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

Abstract

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 (to --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 < to < 3f. In contrast to the result of experiment I, high-vertical-wavenumber nearinertial 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 < to < 2f. 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 < to < 2f) 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. IntroductionThe pattern and magnitude of the numerically reproduced general ocean circulation strongly depend on the values of eddy viscosity and diffusivity coefficients. This indicates that the evaluation of the intensity of turbulent vertical mixing at depth is crucial to accurate modeling of the large-scale general circulation [Bryan, 1987]. Mixing in the stratified ocean interior is generally considered to be associated with sporadic overturning and breaking of internal waves.The energy available for the mixing processes is originally supplied at large scales (a few tens of kilometers) and then transferred across the internal wave spectrum down to small dissipation scales ...

Spatial and temporal distribution of the wind‐induced internal wave energy available for deep water mixing in the North Pacific

“…The energy applied to the internal wave spectrum at large scales is most effectively transferred to small dissipation scales by parametric subharmonic instability (PSI) [Hibiya et al, 1998] It is believed that barotropic tidal currents interacting with bottom topography can be another important source of the mechanical energy for diapycnal mixing. In particular, semidiurnal internal tides generated at latitudes lower than 30øN are considered to be significant [Hirst, 1996;Munk, 1997], since the spectral cascade of their energy down to small dissipation scales is promoted by the PSI mechanism.…”

Response of the deep ocean internal wave field to traveling midlatitude storms as observed in long‐term current measurements

“…The distinguished properties of the low-vertical-mode, superinertial waves with frequencies over 2f are that they are believed to propagate significant horizontal distances from their source region while feeding their energy to the local internal wave field [Olbers, 1983]; the energy supplied to the local internal wave spectrum is considered to cascade down to small dissipation scales through resonant interaction mechanism called parametric subharmonic instability (PSI) [McComas and MUller, 1981;Hibiya et al, 1996Hibiya et al, , 1998]. Thus the low-vertical-mode, superinertial waves might play significant roles in diapycnal mixing in the deep ocean, whose parameterization is essential for accurate modeling of the oceanic general circulation [Bryan, 1987].…”

“…It has been demonstrated in a recent numerical experiment that double-inertial frequency internal waves may play a crucial role in diapycnal mixing processes in the deep ocean, with the energy effectively transferred across the internal wave spectrum down to small dissipation scales by nonlinear wave-wave interactions [Hibiya et al, 1998]. To examine whether or not such double-inertial frequency waves are actually generated in the real deep ocean, current meter data from long-term moorings in the northwest Pacific basin are analyzed together with global sea surface wind data.…”

Comparison of calculated energy flux of internal tides with microstructure measurements

“…Of particular importance are scattering on bottom topography and waveÁwave interaction, such as parametric subharmonic instability (PSI). For the M 2 tidal constituent, PSI is an effective mechanism equatorward of the latitude 28.88 (Hibiya et al, 1998(Hibiya et al, , 2002(Hibiya et al, , 2006(Hibiya et al, , 2007Hibiya and Nagasawa, 2004;MacKinnon and Winters, 2005;Nikurashin and Legg, 2011), which is where the BBTRE, LADDER3, and IZU measurements were conducted. A consideration of these processes is necessary for a full explanation of the widely different values of the local dissipation efficiency q found in different regions, as well as for a prediction of how the dissipation is distributed vertically.…”