Weak turbulence of short equatorial waves

We derive a normal form of nonlinear equations for short equatorial waves considered in the framework of the rotating shallow water model. We show dynamical splitting of equatorial Rossby and inertia-gravity waves. We derive an effective Hamiltonian for the short inertia-gravity waves and consider their kinetics using the weak turbulence approach. Stationary power-law energy spectra are obtained. They have different slopes for eastward and westward propagating waves due to the fact that resonant triads of inertia-gravity waves exist only in specific regions of the phase-space.