IPSL, Paris, December 19-20th, 2001
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Claude
Cambon Turbulent diffusion in rapidly rotating flows with and without stable stratification Given the large scale disparity of the turbulent eddies and the filaments of tracer material, the single-particle diffusion in rotating stratified turbulence involves complex Lagrangian and Eulerian statistics. From previous analyses, it is clear that the anisotropic diffusivity in rotating stratified turbulence involves two different effects. The first one is a direct effect of the body forces, and can be tackled by only considering the linear dynamics (or so-called Rapid Distortion Theory, RDT) of the velocity field. Non trivial results were obtained, either by connecting Lagrangian two-time correlations to their RDT Eulerian counterparts (Kaneda & Ishida, 2000, Kaneda 2000), or by computing Lagrangian statistics in a KS (Kinematic Simulation) in which the unsteadiness of the velocity field incorporates RDT linear dynamics (Nicolleau & Vassilicos, 2000, 2002). An additional effect is due to the increasingly anisotropic structuring of the velocity field itself, with the emergence of pancake or cigar structures. The latter effect is essentially nonlinear in quasi-homogeneous rotating stratified flows, and thus can be only accounted for using full DNS or nonlinear two-point closure theories (Cambon 2001).In this talk, we revisit the models and theories which make use of RDT Eulerian dynamics, with emphasis on the case of rapid rotation. As soon as the stratification is present, a plateau can be found for the square of the vertical rms excursion length, with similar scaling obtained from analytical (RDT+SCH) and KS procedures. More generally, the presence of the plateau, irrespectively of its refined scaling, can be expected from the link between the vertical displacement and the necessarily bounded potential energy. The most interesting case is rotation without stratification, since the steady velocity part identicaly vanishes and vertical rms displacement is not connected to a potential energy anymore. Accordingly, all the velocity field is affected by inertial waves, but, surprisingly, the RDT calculation using SCH does not yield a plateau , as for the stratified case, but an eventual (large-time) Brownian behaviour which follows the (short-time) ballistic one. This illustates the subtelties of the linear phase-mixing, and its strong sensitivity to the dispersion law. Similar results are obtained by KS, but the scaling in terms of Rossby and Reynolds of the large-time Brownian regime is different. |