Symmetry in anisotropic rotating turbulence
The classical theory of fully developed turbulence applies to maximally symmetric states, namely, invariant under the translation and rotation group. The archetype of homogeneous turbulence with only axisymmetry is rotating turbulence. This symmetry reduction leads one to consider the most general axisymmetric "viscosity tensor" for a Newtonian fluid, which can be obtained by group theory methods. This tensor generates new turbulent effective forces on large scales, in addition to the microscopic viscous force. Finally, we use perturbation theory of the randomly forced rotating Navier-Stokes equation to derive the first order effective force, which is nondissipative and can be considered as a Coriolis-like fluctuating force.