Nonlinear energy transfer among ocean internal waves in the wake of a moving cyclone

The nonlinear dynamics leading to the generation of superinertial internal waves in the ocean, in the wake of a cyclonic storm, is investigated by means of theoretical arguments and of numerical integration of the hydrostatic Boussinesq equations in a simplified, realistic, open-ocean setting. The velocity fields are first decomposed into internal baroclinic modes, and then the energy transfer across modes and at different frequencies is calculated analytically. The energy transfer across modes is dominated by the advection of high-mode m waves by the second- and third-mode waves (n = 2 or 3), which are the most energetic, and this results in the excitation of the l = m - 2 or m - 3 mode wave at the double-inertial frequency. The analyzed nonlinear interactions lead to a transfer of energy from near-inertial waves, directly excited by the storm, to superinertial waves, which typically propagate faster and farther than their lower-frequency parents and can lead to internal mixing even at large distances from the region of large air-sea momentum fluxes. Energy is found to flow from large to small scales as well. Thus, the double-inertial peak formation is thought to represent a small but fundamental intermediate step in the energy cascade toward dissipation.