title: Weak inertial-wave turbulence theory.
abstract: A weak wave turbulence theory is established for incompressible fluids under rapid rotation using a helicity decomposition, and the kinetic equations for energy E and helicity H are derived for three-wave coupling. As expected, nonlinear interactions of inertial waves lead to two-dimensional behavior of the turbulence with a transfer of energy and helicity mainly in the direction perpendicular to the rotation axis. For such a turbulence, we find, analytically, the anisotropic spectra E approximately k(-5/2)(perpendicular)k(-1/2)(parallel), H approximately k(-3/2)(perpendicular)k(-1/2)(parallel), and we prove that the energy cascade is to small scales. At lowest order, the wave theory does not describe the dynamics of two-dimensional (2D) modes which decouples from 3D waves.
authors.affiliation: Institut d'Astrophysique Spatiale, CNRS-Université de Paris XI, Bâtiment 121, 91405 Orsay Cedex, France.
authors.forename: Sébastien
authors.initials: S
authors.lastname: Galtier