Analysis of the waves/geostrophic/eddies mix in rotating turbulence

International audience ; The motivation of this work is the understanding and modeling of the interactions between waves, eddies and large-scale motion in geophysical flows. We focus here on rotating turbulent flows after a previous similar analysis of stably stratified turbulence supporting internal gravity waves 1 A fundamental question pertaining to the dynamics of the atmospheric flow concerns the interaction between winds extending over hundreds or thousands of kilometers, and smaller-scale turbulence that is forced and that contains both vortical motion, and inertial waves. The latter are important because they increase the spatial energy propagation, as an addition to turbulent transport, and produce a parallel way of cascading energy through scales down to the dissipative ones, with respect to the more classical turbulent cascade. Our aim in this work is therefore to quantitatively assess the contents of rotating turbulent flows in terms of large geostrophic modes, of eddy motion, and of inertial waves, and to evaluate the energy transfers between them. We first produce a database of rotating turbulent flows by pseudo-spectral direct numerical simulations of forced homogeneous turbulence at variable Rossby number Ro = U/(2Ωl) and Reynolds number Re = Ul/ν (U and l are velocity and length scales, Ω is the rotating rate along z, ν the kinematic viscosity), so that a parametric study can be done. We then analyze the velocity fields by developing a dedicated space-time decomposition that permits to separate the inertial waves from the rest of the motion, in a way similar to that developed in studies for different flows 2 . The decomposition relies on the dispersion relation of inertial waves that states that, for a propagation with vector k = (k x , k y , k z ), the frequency should be ω = 2Ωk z /|k|. This property permits to isolate, in a four-dimensional time-space spectral analysis, the (k, ω) modes that follow the dispersion relation, which we assign to be inertial waves, the modes at k z = 0 that we ...