Skip to main content
Log in

Evaluation of spatial distribution of turbulent mixing in the central Pacific

  • Original Article
  • Published:
Journal of Oceanography Aims and scope Submit manuscript

Abstract

A long-term mean turbulent mixing in the depth range of 200–1000 m produced by breaking of internal waves across the middle and low latitudes (40°S–40°N) of the Pacific between 160°W and 140°W is examined by applying fine-scale parameterization depending on strain variance to 8-year (2005–2012) Argo float data. Results show that elevated turbulent dissipation rate (ε) is related to significant topographic regions, along the equator, and on the northern side of 20°N spanning to 24°N throughout the depth range. Two patterns of latitudinal variations of ε and the corresponding diffusivity (Kρ) for different depth ranges are confirmed: One is for 200–450 m with significant larger ε and Kρ, and the maximum values are obtained between 4°N and 6°N, where eddy kinetic energy also reaches its maximum; The other is for 350–1000 m with smaller ε and Kρ, and the maximum values are obtained near the equator, and between 18°S and 12°S in the southern hemisphere, 20°N and 22°N in the northern hemisphere. Most elevated turbulent dissipation in the depth range of 350–1000 m relates to rough bottom roughness (correlation coefficient = 0.63), excluding the equatorial area. In the temporal mean field, energy flux from surface wind stress to inertial motions is not significant enough to account for the relatively intensified turbulent mixing in the upper layer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Alford MH (2001) Internal swell generation: the spatial distribution of energy flux from the wind to mixed layers near-inertial motions. J Phys Oceanogr 31:2359–2368

    Article  Google Scholar 

  • Alford MH (2003) Improved global maps and 54-year history of wind-work on ocean inertial motions. Geophys Res Lett 30(8). https://doi.org/10.1029/2002GL016614

  • Alford M, Gregg M (2001) Near-inertial mixing: modulation of shear, strain and microstructure at low latitude. J Geophys Res 106:16947–16968

    Article  Google Scholar 

  • Alford MH, MacKinnon JA, Zhao Z, Pinkel R, Klymak J, Peacock T (2007) Internal waves across the Pacific. Geophys Res Lett 34:L24601. https://doi.org/10.1029/2007GL031566

    Article  Google Scholar 

  • Amante C, Eakins BW (2009) ETOPO1: 1 Arc-Minute Global Relief Model: procedures, data sources and analysis, NOAA Technical Memorandum NESDIS NGDC-24. National Geophysical Data Center, Boulder

    Google Scholar 

  • Cheng Lingqiao, Kitade Y (2014) Quantitative evaluation of turbulent mixing in the Central Equatorial Pacific. J Oceanogr 70:63–79. https://doi.org/10.1007/s10872-013-0213-5

    Article  Google Scholar 

  • D’Asaro E (1985) The energy flux from the wind to near-inertial motions in the mixed layer. J Phys Oceanogr 15:943–959

    Article  Google Scholar 

  • Egbert GD, Ray RD (2003) Semi-diurnal and diurnal tidal dissipation from TOPEX/Poseidon altimetry. Geophys Res Lett 30(17):1907. https://doi.org/10.1029/2003GL017676

    Article  Google Scholar 

  • Gargett AE (1990) Do we really know how to scale the turbulent kinetic energy dissipation rate ε due to breaking of oceanic internal wave? J Geophys Res 95(C9):15971–15974

    Article  Google Scholar 

  • Garrett CJR, Munk WH (1975) Space-time scales of internal waves: a progress report. J Geophys Res 80:291–297. https://doi.org/10.1029/JC080i003p00291

    Article  Google Scholar 

  • Garrett CJR, Munk WH (1979) Internal waves in the ocean. Annu Rev Fluid Mech 11:339–369

    Article  Google Scholar 

  • Gregg MC (1989) Scaling turbulent dissipation in the thermocline. J Geophys Res 94(C7):9686–9698

    Article  Google Scholar 

  • Gregg MC, Sanford TB, Winkel DP (2003) Reduced mixing from the breaking of internal waves in equatorial waters. Nature 422:513–515

    Article  Google Scholar 

  • Henyey FS, Wright J, Flatte SM (1986) Energy and action flow through the internal waves field: an eikonal approach. J Geophys Res 91(C7):8487–8495

    Article  Google Scholar 

  • Hibiya T, Nagasawa M (2004) Latitudinal dependence of diapycnal diffusivity in the thermocline estimated using a finescale parameterization. Geophys Res Lett 31:L01301. https://doi.org/10.1029/2003GL017998

    Article  Google Scholar 

  • Kalnay EM et al (1996) The NCEP/NCAR 40-year reanalysis project. Bull Am Meteorol Soc 77:437–470

    Article  Google Scholar 

  • Kunze E, Smith SGL (2004) The role of small-scale topography in turbulent mixing of the global ocean. Oceanography 17(1):55–64

    Article  Google Scholar 

  • Kunze E, Hummon JM, Chereskin TK, Thurnherr AM (2006) Global abyssal mixing inferred from lowered ADCP shear and CTD strain profiles. J Phys Oceanogr 36:1553–1576

    Article  Google Scholar 

  • McComas CH, Muller P (1981) The dynamic balance of internal waves. J Phys Oceanogr 11:970–986

    Article  Google Scholar 

  • Munk WH (1966) Abyssal recipes. Deep-Sea Res 13:707–730

    Google Scholar 

  • Munk W (1981) Internal waves and small-scale processes. In: Wunsch WBAC (eds) Evolution of physical oceanography: scientific surveys in honor of henry stommel, MIT Press, pp 264–291. https://doi.org/10.1121/1.3425741

  • Munk W, Wuncsh C (1998) Abyssal recipes II: energetics of tidal and wind mixing. Deep-Sea Res 45:1977–2010

    Article  Google Scholar 

  • Osborn TR (1980) Estimates of the local rate of vertical diffusion from dissipation measurements. J Phys Oceanogr 10:83–89

    Article  Google Scholar 

  • Polzin KL, Toole JM, Schmitt RW (1995) Finescale parameterizations of turbulent dissipation. J Phys Oceanogr 25:306–328

    Article  Google Scholar 

  • Polzin KL, Naveira Garabato AC, Huussen TN, Sloyan BM, Waterman S (2014) Finescale parameterizations of turbulent dissipation. J Geophys Res Oceans 119:1383–1419. https://doi.org/10.1002/2013JC008979

    Article  Google Scholar 

  • Watanabe M, Hibiya T (2002) Global estimates of the wind-induced energy flux to inertial motions in the surface mixed layer. Geophys Res Lett 29(8):1239. https://doi.org/10.1029/2001GL014422

    Article  Google Scholar 

  • Whalen CB, Talley LD, MacKinnon JA (2012) Spatial and temporal variability of global ocean mixing inferred from Argo profiles. Geophys Res Lett 39:L18612. https://doi.org/10.1029/2012GL053196

    Article  Google Scholar 

  • Whalen CB, MacKinnon JA, Talley LD, Waterhouse AF (2015) Estimating the mean diapycnal mixing using a finescale strain parameterization. J Phys Oceanogr 45:1174–1188. https://doi.org/10.1175/JPO-D-14-0167.1

    Article  Google Scholar 

  • Wijesekera H, Padman L, Dillon T, Levine M, Paulson C, Rinkel R (1993) The application of internal-wave dissipation models to a region of strong mixing. J Phys Oceanogr 23:269–286

    Article  Google Scholar 

  • Wu Lixin, Jing Z, Riser S, Visbeck M (2011) Seasonal and spatial variations of Southern Ocean diapycnal mixing from Argo profiling floats. Nat Geosci 4(6):363–366. https://doi.org/10.1038/NGEO1156

    Article  Google Scholar 

  • Wyrtki K, Kilonsky B (1984) Mean water and current structure during the Hawaii-to-Tahiti Shuttle Experiment. J Phys Oceanogr 14:242–254

    Article  Google Scholar 

Download references

Acknowledgements

We would like to thank Prof. Kitade Yujiro from Tokyo University of Marine Science and Technology for his helpful advices and comments. We are also grateful to the three anonymous reviewers for their constructive comments to improve this study. Argo float data were collected and made freely available by the International Argo Program and the national programs that contribute to it (http://www.argo.ucsd.edu, http://argo.jcommops.org). The Argo Program is part of the Global Ocean Observing System. NCEP Reanalysis data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, USA, from their website at http://www.esrl.noaa.gov/psd/. This work is supported by Shanghai Pujiang Program (Grant No. 15PJ1403000) and the National Natural Science Foundation of China (Grant No. 41506219).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guoping Gao.

Appendix

Appendix

The damped slab model (D’Asaro 1985).

Mixed layer currents are triggered by sea surface wind stress, which can be expressed as

$$\frac{{{\text{d}}u}}{{{\text{d}}t}} - fv = \frac{{\tau_{x} }}{H\rho } - ru,$$
(9)
$$\frac{{{\text{d}}v}}{{{\text{d}}t}} + fu = \frac{{\tau_{y} }}{H\rho } - rv,$$
(10)

where, u and v are zonal and meridional components of the mixed layer velocity, t is time, f is inertial frequency, H is the mixed layer depth, \(\tau_{x}\) and \(\tau_{y}\) are zonal and meridional components of wind stress, and r is an artificial damping constant that parameterizes the transfer of energy from the mixed layer to the deeper ocean. Equations (9) and (10) can be expressed as

$$\frac{{{\text{d}}Z}}{{{\text{d}}t}} + \omega Z = \frac{T}{H},$$
(11)

by using complex quantities

$$Z = u + iv,$$
(12)
$$T = \frac{{\left( {\tau_{x} + i\tau_{y} } \right)}}{\rho },$$
(13)
$$\omega = r + if.$$
(14)

For a steady wind, the solution of Eq. (11) is \(Z_{\text{E}} = \frac{T}{\omega H}\), which is the Ekman transport. Then, the inertial oscillations \(Z_{\text{I}} = Z - Z_{\text{E}}\) in the rest solution can be described by

$$\frac{{{\text{d}}Z_{I} }}{{{\text{d}}t}} + \omega Z_{I} = - \frac{{{\text{d}}Z_{E} }}{{{\text{d}}t}} = - \frac{{{\text{d}}\left( {\frac{T}{H}} \right)}}{{{\text{d}}t}}\frac{1}{\omega } = - \frac{{{\text{d}}t}}{{{\text{d}}t}}\frac{1}{\omega H} - \frac{{{\text{d}}(1/H)}}{{{\text{d}}t}}\frac{T}{\omega },$$
(15)

in which H changes much slower than the wind stress, thus dH/dt can be ignored.

An energy equation for the inertial motions is obtained by multiplying (15) by \(Z_{I}^{*}\), the complex conjugate of \(Z_{I}\),

$$\frac{{{\text{d}}\left| {\frac{1}{2}Z_{I} } \right|}}{{{\text{d}}t}} = - \;r|Z_{I} |^{2} - \text{Re} \left[ {\frac{{Z_{I} }}{{\omega^{*} H}}\frac{{{\text{d}}T^{*} }}{{{\text{d}}t}}} \right] = - \;r|Z_{I} |^{2} - \varPi (H),$$
(16)

where \(\varPi (H)\) is the energy flux from the wind stress into inertial motions in the mixed layer. For a short time interval \(\Delta t\) from t1 to t2, in Eq. (15), ZI2 can be solved as

$$Z_{I2} = Z_{I1} e^{ - w\Delta t} - \frac{{T_{t} }}{{H\omega^{2} }}(1 - e^{ - W\Delta t} ),$$
(17)

where \(T_{t} = \Delta T/\Delta t\). The average flux of energy transferred to the inertial motions is finally obtained by

$$\varPi = \text{Re} \left\{ {\frac{{T_{t}^{*} }}{{\Delta t|\omega |^{2} H}}\left[ {\left( {Z_{I1} + \frac{{T_{t} }}{{\omega^{2} H}}} \right)(e^{ - w\Delta t} - 1) + \frac{{T_{t} }}{\omega H}\Delta t} \right]} \right\}.$$
(18)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cheng, L., Gao, G. Evaluation of spatial distribution of turbulent mixing in the central Pacific. J Oceanogr 74, 471–483 (2018). https://doi.org/10.1007/s10872-018-0473-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10872-018-0473-1

Keywords

Navigation