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Complete Hamiltonian formalism for inertial waves in rotating fluids

A complete Hamiltonian formalism is suggested for inertial waves in rotating incompressible fluids. Resonance three-wave interaction processes – decay instability and confluence of two waves – are shown to play a key role in the weakly nonlinear dynamics and statistics of inertial waves in the rapid rotation case. Future applications of the Hamiltonian approach to inertial wave theory are investigated and discussed.