Skip to main content

Thank you for visiting nature.com. 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.

  • Letter
  • Published:

Resonant internal waves in fluid flow

Abstract

UNDERSTANDING the flow of a stratified fluid over an uneven bed is an important problem in hydrodynamics. Previous field experiments using acoustic imagery1–3 have enhanced our understanding of internal-wave generation mechanisms. These studies have generally concentrated on isolated topographic features that show large-amplitude long internal waves and hydraulic jumps as the flow becomes critical defined in the hydraulic sense such that a long-wave speed vanishes with respect to a fixed coordinate system. We present field observations of stratified fluid flow over a nearly periodic topographic relief which show a unique series of resonant internal waves. The observations, carried out in the Rotterdam Waterway, show the presence of internal waves with wavelengths commensurate with those of the topography of the waterway bed and amplitudes that are three to four times larger than the relief of the topography generating them. Resonant internal waves may be important in understanding the flow dynamics of stratified coastal environments and may have consequences for atmospheric flows over mountain ranges.

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

Access options

Buy this article

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

Similar content being viewed by others

References

  1. Farmer, D. M. & Smith, J. D. Deep Sea Res. 17, 239–254 (1980).

    Article  ADS  Google Scholar 

  2. Farmer, D. M. & Freeland, H. J. Prog. Oceanogr. 12, 147–220 (1983).

    Article  ADS  Google Scholar 

  3. Chereskin, T. K. J. geophys. Res. 88, 2649–2661 (1983).

    Article  ADS  Google Scholar 

  4. Long, R. R. Tellus 5, 42–58 (1953).

    Article  ADS  MathSciNet  Google Scholar 

  5. Long, R. R. Tellus 6, 97–115 (1954).

    ADS  Google Scholar 

  6. Long, R. R. Tellus 7, 342–357 (1955).

    Article  ADS  Google Scholar 

  7. Baines, P. G. J. Fluid Mech. 82, 147–159 (1977).

    Article  ADS  Google Scholar 

  8. Baines, P. G. Tellus 31, 351–371 (1979).

    Article  ADS  Google Scholar 

  9. Maxworthy, T. J. geophys. Res. 84, 338–346 (1979).

    Article  ADS  Google Scholar 

  10. Lamb, H. Hydrodynamics (Dover, New York, 1932).

    MATH  Google Scholar 

  11. Smith, R. B. J. atmos. Sci. 33, 507–519 (1976).

    Article  ADS  Google Scholar 

  12. Farmer, D. M. & Smith, J. D. in Hydrodynamics of Estuaries and Fjords (ed. Nihoul, J. C. J.) (Elsevier, Amsterdam, 1978).

    Google Scholar 

  13. Abraham, G. de Jong, P. & van Kruiningen, F. E. in Lecture Notes on Coastal and Estuarine Studies 16, (ed. van de Kreeke, J.) 6–21 (Springer, Berlin, 1986).

    Google Scholar 

  14. Pietrzak, J. D., Abraham, G. & Kranenburg, C. Stratified Flows Rep. 6, (Rijkswaterstaat, Delft Hydraulics, Delft University of Technology, 1989).

  15. Bell, T. H. J. Fluid Mech 67, 705–722 (1975).

    Article  ADS  Google Scholar 

  16. Gill, A. E. Atmosphere-Ocean Dynamics (Int. Geophys. Ser. 30) (Academic Press, New York, 1982).

    Google Scholar 

  17. New, A. & Dyer, K. R. in Physical processes in Estuaries (eds Dronkers, J. & van Leussen, W.) 239–254 (Springer, Berlin, 1988).

    Book  Google Scholar 

  18. Grimshaw, R. H. J. & Smythe, N. J. Fluid Mech. 169, 429–464 (1986).

    Article  ADS  Google Scholar 

  19. Bretherton, F. P. Q. JI. met. Soc. 95, 213–243 (1969).

    Article  ADS  Google Scholar 

  20. Smith, R. B. Adv. Geophys. 21, 87–230 (1979).

    Article  ADS  Google Scholar 

  21. Geyer, W. R. & Smith, J. D. J. phys. Oceanogr. 17, 1668–1679 (1987).

    Article  ADS  Google Scholar 

  22. Kranenburg, C. Estuar. Coastal Shelf Sci. 27, 15–32 (1988).

    Article  ADS  Google Scholar 

  23. Dyer, K. R. Sedimentology 29, 885–889 (1982).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pietrzak, J., Kranenburg, C. & Abraham, G. Resonant internal waves in fluid flow. Nature 344, 844–847 (1990). https://doi.org/10.1038/344844a0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/344844a0

Comments

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.

Search

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