Numerical simulations of internal gravity wave resonant triads

Abstract

We investigate the triadic resonance interactions using numerical simulations of freely propagating internal waves at near-inertial frequency. We force multiple combinations of normal modes at primary frequency ω0 from the left boundary of the computational domain and study the spatiotemporal evolution of the superharmonic waves. Both the resonant and off-resonant simulations show distinct peaks of energy in the higher harmonics at 2ω0,3ω0, and 4ω0 close to the forcing region. The spatial evolution of modal amplitudes shows that higher normal modes of primary wave decay faster and the higher normal modes of superharmonic waves grow faster. Away from the forcing region, these distinct peaks in the resonant simulations weaken and redistribute the energy into continuous spectra, whereas in the off-resonant simulations, these distinct peaks at superharmonic frequencies sustain throughout the domain. The off-resonant simulations also show significant energy in sub-harmonic frequencies, and we see a buildup of energy in the near-inertial frequency regime far from the forcing region. The frequency and the wavenumber spectra for resonant simulations reveal a −2 power law consistent with the Garrett–Munk spectrum (E(ω,m)∝ω−2m−2).