Rotating stratified turbulence (RST) is ubiquitous in the Universe playing a crucial role in fluids (atmosphere, Oceans) and plasmas (stars, galaxies) whereadvective non-linear interactions have to compete with the waves. One common modeling approach to RST is to tackle the problem in its entirety and construct a succession of systems with increasing degrees of complexity. Together with the use of models, one also needs to try the opposite approach: simplifying the physics and studying in detail the effects of all dimensionless parameters. It is this latter approach that will be taken here, focusing the problem on the study of the Boussinesq equations. In this framework the formation of large scale structures through inverse energy cascades and the interplay between waves and turbulence will be studied by means of direct numerical simulations (DNS) while varying the relative frequency of gravity to inertial waves, and the Reynolds number.
After introducing the main features of turbulence in fluids and plasmas, I will show how a moderate stratification in rotating stratified flows can produce agrowth of energy at large scale faster than in the purely rotating case. Using high resolution DNS (up to 2048^3 grid points) of the Boussinesq equations withrotation and stratification I will also show evidences of the simultaneous generation of large and small scales in a dual energy cascade. These numericalresults point out to the possibility of the coexistence of idealized large-scale dynamics together with the production of small scales, essential to mixing.
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