Instability and focusing of internal tides in the deep ocean

Oliver Buhler, Caroline J. Muller

Research output: Contribution to journalArticle

Abstract

The interaction of tidal currents with sea-floor topography results in the radiation of internal gravity waves into the ocean interior. These waves are called internal tides and their dissipation due to nonlinear wave breaking and concomitant three-dimensional turbulence could play an important role in the mixing of the abyssal ocean, and hence in controlling the large-scale ocean circulation. As part of on-going work aimed at providing a theory for the vertical distribution of wave breaking over sea-floor topography, in this paper we investigate the instability of internal tides in a very simple linear model that helps us to relate the formation of unstable regions to simple features in the sea-floor topography. For two-dimensional tides over one-dimensional topography we find that the formation of overturning instabilities is closely linked to the singularities in the topography shape and that it is possible to have stable waves at the sea floor and unstable waves in the ocean interior above. For three-dimensional tides over two-dimensional topography there is in addition an effect of geometric focusing of wave energy into localized regions of high wave amplitude, and we investigate this focusing effect in simple examples. Overall, we find that the distribution of unstable wave breaking regions can be highly non-uniform even for very simple idealized topography shapes.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalJournal of Fluid Mechanics
Volume588
DOIs
StatePublished - Oct 10 2007

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Tides
tides
oceans
Topography
topography
vertical distribution
Gravity waves
gravity waves
Turbulence
dissipation
turbulence
Radiation
radiation

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Instability and focusing of internal tides in the deep ocean. / Buhler, Oliver; Muller, Caroline J.

In: Journal of Fluid Mechanics, Vol. 588, 10.10.2007, p. 1-28.

Research output: Contribution to journalArticle

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