Combined effect of rotation and topography on shoaling oceanic internal solitary waves
Grimshaw, Roger H. J.
Helfrich, Karl R.
MetadataShow full item record
KeywordCirculation/ Dynamics; Internal waves; Solitary waves; Models and modeling; Nonlinear models
Internal solitary waves commonly observed in the coastal ocean are often modeled by a nonlinear evolution equation of the Korteweg–de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth’s background rotation is potentially significant. The relevant extension of the Kortweg–de Vries is then the Ostrovsky equation, which for internal waves does not support a steady solitary wave solution. Recent studies using a combination of asymptotic theory, numerical simulations, and laboratory experiments have shown that the long time effect of rotation is the destruction of the initial internal solitary wave by the radiation of small-amplitude inertia–gravity waves, and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. However, in the ocean, internal solitary waves are often propagating over variable topography, and this alone can cause quite dramatic deformation and transformation of an internal solitary wave. Hence, the combined effects of background rotation and variable topography are examined. Then the Ostrovsky equation is replaced by a variable coefficient Ostrovsky equation whose coefficients depend explicitly on the spatial coordinate. Some numerical simulations of this equation, together with analogous simulations using the Massachusetts Institute of Technology General Circulation Model (MITgcm), for a certain cross section of the South China Sea are presented. These demonstrate that the combined effect of shoaling and rotation is to induce a secondary trailing wave packet, induced by enhanced radiation from the leading wave.
Author Posting. © American Meteorological Society, 2014. 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 44 (2014): 1116–1132, doi:10.1175/JPO-D-13-0194.1.
Showing items related by title, author, creator and subject.
Helfrich, Karl R.; White, Brian L. (Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union, 2010-07-15)Large-amplitude internal solitary waves in continuously stratified systems can be found by solution of the Dubreil-Jacotin-Long (DJL) equation. For finite ambient density gradients at the surface (bottom) for waves of ...
Helfrich, Karl R. (2006-12-18)The effect of rotation on the propagation of internal solitary waves is examined. Wave evolution is followed using a new rotating extension of a fully-nonlinear, weakly nonhydrostatic theory for waves in a two-layer ...
Luzzatto-Fegiz, Paolo; Helfrich, Karl R. (2014-06)We perform simultaneous coplanar measurements of velocity and density in solitary internal waves with trapped cores, as well as viscous numerical simulations. Our set-up comprises a thin stratified layer (approximately 15 ...