| A statistically homogeneous three-dimensional (3D) turbulent flowis considered in a rotating frame and possibly in a stably stratified medium. Both angular velocity and mean density gradient are in thevertical direction, with constant system vorticity and Brumt Waisalafrequency. In addition to various DNS inperiodic boxes, a recent experimental study (Praud andFincham) has been performed in a very large rotating tank, giving access to much larger Reynolds numbers. The structure of isotropic turbulence is deeply altered by dominantrotation, with emergence of columnar structures (`cigar′ type), and with polarized sheets (`pancake′ type) if stratification is dominant . The mechanisms responsible for this structuring arebriefly reviewed here, and statistical theory/modelling is used, ranging fromwave-turbulence theory to EDQNM (Eddy Damped Quasi Normal Markovian).In the presence of rapid rotation, without stratification, the flowconsists of superimposed inertial waves, which are weakly coupledthrough nonlinearity. Wave-turbulence theory is really relevant toexplore a transition from 3D to 2D structure with the Rossby numberbeing the small control parameter. By contrast, the well-known Proudmantheorem only says that the slow motion is the 2D one, butcannot explain the `nonlinear′ 3D to 2D transition. Using the slow amplitudes of the eigenmodes of thelinear operator as new dependent variables, an EDQNM technique is shownto be equivalent to an Eulerian wave-turbulence theory, at least in the limit of vanishingeddy damping. The energy transfer in Fourier space reduces to surfacic integrals along the surfaces of resonant triads.The spectral density ofkinetic energy appears to be governed by a strongly anisotropic energy flux,with evolution (in term of a `slow′ time) tending to concentrate thisenergy towards horizontal wavevectors. A complete two-dimensionalisation,however, cannot be achieved, but the trend is quantified in a reliableway. In the presence of stable stratification, things are different. The wave-turbulence theory is not valid ingeneral, since the eigenmodes decomposition includes a non-wavy mode:this is the part of the toroidal velocity field which correspondsto the quasi-geostrophic mode in geophysics. Except for pure poloidal turbulence,nonlinearity does not vanish with the Froude number, and resonant inertia-gravity waves are only marginally involved. Without rotation, the initially 3D flow is shown to evolve towards the slow mode (zero frequency) of gravity waves, but this slow mode (Fourier mode related to verticalwave-vector) has nothing to do with the 2D mode, and may be consideredas 1D instead. If the flow is initially quasi-2D or forcedin a quasi-2D manner, a good candidate for explaining a partial transition2D-1D is the zig-zag instability, evidenced at length by Billand andChomaz. An alternative scenario for the transition 3D-1D is proposedhere, based on consistent EDQNM/DNS results, with no need fororganized vertical vortices in the initial data. |
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