ROTATING FREE-SHEAR FLOWS .2. NUMERICAL SIMULATIONS

The three-dimensional dynamics of the coherent vortices in periodic pl anar mixing layers and in wakes subjected to solid-body rotation of ax is parallel to the basic vorticity are investigated through direct (DN S) and large-eddy simulations (LES). Initially, the flow is forced by a weak random perturbation superposed on the basic shear, the perturba tion being either quasi-two-dimensional (forced transition) or three-d imensional (natural transition). For an initial Rossby number R(o)((i) ), based on the vorticity at the inflexion point, of small modulus, th e effect of rotation is to always make the flow more two-dimensional, whatever the sense of rotation (cyclonic or anticyclonic). This is in agreement with the Taylor-Proudman theorem. In this case, the longitud inal vortices found in forced transition without rotation are suppress ed. It is shown that, in a cyclonic mixing layer, rotation inhibits th e growth of three-dimensional perturbations, whatever the value of the Rossby number. This inhibition exists also in the anticyclonic case f or \R(o)((i))\ less than or equal to 1. At moderate anticyclonic rotat ion rates (R(o)((i)) < -1), the flow is strongly destabilized. Maximum destabilization is achieved for \R(o)((i))\ approximate to 2.5, in go od agreement with the linear-stability analysis performed by Yanase et al. (1993). The layer is then composed of strong longitudinal alterna te absolute vortex tubes which are stretched by the flow and slightly inclined with respect to the streamwise direction. The vorticity thus generated is larger than in the nonrotating case. The Kelvin-Helmholtz vortices have been suppressed. The background velocity profile exhibi ts a long range of nearly constant shear whose vorticity exactly compe nsates the solid-body rotation vorticity. This is in agreement with th e phenomenological theory proposed by Lesieur, Yanase and Metais (1991 ). As expected, the stretching is more efficient in the LES than in th e DNS. A rotating wake has one side cyclonic and the other anticycloni c. For \R(o)((i))\ less than or equal to 1, the effect of rotation is to make the wake more two-dimensional. At moderate rotation rates (\R( o)((i))\ > 1), the cyclonic side is composed of Karman vortices withou t longitudinal hairpin vortices. Karman vortices have disappeared from the anticyclonic side, which behaves like the mixing layer, with inte nse longitudinal absolute hairpin vortices. Thus, a moderate rotation has produced a dramatic symmetry breaking in the wake topology. Maximu m destabilization is still observed for \R(o)((i))\ approximate to 2.5 , as in the linear theory. The paper also analyses the effect of rotat ion on the energy transfers between the mean flow and the two-dimensio nal and three-dimensional components of the field.