Nonlinear disintegration of the internal tide
MetadataShow full item record
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.
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.
Suggested CitationArticle: Helfrich, Karl R., Grimshaw, Roger H. J., "Nonlinear disintegration of the internal tide", Journal of Physical Oceanography 38 (2008): 686-701, DOI:10.1175/2007JPO3826.1, https://hdl.handle.net/1912/4047
Showing items related by title, author, creator and subject.
International marine science research projects : second inventory of international projects at Sea Grant institutions, 1990 Fenwick, Judith; Ross, David A.; Schramm, Cynthia T. (Woods Hole Oceanographic Institution, 1991-03)This inventory of marine science projects at Sea Grant institutions was completed in order to gauge the level and enhance a database of U.S./foreign collaboration in international marine research initiated at U.S. Sea ...
Frankignoul, Claude; Joyce, Terrence M. (Woods Hole Oceanographic Institution, 1981-04)The relation between internal wave variability and larger and smaller scales of motion is investigated, using the IWEX data set. To investigate the role of internal waves in the vertical diffusion of large scale momentum, ...
South China Sea internal tide/internal waves-impact on the temporal variability of horizontal array gain at 276 Hz Orr, Marshall H.; Pasewark, Bruce H.; Wolf, Stephen N.; Lynch, James F.; Schroeder, Theodore; Chiu, Ching-Sang (IEEE, 2004-10)The temporal variability of the spatial coherence of an acoustic signal received on a bottomed horizontal array has been calculated for 276-Hz narrow-band signals. A conventional plane wave beamformer was applied to the ...