) turbulence are investigated using an eddy-damped quasi-normal markovianized approximation of the nonlinear term. This analysis shows that a special role is played by the wave vectors contained in the equatorial plane, i.e., the plane perpendicular to gravity. It is indeed in this plane that turbulent spectra reach their maxima and evolve linearly from their initial condition when their initial infrared exponent is smaller than 4. At other angles, this property is not satisfied and turbulent spectra eventually undergo an evolution dominated by nonlinear backscattering processes. The self-similar evolution of USH turbulence is also shown to be related to the properties of large scales. In particular, the asymptotic growth rate of the mixing length depends on the initial infrared exponent in the equatorial plane. Besides, the self-similar asymptotic values of the concentration and velocity correlations also depend on the properties of large scales. This allows to derive relations between the correlations and the growth rate parameter.