Deep Ocean Internal Wave Research Articles

Eikonal Calculations for Energy Transfer in the Deep-Ocean Internal Wave Field near Mixing Hotspots

AbstractIn the proximity of mixing hotspots in the deep ocean, the observed internal wave spectra are usually distorted from the Garrett–Munk (GM) spectrum and are characterized by the high energy level E as well as a shear–strain ratio Rω quite different from that of the GM spectrum. On the basis of the eikonal theoretical model, Ijichi and Hibiya (IH) recently proposed the revised finescale parameterization of turbulent dissipation rates in the distorted internal wave field, although the vertical velocity associated with background internal waves and the strict WKB scale separation, for example, were not taken into account. To see the effects of such simplifying assumptions on the revised parameterization, this study carries out a series of eikonal calculations for energy transfer through various internal wave spectra distorted from the GM. Although the background vertical velocity and the strict WKB scale separation somewhat affect the calculated energy transfer rates, their parameter dependence is confirmed as expected; the calculated energy transfer rates ε follow the basic scaling ε ∝ E2N2f with the local buoyancy frequency N and the local inertial frequency f and exhibit strong Rω dependence quite similar to that predicted by IH.

Self-organized Criticality Model for Ocean Internal Waves

In this paper, we present a simple spring-block model for ocean internal waves based on the self-organized criticality (SOC). The oscillations of the water blocks in the model display power-law behavior with an exponent of –2 in the frequency domain, which is similar to the current and sea water temperature spectra in the actual ocean and the universal Garrett and Munk deep ocean internal wave model [Geophysical Fluid Dynamics 2 (1972) 225; J. Geophys. Res. 80 (1975) 291]. The influence of the ratio of the driving force to the spring coefficient to SOC behaviors in the model is also discussed.

Response of internal waves to 2005 Typhoon Damrey over the northwestern shelf of the South China Sea

Continuous observation of sea water temperature and current was made at Wenchang Station (19°35′N, 112°E) in 2005. The data collected indicate vigorous internal waves of both short periods and tidal and near-inertial periods. The temperature and current time series during 18–30 September were examined to describe the upper ocean internal wave field response to Typhoon Damrey (0518). The strong wind associated with the typhoon, which passed over the sea area about 45 km south of Wenchang Station on 25 September, deepened the mixed layer depth remarkably. It decreased the mixed layer temperature while increasing the deep layer temperature, and intensified the near-inertial and high-frequency fluctuations of temperature and current. Power spectra of temperature and current time series indicate significant deviations from those obtained by using the deep ocean internal wave models characterized by a power law. The frequency spectra were dominated by three energetic bands: around the inertial frequency (7.75×10−6 Hz), tidal frequencies (1.0×10−5 to 2.4×10−5 Hz), and between 1.4×10−4 and 8.3×10−4 Hz. Dividing the field data into three phases (before, during and after the typhoon), we found that the typhoon enhanced the kinetic energy in nearly all the frequency bands, especially in the surface water. The passage of Damrey made a major contribution to the horizontal kinetic energy of the total surface current variances. The vertical energy density distribution, with its peak value at the surface, was an indication that the energy injected by the strong wind into the surface current could penetrate downward to the thermocline.

Estimates of Energy Dissipation Rates in the Three-Dimensional Deep Ocean Internal Wave Field

Using the “Eikonal Approach” (Henyey et al., 1986), we estimate energy dissipation rates in the three-dimensional Garrett-Munk internal wave field. The total energy dissipation rate within the undisturbed GM internal wave field is found to be 4.34 × 10−9 W kg−1. This corresponds to a diapycnal diffusivity of about 0.3 × 10−4 m2s−1, which is less than the value 10−4 m2s−1 required to sustain the global ocean overturning circulation. Only when the high vertical wavenumber, near-inertial current shear is enhanced can diapycnal diffusivity reach ∼10−4 m2s−1. It follows that the energy supplied at low vertical wavenumbers and low frequencies is efficiently transferred to high vertical wavenumbers and near-inertial frequencies in the mixing hotspots in the real ocean.

Distribution of fine‐scale shear in the deep waters of the North Pacific obtained using expendable current profilers

Recent numerical experiments [Hibiya et al., 1996, 1998, 2002] predicted that the energy cascade across the internal wave spectrum down to small dissipation scales was under strong control by parametric subharmonic instabilities that transfer energy from the low vertical wave number, double‐inertial frequency wave band to a high vertical wave number, near‐inertial frequency wave band. To test whether or not the numerically predicted energy cascade process is actually dominant in the real deep ocean, we deployed a total of 106 expendable current profilers over a large area in the North Pacific to examine the spatial distribution of high vertical wave number (vertical wavelength ∼25 m) shear. At midlatitudes, significant enhancement of the 25 m vertical shear was found over prominent generation regions of semidiurnal internal tides such as the Hawaiian Ridge and the Izu‐Ogasawara Ridge where the semidiurnal tidal frequency exceeds twice the local inertial frequency. At high latitudes, in contrast, no significant enhancement of the 25 m vertical shear was found to occur even over another prominent generation region of semidiurnal internal tides, the Aleutian Ridge, where the semidiurnal tidal frequency is less than twice the local inertial frequency. We find that the spatial distribution of the intensity of the 25 m vertical shear correlates very well with that of the low vertical wave number, double‐inertial frequency internal wave energy numerically predicted by Nagasawa et al. [2000] and Niwa and Hibiya [2001a, 2001b]. This is the first in situ evidence for the dominant role of parametric subharmonic instability in transferring deep ocean internal wave energy down to small dissipation scales. This study provides a theoretical framework for future attempts to determine the large‐scale structure of mixing over the world's oceans.

Wind-induced internal wave dynamics near the Adriatic shelf break

Current and temperature measurements from a thermistor chain and current meter mooring were analysed to describe the near-surface internal wave field close to the middle Adriatic shelf break. Wind speed and direction from the nearby meteorological station Lastovo were analysed too, being a possible internal waves generating force. Spectral properties of currents and temperatures in the surface mixed and thermocline layers indicate strong deviations from the Garrett and Munk (Geophysical Fluid Dynamics 2 (1972) 225; Journal of Geophysical Research 80 (1975) 291) deep ocean internal wave models. The frequency spectra were dominated by three energetic bands: at 0.060 cph (near-inertial frequency), 0.080 cph (M 2 tidal frequency) and between 3 and 4 cph. Near-inertial and high-frequency (3–4 cph) internal waves were generated by wind and/or surface wind waves. The frequency band 3–4 cph of high-frequency energetic waves does not correspond to the local Brunt–Väisälä frequency (30 cph), but to the thickest constant N layer below the thermocline—Sabinin (Izvestiya Academy of Sciences, USSR, Atmospheric and Oceanic Physics, English Edition 2 (1966) 872) “resonance layer”. Near-inertial oscillations represented a major contribution to the horizontal kinetic energy accounting for about 25% (10%) of the total surface (bottom) current variances. Vertically, the clockwise current vector rotations in the surface layer are out of phase by 180° compared with those below the thermocline. The level of surface near-inertial spectral peak was very high compared to the Garrett–Munk level, because of the proximity of wind generating force, while its bandwidth was typical for mid-latitudes.

Correction to “Response of the deep ocean internal wave field to traveling midlatitude storms as observed in long‐term current measurements” by Yoshihiro Niwa and Toshiyuki Hibiya

Correction to “Response of the deep ocean internal wave field to traveling midlatitude storms as observed in long‐term current measurements” by Yoshihiro Niwa and Toshiyuki Hibiya

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.

Internal waves and tides in shallow water

The well-known Garrett and Munk description of the internal wave spectrum synthesizes many observations into a spectral model that reproduces the general features of the mid-latitude, deep-ocean internal wave field. The general applicability of this ‘‘kinematic’’ spectral model is related to the dynamic balance of the internal wave field, but the model itself includes no dynamics and is meant to represent only the average or steady-state spectrum, away from the direct influence of sources, sinks, or boundaries. In shallow water, the kinematic model is typically not appropriate, since some or all of the simplifying assumptions about the wave field may be invalidated. Variable topography, strong tidal currents, fronts, and ice cover (at high latitudes) are the principal reasons for these complications, and result in an internal wave field which varies both spatially and temporally from the steady-state kinematic description. The most straightforward way to address the inadequacy of steady-state models for shallow water acoustics experiments is direct observation of the internal wave field at the site. Profiles sufficient to define the ‘‘mean’’ or background density gradient along with time series of temperature and horizontal velocity are the most common observations.

Simultaneous spatial and temporal measurements of the internal wave field during MATE

A statistical description of the deep ocean internal wave field is presented using measurements from the Midocean Acoustic Transmission Experiment, conducted near Cobb Seamount in the NE Pacific (46°46′N, 130°47′W) during June–July 1977. The unique feature of this experiment is the variety of data obtained simultaneously from the same location: time series of temperature and velocity, and vertical and horizontal profiles of temperature. A generalized form of the Garrett‐Munk (GM) internal wave spectrum is developed and used to interpret the data. This spectral model is specified by three parameters, , t, and p (energy level, wave number bandwidth, and frequency spectral slope, respectively). The variety of measurement types permit these three model parameters to be estimated from more than one measurement. The overall best fit values to the MATE data were p = 2.7 (GM use p = 3), t = 3.1 m−1 s (equivalent to j* = 6, twice the GM value), and (within 20% of the GM level). Although significant differences were found in the values of the bandwidth (t) and spectral slope (p) from those specified by Garrett‐Munk, the deviations are consistent with the behavior expected in a random internal wave field.

Observations of internal wave reflection off sloping bottoms

Current and temperature spectra exhibit intensification and polarization near sloping bottoms over a band of frequencies centered at the local internal wave critical frequency. Examples are drawn from a variety of island, seamount, and continental slope observations. Waves propagating down from mid‐depth change energy density, wave number, and azimuth when they reflect off the bottom, providing a natural perturbation to the deep ocean interior internal wave spectrum. Deviations from linear theory are interpreted as evidence for dissipation through subsequent shear instability and/or nonlinear interaction. Topographic features appear likely to be energy sinks for internal wave energy.

Bispectra of internal waves

Abstract : Derived from the equations of motion, the bispectrum of power indicates the rate of energy transfer among components of the internal wave field. This, or any other bispectrum, can be evaluated from weak resonant interaction theory given the wave spectrum. Using the Garrett and Munk model of the deep open ocean internal wave spectrum, the bispectrum of power and the closely related auto-bispectrum of vertical displacements are evaluated numerically with the intention of providing an observational test of the weak interaction theory and its predictions. The resulting levels of the bispectra for typical deep ocean internal waves are generally too low to be observed with any statistical confidence in an experiment of reasonable length and cost. (AN)

Temperature fine structure observations in the tropical North Pacific Ocean

Temperature profiles at two locations in the tropical North Pacific Ocean (8°27′N, 150°47′W and 11°43′N, 138°23′W) are analyzed and compared with similar data from the central gyres of the Atlantic and Pacific oceans. The vertical fine structure spectra in the thermocline (300–600 m) divide into two wave number bands, each of which has a distinct slope. For 0.003 < k < 0.1 cpm the power law dependence is about k−2. For 0.1 < k < 0.5 cpm the power law is k−3. The low‐wave number band results agree with internal wave models, and comparison of our data with the other measurements supports the universality of deep ocean internal wave spectra. The high‐wave number spectra suggest that different processes are responsible for these features. Time‐lagged coherence between temperature profiles at one location separated by time lags of up to 10 hours was calculated at the 11°43′N, 138°23′W site. This coherence depended upon the wave number band. For k < 0.04 cpm the coherence had wavelike behavior; however, the semidiurnal tide appeared important. At higher wave numbers, no significant coherence was found.