Nonlinear disintegration of the internal tide


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dc.contributor.author Helfrich, Karl R.
dc.contributor.author Grimshaw, Roger H. J.
dc.date.accessioned 2010-11-02T18:31:04Z
dc.date.available 2010-11-02T18:31:04Z
dc.date.issued 2008-03
dc.identifier.citation Journal of Physical Oceanography 38 (2008): 686-701 en_US
dc.identifier.uri http://hdl.handle.net/1912/4047
dc.description Author Posting. © American Meteorological Society, 2008. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 38 (2008): 686-701, doi:10.1175/2007JPO3826.1. en_US
dc.description.abstract The disintegration of a first-mode internal tide into shorter solitary-like waves is considered. Since observations frequently show both tides and waves with amplitudes beyond the restrictions of weakly nonlinear theory, the evolution is studied using a fully nonlinear, weakly nonhydrostatic two-layer theory that includes rotation. In the hydrostatic limit, the governing equations have periodic, nonlinear inertia–gravity solutions that are explored as models of the nonlinear internal tide. These long waves are shown to be robust to weak nonhydrostatic effects. Numerical solutions show that the disintegration of an initial sinusoidal linear internal tide is closely linked to the presence of these nonlinear waves. The initial tide steepens due to nonlinearity and sheds energy into short solitary waves. The disintegration is halted as the longwave part of the solution settles onto a state close to one of the nonlinear hydrostatic solutions, with the short solitary waves superimposed. The degree of disintegration is a function of initial amplitude of the tide and the properties of the underlying nonlinear hydrostatic solutions, which, depending on stratification and tidal frequency, exist only for a finite range of amplitudes (or energies). There is a lower threshold below which no short solitary waves are produced. However, for initial amplitudes above another threshold, given approximately by the energy of the limiting nonlinear hydrostatic inertia–gravity wave, most of the initial tidal energy goes into solitary waves. Recent observations in the South China Sea are briefly discussed. en_US
dc.description.sponsorship KRH was supported by a Woods Hole Oceanographic Institution Mellon Independent Study Award and ONR Grant N000140610798. en_US
dc.format.mimetype application/pdf
dc.language.iso en_US en_US
dc.publisher American Meteorological Society en_US
dc.relation.uri http://dx.doi.org/10.1175/2007JPO3826.1
dc.subject Tides en_US
dc.subject Internal waves en_US
dc.subject Solitary waves en_US
dc.subject Inertia–gravity waves en_US
dc.subject Rotation en_US
dc.title Nonlinear disintegration of the internal tide en_US
dc.type Article en_US
dc.identifier.doi 10.1175/2007JPO3826.1

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