  Wave kinetic theory for rapidly rotating flows is developed in this paper
using a rigorous application of multiple scales perturbation theory. The
governing equations are an asymptotically reduced set of equations that are
derived from the incompressible Navier-Stokes equations. These equations are
applicable for rapidly rotating flow regimes and are best suited to describe
anisotropic dynamics of rotating flows. The independent variables of these
equations inherently reside in a helical wave basis that is the most suitable
basis for inertial waves. A coupled system of equations for the two global
invariants: \textit{energy} and \textit{helicity}, is derived by extending a
simpler symmetrical system to the more general non-symmetrical helical case.
This approach of deriving the kinetic equations for helicity follows naturally
by exploiting the symmetries in the system and is different from the
derivations presented in earlier work of \citet{Galtier03, Galtier14} that uses
multiple correlation functions to account for the asymmetry due to helicity.
Stationary solutions, including Kolmogorov solutions, for the flow invariants
are obtained as a scaling law of the anisotropic wave numbers. The scaling law
solutions compare affirmatively with results from recent experimental and
simulation data. The theory developed in this paper pertains to the wave
dynamics supported by an asymptotically reduced set of hydrodynamic equations
and therefore encompasses a different dynamical regime compared to the weak
turbulence theory presented in the work of \citet{Galtier03, Galtier14}.
