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.

  • News & Views
  • Published:

Fluid dynamics

A fractal world of cloistered waves

Nature volume 388, pages 518–519 (1997)Cite this article

The propagation properties of internal gravity waves are much stranger than those of sound or electromagnetic waves. In particular, there is a maximum frequency that the waves may have (the buoyancy frequency); the direction in which they transmit energy (the group velocity) is perpendicular to the direction in which they propagate (the phase velocity); and in a uniformly stratified fluid, all waves of any given frequency propagate at the same angle to the horizontal, regardless of their length or structure. This last property means that if a density-stratified fluid is forced at a frequency less than the buoyancy frequency, all the wave energy must propagate at these fixed directions. This must also apply to the waves after they reflect from solid boundaries, regardless of the orientation of the reflecting boundary. If the waves happen to be generated inside a closed container that has an irregular shape, a complex and apparently messy field of motion can result. Further, the mathematical problem of determining these properties is ill posed, and is equivalent to solving a hyperbolic partial differential equation with elliptic boundary conditions. The ‘solution’ is very sensitive to the geometry of the wave rays (or characteristics) inside the container. This system has an important analogue: inertial waves (due to the Coriolis force) in rotating bodies of fluid, which have similar properties.

In geophysical fluids, the principal manifestations of the unidirectional property of internal wave propagation at a particular frequency are the internal tides in the ocean. These are internal gravity waves of tidal period, generated by the oscillatory advection of the stratified ocean over topographical features on the floor of the ocean by the surface tide forced by the Sun and the Moon. Here the internal tide propagates away from the source regions into the vastness of the ocean on rays at the required vertical angle. This mathematical problem is (mostly) well posed2, and these properties have been experimentally verified3 and well known for at least three decades. Field observations in the Bay of Biscay4 have confirmed the essential features of the wave propagation theory.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Models of attractor.
Figure 2: A wave in a bucket.

References

  1. Maas, L. R. M., Benielli, D., Sommeria, J. & Lam, F.-P. A. Nature 388, 557–561 (1997).

    Article  ADS  CAS  Google Scholar 

  2. Baines, P. G. Deep-Sea Res. 29, 307–338 (1982).

    Google Scholar 

  3. Mowbray, D. E. & Rarity, B. S. H. J. Fluid Mech. 28, 1–16 (1967).

    Google Scholar 

  4. Pingree, R. D. & New, A. L. Deep-Sea Res. 36 735-758 (1989); J. Phys. Oceanogr.21, 28–39 (1991).

    Google Scholar 

  5. Maas, L. R. M. & Lam, F.-P. J. Fluid Mech. 300, 1–41 (1995).

    Google Scholar 

  6. Heller, E. J. Nature 380, 583–584 (1996).

    Article  ADS  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CSIRO Division of Atmospheric Research, 3195, Aspendale, Australia

    Peter G. Baines

Authors
  1. Peter G. Baines
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baines, P. A fractal world of cloistered waves. Nature 388, 518–519 (1997). https://doi.org/10.1038/41429

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/41429

This article is cited by

Search

Advanced 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