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Wave kinetic theory for rapidly rotating flows is developed in this paperusing a rigorous application of multiple scales perturbation theory. Thegoverning equations are an asymptotically reduced set of equations that arederived from the incompressible Navier-Stokes equations. These equations areapplicable for rapidly rotating flow regimes and are best suited to describeanisotropic dynamics of rotating flows. The independent variables of theseequations inherently reside in a helical wave basis that is the most suitablebasis for inertial waves. A coupled system of equations for the two globalinvariants: \textit{energy} and \textit{helicity}, is derived by extending asimpler symmetrical system to the more general non-symmetrical helical case.This approach of deriving the kinetic equations for helicity follows naturallyby exploiting the symmetries in the system and is different from thederivations presented in earlier work of \citet{Galtier03, Galtier14} that usesmultiple correlation functions to account for the asymmetry due to helicity.Stationary solutions, including Kolmogorov solutions, for the flow invariantsare obtained as a scaling law of the anisotropic wave numbers. The scaling lawsolutions compare affirmatively with results from recent experimental andsimulation data. The theory developed in this paper pertains to the wavedynamics supported by an asymptotically reduced set of hydrodynamic equationsand therefore encompasses a different dynamical regime compared to the weakturbulence theory presented in the work of \citet{Galtier03, Galtier14}.

Multiple scales kinetic theory for rotationally constrained slow inertial waves and anisotropic dynamics