Yoshihiro Niwa

Three‐dimensional numerical simulation of M2 internal tides in the East China Sea

The East China Sea and adjacent seas are one of the most significant generation regions of the M 2 internal tide in the worlds oceans. In the present study, we investigate the distribution and energetics of the M 2 internal tide around the continental shelf edge in the East China Sea using a three-dimensional numerical model. The numerical experiment shows that M 2 internal tides are effectively generated over prominent topographic features such as the subsurface ridges in the Bashi/Luzon and Tokara Straits, the ridges along the Ryukyu Island chain, and the continental shelf slope in the East China Sea, the former particularly so. All of these topographic features are characterized by steep slopes at the depth of the thermocline onto which the M 2 barotropic tide is almost normally incident. The M 2 internal tides propagating away from these multiple source regions interfere with each other to create a complicated wave pattern. It is found that the calculated pattern of the M 2 internal tide agrees well with TOPEX/Poseidon altimeter observations. The conversion rate from M 2 barotropic to baroclinic energy over the whole analyzed model domain is estimated to be 35 GW. Roughly 10% of the energy in the M 2 surface tide incident on the prominent topographic features is converted to the M 2 internal tide, although about half of the M 2 internal tidal energy is subject to local dissipation in close proximity to the generation sites.

Numerical study of the spatial distribution of the M2 internal tide in the Pacific Ocean

As a first step toward numerical modeling of global internal tides, we clarify the distribution of the M 2 internal tide in the Pacific Ocean using a three-dimensional primitive equation numerical model. The numerical simulation shows that energetic internal tides are generated over the bottom topographic features in the Indonesian Archipelago, the Solomon Archipelago, the Aleutian Archipelago, and the Tuamotu Archipelago, the continental shelf slope in the East China Sea, and the mid-oceanic ridges such as the Izu-Ogasawara Ridge, the Hawaiian Ridge, the Norfolk Ridge, the Kermadec Ridge, and the Macquarie Ridge. The calculated spatial patterns of the M 2 internal tide around the Hawaiian Ridge and the Izu-Ogasawara Ridge agree well with the TOPEX/ Poseidon altimetric observation. The conversion rate from the M 2 surface to internal tide energy integrated over the whole model domain amounts to 338 GW (1 GW = 10 9 W), 84% of which are found to be generated over the prominent topographic features mentioned above. Reflecting the spatial distribution of the prominent topographic features in the Pacific Ocean, the energy level of the M 2 internal tide in the western and central Pacific is 2-3 orders of magnitude higher than that in the eastern Pacific. This remarkable asymmetry shows that extensive microstructure measurements in the western and central Pacific are indispensable to determining the representative value of diapycnal mixing rates in the global ocean.

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

Using a three-dimensional multilevel numerical model, we examine the distribution of the wind-induced near-inertial internal wave energy in the North Pacific. Energetic low vertical mode near-inertial internal waves are excited at 30°-45°N in the western and central North Pacific by traveling midlatitude storms during winter and at 10°-30°N in the western North Pacific by tropical cyclones during fall. Thus excited internal waves propagate equatorward down to 5°-15°N, where their frequencies are twice the local inertial frequencies. Parametric subharmonic instability can then transfer their energy across the local internal wave vertical wavenumber spectrum to small dissipation scales. The calculated results show that low vertical mode double-inertial frequency internal waves are very weak at the times and locations of previous microstructure measurements, which suggests that the observed value of diapycnal diffusivity of ∼10 -5 m 2 s -1 , an order of magnitude lower than required to satisfy the large-scale advective-diffusive balance of the thermohaline circulation, may not be representative.

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

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<ω<3f. 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<ω<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<ω<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.

Direct numerical simulation of the roll-off range of internal wave shear spectra in the ocean

Oceanic internal gravity waves play an important role in the dynamics of the ocean, providing a link in the overall energy cascade from large forcing scales to small dissipation scales. Quantifying the cascade of energy available for mixing processes in the ocean interior, for example, is essential to accurate modeling of the oceanic general circulation. In the present study, based on an extensive numerical model that resolves most of the internal wave spectrum, the dynamics of the process by which internal waves dissipate their energy in the deep ocean are investigated. Putting all the calculated results together, we propose here a model for the dynamic balance of the internal wave spectrum wherein a downscale energy flux into the high vertical wavenumber near-inertial portion of the spectrum is balanced by energy dissipation at critical layers formed by high vertical wavenumber near-inertial flows.

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

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. By incorporating the wind data into a simple damped slab model, predominant inertial currents are shown to be excited in the mixed layer in the northwest Pacific basin by traveling midlatitude storms during fall and winter. The multiple filter analysis demonstrates that double-inertial frequency waves as well as near-inertial frequency waves are significantly amplified in the deep ocean internal wave field during the periods strong inertial currents are excited in the mixed layer. This suggests that in addition to near-inertial frequency waves, double-inertial frequency waves are actually excited by strong atmospheric disturbances through nonlinear effects as demonstrated in the numerical experiment by Niwa and Hibiya [1997]. Double-inertial frequency waves thus excited seem to propagate over horizontal distances of the order of 1000 km from their source region while feeding their energy to the local internal wave field, consistent with the theoretical prediction based on the magnitudes of group velocity and nonlinear interaction time [Olbers, 1983].

Nonlinear processes of energy transfer from traveling hurricanes to the deep ocean internal wave field

Generation of large-scale internal waves by a hurricane traveling over the ocean with a uniform velocity is investigated by using a three-dimensional, multilevel numerical model. It is found that two distinctive kinds of internal waves are excited in the wake of the hurricane, namely, near-inertial waves, which can be explained based on the linear theory, and superinertial waves with frequencies 2ƒ0 and 3ƒ0(ƒ0 is the inertial frequency at the latitude of the hurricane track), which are generated through nonlinear effects. Our special attention is directed to the superinertial waves with frequencies 2ƒ0 and 3ƒ0 because these internal waves are considered to be efficient energy sources for small-scale mixing in the deep ocean. These superinertial waves predominantly have low-vertical-mode structures and satisfy the dispersion relation for lee waves. In areas away from the hurricane track, in particular, the double-inertial frequency waves become larger than the near-inertial waves. The nonlinear resonant triads causing the generation of such superinertial waves are examined by calculating the bispectrum, which clearly shows that the lowest-vertical-mode double-inertial frequency wave is generated efficiently through the nonlinear interaction between the high-vertical-mode near-inertial waves.

Estimates of tidal energy dissipation and diapycnal diffusivity in the Kuril Straits using TOPEX/POSEIDON altimeter data

The Kuril Straits separating the Okhotsk Sea from the North Pacific Ocean are representative regions of strong tidal mixing in the worlds oceans. In the present study, we first carry out numerical simulation of the barotropic tidal elevation field in the Okhotsk Sea using a horizontally two-dimensional primitive equation model. It is found that, to reproduce realistic tidal elevations in the Okhotsk Sea, the energy lost by the incoming barotropic tides to internal waves within the Kuril Straits should be taken into account. The numerical experiments show that the model predicted tidal elevations in the Okhotsk Sea best fit the TOPEX/POSEIDON altimeter data when we take into account the baroclinic energy conversion in the Kuril Straits ∼16 GW for the K 1 tidal constituent and ∼37 GW for the major four tidal constituents (K 1, O 1, M 2, S 2 ). For this baroclinic energy conversion, diapycnal diffusivity averaged over the whole area of the Kuril Straits is estimated to be ∼8 x 10 -4 m 2 s -1 . This value is about 1 order of magnitude less than assumed for the Kuril Straits in previous ocean general circulation models. We offer this study as a warning against using diapycnal diffusivity just as a tuning parameter to reproduce large-scale phenomena.

Bispectral Analysis of Energy Transfer within the Two-Dimensional Oceanic Internal Wave Field

Abstract Bispectral analysis of the numerically reproduced spectral responses of the two-dimensional oceanic internal wave field to the incidence of the low-mode semidiurnal internal tide is performed. At latitudes just equatorward of 30°, the low-mode semidiurnal internal tide dominantly interacts with two high-vertical-wavenumber diurnal (near inertial) internal waves, forming resonant triads of parametric subharmonic instability (PSI) type. As the high-vertical-wavenumber near-inertial energy level is raised by this interaction, the energy cascade to small horizontal and vertical scales is enhanced. Bispectral analysis thus indicates that energy in the low-mode semidiurnal internal tide is not directly transferred to small scales but via the development of high-vertical-wavenumber near-inertial current shear. In contrast, no noticeable energy cascade to high vertical wavenumbers is recognized in the bispectra poleward of ∼30° as well as equatorward of ∼25°. A new finding is that, although PSI is possib...

Assessment of turbulence closure models for resonant inertial response in the oceanic mixed layer using a large eddy simulation model

Large eddy simulation (LES) of the resonant inertial response of the upper ocean to strong wind forcing is carried out; the results are used to evaluate the performance of each of the two second-order turbulence closure models presented by Mellor and Yamada (Rev Geophys Space Phys 20:851–875, 1982) (MY) and by Nakanishi and Niino (J Meteorol Soc Jpn 87:895–912, 2009) (NN). The major difference between MY and NN is in the formulation of the stability functions and the turbulent length scale, both strongly linked with turbulent fluxes; in particular, the turbulent length scale in NN, unlike that in MY, is allowed to decrease with increasing density stratification. We find that MY underestimates and NN overestimates the development of mixed layer features, for example, the strong entrainment at the base of the oceanic mixed layer and the accompanying decrease of sea surface temperature. Considering that the stability functions in NN perform better than those in MY in reproducing the vertical structure of turbulent heat flux, we slightly modify NN to find that the discrepancy between LES and NN can be reduced by more strongly restricting the turbulent length scale with increasing density stratification.