Inverse cascades in turbulence and the case of rotating flows

We first summarize briefly several properties concerning the dynamics of two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of energy to the largest accessible scale of the system. In order to study a similar phenomenon in 3D turbulence undergoing strong solid-body rotation, we test a previously developed large eddy simulation (LES) model against a high-resolution direct numerical simulation of rotating turbulence on a grid of 3072(3) points. We then describe new numerical results on the inverse energy cascade in rotating flows using this LES model and contrast the case of 2D versus 3D forcing, as well as non-helical forcing (i.e. with weak overall alignment between velocity and vorticity) versus the fully helical Beltrami case, for both deterministic and random forcing. The different scaling laws for the inverse energy cascade can be attributed to the dimensionality of the forcing, with either a k(perpendicular to)(-3) or a k(perpendicular to)(-5/3) energy spectrum of slow modes at large scales, k(perpendicular to) referring to a direction perpendicular to that of rotation. We finally invoke the role of shear in the case of a strongly anisotropic deterministic forcing, using the so-called ABC flow; in that case, a k(perpendicular to)(-5/3) is again observed for the slow modes, together with a k(-1) spectrum for the total energy ? associated with enhanced shear at a large scale [92].