Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Redistribution of energy available for ocean mixing by long-range propagation of internal waves


Ocean mixing, which affects pollutant dispersal, marine productivity and global climate1, largely results from the breaking of internal gravity waves—disturbances propagating along the ocean's internal stratification. A global map of internal-wave dissipation would be useful in improving climate models, but would require knowledge of the sources of internal gravity waves and their propagation. Towards this goal, I present here computations of horizontal internal-wave propagation from 60 historical moorings and relate them to the source terms of internal waves as computed previously2,3. Analysis of the two most energetic frequency ranges—near-inertial frequencies and semidiurnal tidal frequencies—reveals that the fluxes in both frequency bands are of the order of 1 kW m-1 (that is, 15–50% of the energy input) and are directed away from their respective source regions. However, the energy flux due to near-inertial waves is stronger in winter, whereas the tidal fluxes are uniform throughout the year. Both varieties of internal waves can thus significantly affect the space-time distribution of energy available for global mixing.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Figure 1: Hydrographic profiles, mode structure and instrument depths for a typical mooring.
Figure 2: Typical near-inertial time series.
Figure 3: Source terms and energy-flux vectors.


  1. Gregg, M. Diapycnal mixing in the thermocline. J. Geophys. Res. 92, 5249–5286 (1987)

    Article  ADS  Google Scholar 

  2. Egbert, G. D. & Ray, R. D. Significant dissipation of tidal energy in the deep ocean inferred from satellite altimeter data. Nature 405, 775–778 (2000)

    Article  ADS  CAS  Google Scholar 

  3. Alford, M. H. Improved global maps and 54-year history of wind-work on ocean inertial motions. Geophys. Res. Lett. 30(8), doi:10.1029/2002GL016614 (2000)

  4. Manabe, S. & Stouffer, R. J. Two stable equilibria of a coupled ocean-atmosphere model. J. Clim. 1, 841–866 (1988)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  6. Ganchaud, A. & Wunsch, C. Improved estimates of global ocean circulation, heat transport and mixing from hydrographic data. Nature 408, 453–456 (2000)

    Article  ADS  Google Scholar 

  7. Webb, D. J. & Suginohara, N. Vertical mixing in the ocean. Nature 409, 37–39 (2001)

    Article  ADS  CAS  Google Scholar 

  8. Wunsch, C. The work done by the wind on the oceanic general circulation. J. Phys. Oceanogr. 28, 2332–2340 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Ledwell, J. R., Watson, A. J. & Law, C. S. Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature 364, 701–703 (1993)

    Article  ADS  CAS  Google Scholar 

  11. Polzin, K. L., Toole, J. M., Ledwell, G. R. & Schmitt, R. W. Spatial variability of turbulent mixing in the abyssal ocean. Science 276, 93–96 (1997)

    Article  CAS  Google Scholar 

  12. Samelson, R. M. Large-scale circulation with locally enhanced vertical mixing. J. Phys. Oceanogr. 28, 712–726 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Gill, A. E. On the behavior of internal waves in the wake of a storm. J. Phys. Oceanogr. 14, 1129–1151 (1984)

    Article  ADS  Google Scholar 

  15. D'Asaro, E. et al. Upper-ocean inertial currents forced by a storm, I, data and comparisons with linear theory. J. Phys. Oceanogr. 25, 2909–2936 (1995)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Ray, R. D. & Mitchum, G. T. Surface manifestations of internal tides in the deep ocean: observations from altimetry and island gauges. Prog. Oceanogr. 40, 135–162 (1997)

    Article  ADS  Google Scholar 

  18. Ray, R. D. & Cartwright, D. E. Estimates of internal tide energy fluxes from TOPEX/ POSEIDON altimetry: central North Pacific. Geophys. Res. Lett. 28, 1259–1262 (2001)

    Article  ADS  Google Scholar 

  19. D'Asaro, E. A. in Proc. Dynamics of Oceanic Internal Gravity Waves II (eds Müller, P. & Henderson, D.) 451–466 (‘Aha Huliko'a Hawaiian Winter Workshop, Hawaii Institute of Geophysics, Honolulu, 1991)

    Google Scholar 

  20. Garrett, C. What is the “near-inertial” band and why is it different from the rest of the internal wave spectrum? J. Phys. Oceanogr. 31, 962–971 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  21. Levitus, S. & Boyer, T. World Ocean Atlas 1994 (NOAA Atlas NESDIS 4, US Department of Commerce, Washington DC, 1994).

  22. Thorpe, S. A. On internal wave groups. J. Phys. Oceanogr. 29, 1085–1095 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  23. Pingree, R. D. & New, A. L. Abyssal penetration and bottom reflection of internal tidal energy in the Bay of Biscay. J. Phys. Oceanogr. 21, 28–39 (1991)

    Article  ADS  Google Scholar 

  24. Dushaw, B., Cornuelle, B., Worcester, P. F., Howe, B. & Luther, D. Barotropic and baroclinic tides in the Central North Pacific Ocean determined from long-range reciprocal acoustic transmissions. J. Phys. Oceanogr. 25, 631–647 (1995)

    Article  ADS  Google Scholar 

  25. Doherty, K. W., Frye, D. E., Liberatore, S. P. & Toole, J. M. A moored profiling instrument. J. Atmos. Ocean Technol. 16, 1816–1829 (1999)

    Article  ADS  Google Scholar 

  26. St Laurent, L. & Garrett, C. The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr. 32, 2882–2899 (2001)

    Article  ADS  Google Scholar 

  27. Merrifield, M. A. & Holloway, P. E. Model estimates of M2 internal tide energetics at the Hawaiian Ridge. J. Geophys. Res. 107, doi:10.1029/2001JC000996 (2002)

  28. Garrett, C. J. R. & Munk, W. H. Space-time scales of internal waves: a progress report. J. Geophys. Res. 80, 291–297 (1975)

    Article  ADS  Google Scholar 

  29. Fu, L. L. Observations and models of inertial waves in the deep ocean. Rev. Geophys. Space Phys. 19, 141–170 (1981)

    Article  ADS  Google Scholar 

  30. Kunze, E., Rosenfield, L., Carter, G. & Gregg, M. C. Internal waves in Monterey submarine canyon. J. Phys. Oceanogr. 32, 1890–1913 (2002)

    Article  ADS  Google Scholar 

Download references


I thank E. D'Asaro, E. Kunze and C. Garrett for insights and discussions, and M. Whitmont for quality control and preparation of the mooring data. This work was supported by the Office of Naval Research Young Investigator award.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Matthew H. Alford.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Alford, M. Redistribution of energy available for ocean mixing by long-range propagation of internal waves. Nature 423, 159–162 (2003).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing