Advances in Rapid Distortion Theory: From Rotating Shear Flows to the Baroclinic Instability

Abstract

The essentials of Rapid Distortion Theory (RDT) are recalled for homogeneous turbulence subjected to rotational mean flows, including its linkage to stability analysis. The latter ‘linkage’ is of particular importance from our viewpoint, since it also attracted the attention of Charles Speziale, resulting in at least two papers (Speziale et al., 1996; Salhi et al., 1997) with particular emphasis on rotating flows. New analytical solutions and related RDT results are presented for shear flows possibly including buoyancy forces, with system rotation or mean density stratification. Finally, combining shear, rotation and stratification, RDT is shown to be pertinent to revisiting the baroclinic instability. This instability results from the tilting of mean isopycnal surfaces under combined effects of vertical shear and system rotation, in a vertically (stably) stratified medium rotating around the vertical direction. In conclusion, the challenge of reproducing RDT dynamics in single-point closure models is briefly discussed, from the viewpoint of structure-based modeling (Cambon et al., 1992; Kassinos et al., 2000).