Energy spectrum of two-dimensional isotropic rapidly rotating turbulence

In rotating turbulence, the energy spectrum with -2 exponent was initially proposed under the assumption of isotropy (Zeman 1994; Zhou 1995). However, rotation inevitably induces anisotropy. To fill the gap between theoretical assumptions and realizability, we study the turbulence of inertial waves in an idealized two-dimensional isotropic rotating turbulence system by introducing an artificial horizontal rotation. In the limit of a small Rossby number, we asymptotically derive a nonlinear amplitude equation for inertial waves which gives the energy spectrum with -2 exponent using a strong turbulence argument. This scaling is justified by numerical simulations.