A fractal world of cloistered waves

Access through your institution Buy or subscribe 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.

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calculated during checkout ADDITIONAL ACCESS OPTIONS: * Log in * Learn about institutional subscriptions * Read our FAQs * Contact customer support REFERENCES * Maas, L. R. M., Benielli, D.,

Sommeria, J. & Lam, F.-P. A. _Nature_ 388, 557–561 (1997). Article  ADS  CAS  Google Scholar  * Baines, P. G. _Deep-Sea Res._ 29, 307–338 (1982). Google Scholar  * Mowbray, D. E. &

Rarity, B. S. H. _J. Fluid Mech._ 28, 1–16 (1967). Google Scholar  * Pingree, R. D. & New, A. L. _Deep-Sea Res. 36 735-758 (1989);_ _J. Phys. Oceanogr._21, 28–39 (1991). Google Scholar 

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AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * CSIRO Division of Atmospheric Research, 3195, Aspendale, Australia Peter G. Baines Authors * Peter G. Baines View author publications You can

also search for this author inPubMed 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: 07 August 1997 * DOI: https://doi.org/10.1038/41429 SHARE THIS ARTICLE Anyone you share the

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