Nonlinear Disintegration of the Internal Tide

• Published in: Journal of physical oceanography Vol. 38; no. 3; pp. 686 - 701
• Main Authors: HELFRICH, Karl R, GRIMSHAW, Roger H. J
• Format: Journal Article
• Language: English
• Published: Boston, MA American Meteorological Society 01.03.2008
• Subjects: Dynamics of the ocean (upper and deep oceans); Earth, ocean, space; Exact sciences and technology; External geophysics; Farmers; Gravity waves; Mathematical models; Physics of the oceans; Solitary waves; Tidal energy; Tides; West Pacific; South China Sea; Pacific Ocean; ISEW, South China Sea; Solitary wave; Rotating flow; internal waves; Wave packet; Desintegration; mathematical models; two-layer models; Observation data; Gravity inertial wave; Wave generation; Non linear wave
• ISSN: 0022-3670; 1520-0485
• DOI: 10.1175/2007jpo3826.1

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.