Numerical experiments of nonlinear energy transfer within the oceanic internal wave spectrum

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Abstract
From the fact that the Garrett‐Munk‐like (GM‐like) internal wave spectrum is maintained even in regions of weak local energy sources, it is believed that energy is continuously supplied to the local wave spectrum by internal waves propagating from source regions where they are generated by wind stress fluctuations or tide‐topography interactions. In order to examine how the energy thus supplied by propagating internal waves cascades through the local wave spectrum down to small dissipation scales, we carry out three sets of numerical experiments where the quasi‐equilibrium internal wave spectrum obtained by Hibiya et al. [1996] is perturbed with forcing applied to different parts of the low‐frequency low‐wavenumber portion. The evolution of the internal wave spectrum is examined over eight inertial periods after the forcing is applied. First, in experiment I the forcing is applied to the low‐vertical‐wavenumber inertial‐frequency (ω=f) portion of the spectrum. In this case, no significant increase or decrease of spectral intensity can be seen within the two‐dimensional wavenumber spectrum. Next, in experiment II the forcing is applied at low‐vertical wavenumbers in the frequency range of 2f<ωf. In contrast to the result of experiment I, high‐vertical‐wavenumber near‐inertial spectral values are seen to increase, exceeding the GM level as time progresses. Finally, in experiment III the forcing is applied at low‐vertical wavenumbers in the frequency range of 1.6f<ωf. Although the spectral location of the forcing is very close to that assumed in experiment II, no appreciable energy transfer to high‐vertical wavenumbers occurs in this case. From the results of these numerical experiments it is shown that the energy transfer to the small dissipation scales is dominated by parametric subharmonic instability which transfers energy from low‐vertical‐wavenumber waves with frequencies over 2f to high‐vertical‐wavenumber near‐inertial (f<ωf) waves. This supports the model for the dynamic balance of the internal wave spectrum proposed by Hibiya et al. [1996] that with the increase (or decrease) of energy supply to the local internal wave spectrum, high‐vertical‐wavenumber near‐inertial current shear is enhanced (or diminished) leading to an increase (or decrease) in the rate of energy dissipation at critical layers.