Homogeneous Rotating Turbulence: Inverse Energy Cascade and the Dissipation Scaling Law

Using direct numerical simulations, this thesis studies primarily fundamental aspects of homogeneous rotating turbulence. Within this context, we first investigate the transition from a split to a forward kinetic energy cascade system with a parametric study covering large aspect ratio domains, which are in the direction of rotation up to 340 times larger than the initial eddy size, and a broad range of rotation rates. This unprecedented database shows that, for fixed geometrical dimensions, the Rossby number governs the amount of energy that cascades to large scales, whereas, for a fixed Rossby number, the control parameter is given by the product between domain size along the rotation axis and forcing wavenumber. Second, we quantify the growth rate of the columnar eddies typical of rotating flows and seek for a scaling law for the energy dissipation rate. Our results indicate that the growth rate of the columnar eddies varies exponentially with the Rossby number, while, for the dissipation scaling law, an analysis based on timescales yields to a power law dependence on the Rossby number. Additionally, we also examine an inertia-gravity wave breaking in the middle-upper mesosphere. We show that optimal perturbations lead to an almost instantaneous wave breaking and secondary bursts of turbulence, a process marked by the formation of fine flow structures around the wave's least stable point. Further, we find that during the breaking events the energy dissipation rate tends to be an isotropic tensor and the local energy transfer, which is predominantly from mean to fluctuating field, is in balance with the pseudo kinetic energy dissipation rate. The latter is relevant to atmospheric flows and a case where rotation and stratification effects coexist.