Structure functions and energy transfers in a decaying rotating turbulence experiment

moisy at fast.u-psud.fr A key feature of rotating turbulence is the anisotropic transfer of energy to-wards horizontal modes, normal to the rotation axis Ω = Ωẑ, eventually driv-ing turbulence to a quasi-two-dimensional state [1, 2, 3]. While nonrotating homogeneous and isotropic turbulence shows direct energy cascade towards small scales, the energy may be transfered in homogeneous rotating turbulence both in scale and direction. In isotropic turbulence, the energy transfers are classically described in the physical space using the 3rd order structure function, S3(r) = 〈δru3〉, where δru = [u(x+ r) − u(x)] · r/r is the longitudinal velocity increment. Exact results for this quantity are S3 = − 45r in 3D turbulence, and S3 = + 32r in 2D turbulence, with the rate of energy injected in the system. The sign of S3(r) is indeed related to the direction of the energy flux: positive (resp. negative) for transfers towards larger (resp. smaller) scales. To date, no ex-act anisotropic extension of the 4/5th law has been derived for homogeneou