Instituto de Matematicas y Fisica Fundamental,

Serrano 123, 28006 Madrid, SPAIN

E-mail: gaite@laeff.esa.es

**Symmetry in anisotropic rotating turbulence**

**Abstract:**

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.