Latitudinal dependence of diapycnal diffusivity in the thermocline estimated using a finescale parameterization

Authors


Abstract

[1] The spatial distribution of diapycnal diffusivity in the thermocline over a large area in the interior of the North Pacific is obtained by incorporating the finescale vertical shear of horizontal velocity measured by expendable current profilers into the empirical formula proposed by Gregg [1989]. It is clearly shown that diapycnal diffusivity in the North Pacific strongly depends on the latitude. For example, the estimated diapycnal diffusivities near the Hawaiian Ridge and the Izu-Ogasawara Ridge exceed 10−4 m2 s−1, whereas those near the Aleutian Ridge and the Emperor Seamounts are of the order of 0.1 × 10−4 m2 s−1, even though the available semidiurnal internal tidal energy is similar among all of these prominent topographic features. The observed results are consistent with the numerical prediction that the cascade of internal tidal energy down to dissipation scales is dominated by parametric subharmonic instability which is expected to occur only below 30°N.

1. Introduction

[2] Diapycnal mixing processes in the thermocline are thought to determine the strength and pattern of the global ocean overturning circulation that controls the climate over much of the earth. This is because a downward mixing of heat across the thermocline at low and middle latitudes of the North Pacific and the Indian Ocean decreases the density of cold deep waters allowing them to upwell into the upper ocean; once upwelled into the upper ocean, water can flow back to the original location of deep water formation in the North Atlantic thus closing the global overturning circulation. The intensity and distribution of diapycnal diffusivity in the ocean interior are, therefore, crucial for the exact modelling of global ocean overturning circulation.

[3] In the present study, we examine the distribution of diapycnal diffusivity in the thermocline over a large area in the interior of the North Pacific. For this purpose, we deployed 120 free-fall current profilers, expendable current profilers (XCPs) manufactured by Sippican Ocean Systems over a large area in the North Pacific, although about one fourth of the XCP probes failed to drop. The XCP measures horizontal velocity relative to an unknown but depth-independent constant by sensing the voltage drop across the instrument's insulating body induced by the motion of conducting sea-water through the earth's magnetic field [Sanford et al., 1982, 1993]. It profiles horizontal velocity from the surface down to 1600 m depth with the rms error ∼10−2 m s−1. The vertical profile of horizontal velocity observed at each location was spectrally analyzed to determine the intensity of high vertical wavenumber shear, which was then normalized by the background buoyancy frequency and incorporated into the empirical formula of Gregg [1989] to estimate diapycnal diffusivity in the thermocline. A major advantage of this method is that it takes only about 7 minutes to complete an XCP survey at each location which enables us to carry out the field observation extending over a large area within a limited available ship time.

2. Observations

[4] Field observations were carried out along the ship tracks of training vessels Oshoro-Maru (June–August, 2000 and 2001, November 2001) and Hokusei-Maru (February–March, 2001) of Hokkaido University as well as training vessel Shinyo-Maru (March, 2002) of the Tokyo University of Fisheries (Figure 1). We can find all of the ship tracks passing by the representative prominent topographic features in the North Pacific such as the Aleutian Ridge, the Emperor Seamounts, the Hawaiian Ridge, and the Izu-Ogasawara Ridge, respectively, where large-amplitude internal tides are generated by strong tide-topography interactions (Figure 1). Actually, three-dimensional numerical experiments predict that the semidiurnal internal tidal energy reaches of the order of 104 Jm−2 over the Hawaiian Ridge, the Izu-Ogasawara Ridge, and the Aleutian Ridge [Niwa and Hibiya, 2001a, 2001b].

Figure 1.

The ship tracks along which XCP observations were carried out are superimposed on the bathymetry ((A) Oshoro-Maru, July–August 2000 and 2001; (B) Hokusei-Maru, February–March 2001; (C) Oshoro-Maru, June–July 2001; (D) Oshoro-Maru, November 2001; (E) Sinyo-Maru, March 2002). Contour interval is 1000 m.

[5] The diapycnal diffusivity in the thermocline is estimated by incorporating the observed finescale vertical shear of horizontal velocity into the empirical formula proposed by Gregg [1989], namely,

equation image

where Fr102 is the squared Froude number of vertical 10 m scales, and FrGM102 is the corresponding value for the Garrett-Munk internal wave field [Garrett and Munk, 1975; Cairns and Williams, 1976] that is shown to be a latitude-independent constant. First, each velocity profile for a depth of 950–1450 m is divided into four half-overlapping 200 m depth bins so that nearly a constant buoyancy frequency can be assumed for each depth bin. The buoyancy frequency is calculated using climatological temperature and salinity data [Antonov et al., 1998; Boyer et al., 1998]. It should be noted that, owing to XCP's instrument noise, the meaningful calculation of Froude number variance is limited up to a vertical wavenumber of 0.04 cpm. Nevertheless, since Gregg's empirical formula assumes that the observed internal wave field in the deep ocean retains GM characteristics, namely, flat Froude spectrum for a wavenumber lower than 0.1 cpm except for the variability of its spectral level, we can reasonably substitute Fr252/FrGM252 for Fr102/FrGM102. The Froude power spectrum calculated for each depth bin is then integrated up to a vertical wavenumber of 0.04 cpm to yield Fr252/FrGM252.

3. Results and Discussion

[6] Figure 2 shows the estimated value of diapycnal diffusivity averaged over a depth range of 950–1450 m at each location on the ship tracks shown in Figure 1. Of special interest here is the fact that the estimated diapycnal diffusivity is strongly dependent on the latitude. As is clearly seen in Figure 2, the estimated diapycnal diffusivity in the thermocline reaches about 1.5 × 10−4 m2 s−1 near the Hawaiian Ridge and the Izu-Ogasawara Ridge, whereas it sharply drops down to about 0.2 × 10−4 m2 s−1 as the latitude exceeds 30°N. In particular, diapycnal diffusivity in the thermocline remains of the order of 0.1 × 10−4 m2 s−1 near the Aleutian Ridge and the Emperor Seamounts, even though the available semidiurnal internal tidal energy is similar among all of these prominent topographic features [Niwa and Hibiya, 2001a, 2001b]. This result strongly indicates that there exists energy cascade process in the deep ocean that is strongly latitude-dependent.

Figure 2.

Estimated value of diapycnal diffusivity averaged over a depth range of 950–1450 m at each location of field observation. Colors denote model-predicted energy of semidiurnal internal tide vertically-integrated at each location of field observation [Niwa and Hibiya, 2001a, 2001b].

[7] The above observed feature can be reasonably explained if the cascade of semidiurnal internal tidal energy down to small dissipation scales is dominated by parametric subharmonic instability that transfers energy from large scale internal waves of twice the local inertial frequency to near-inertial internal waves with a small vertical scale [McComas, 1977; McComas and Bretherton, 1977; McComas and Müller, 1981]. Actually, using a vertical two-dimensional, multi-level numerical model, Hibiya et al. [1996, 1998, 2002] demonstrated that, as the high vertical wavenumber, near-inertial current shear increases, the surrounding internal waves with large horizontal wavenumbers are efficiently Doppler shifted so that the vertical wavenumber rapidly increases and hence enhanced turbulent dissipation takes place. If semidiurnal tidal frequency is less than twice the local inertial frequency, in contrast, parametric subharmonic instability does not work so that the high vertical wavenumber, near-inertial current shear remains unaffected and no significant enhancement of turbulent dissipation takes place. This implies that, even if a large amount of semidiurnal internal tidal energy is available near the Aleutian Ridge and the Emperor Seamounts both located north of 30°N, the energy is not efficiently provided for the local diapycnal mixing processes.

[8] Traveling wind forcing along the winter storm track is thought to be another important energy source for diapycnal mixing in the thermocline. Nagasawa et al. [2000] showed that low vertical mode near-inertial internal waves excited at the winter storm track propagate equatorward down to below 20°N until their frequency is twice the local inertial frequency so that parametric subharmonic instability can transfer their energy to dissipation scales. In order to confirm this mechanism, however, we have to expand the spatial and temporal coverage of the XCP survey.

4. Concluding Remarks

[9] It is generally believed that strong diapycnal mixing in the thermocline is limited over the prominent topographic features where efficient tidal energy conversion takes place. The present study clearly shows that an additional factor, namely, the latitude of each prominent topographic feature should be taken into account when specifying the “mixing hotspots” in the world oceans.

[10] Needless to say, the conclusion of the present study is totally based on the finescale parameterization of Gregg [1989]. In order to check the validity of Gregg's empirical formula, quantitative relationship between the finescale vertical shear and dissipation rates should be examined through detailed microscale profiling and simultaneous XCP survey in these “mixing hotspots”. Incorporating the revised parameterizations of the localized strong mixing into the general circulation models, we can expect significant improvement in the ability of models to predict future climate change.

Acknowledgments

[11] The authors would like to express gratitude to the captains and the officers and crew of T/V Hokusei-Maru and T/V Oshoro-Maru of the Faculty of Fisheries of Hokkaido University as well as T/V Shinyo-Maru of the Tokyo University of Fisheries and the scientific parties on board for their help in collecting the data.

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