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The ocean and the atmosphere, and hence the climate, are governed by multi-scale events that involve waves due to rotation and stratification interacting with nonlinear turbulent eddies. The resulting flow in the presence of such waves is complex and presents a variety of dynamical regimes that can be described, in the simplest case, by the (dry) Boussinesq equations for which four dimensionless parameters are identified a priori: the Reynolds number measuring the nonlinearity of the flow when contrasted to the viscous dissipation, the Rossby and Froude numbers defining how fast the waves in the purely rotating or purely stratified case are compared to nonlinear eddies, and finally the Prandtl number that measures the relative strength of the fluid and thermal dissipation. Other elements can determine the behavior of the flow, such as the scale of the forcing relative to the overall size of the system, the relative amount of waves versus vortices in the forcing, the presence of helicity (velocity-vorticity content) or the recovery of isotropy at small scales.
A review of recent laboratory experiments and direct numerical simulations will be presented for a variety of parameters, having in mind a few specific issues such as the enhanced intermittency of the nocturnal, stably stratified, Planetary boundary Layer or vertical mixing in the abyssal southern ocean at mid latitudes. The issue of a bi-directional constant-flux energy cascade, as observed in a variety of quasi bi-dimensional flows from superfluid turbulence to magnetohydrodynamics (in the presence of a magnetic field), will also be analyzed and put in the context of statistical mechanics of simplified systems. |