Decay and return of internal solitary waves with rotation
Helfrich, Karl R.
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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 system. When a solitary wave solution of the non-rotating equations is used as the initial condition the wave initially decays by radiation of longer inertia-gravity waves. The radiated inertia-gravity wave always steepens, leading to the formation a secondary solitary-like wave. This decay and re-emergence process then repeats. Eventually a nearly localized wavepacket emerges. It consists of a longwave envelope and shorter, faster solitary-like waves that propagate through the envelope. The radiation from this mature state is very weak, leading to a robust, long-lived structure that may contain as much as 50% of the energy in the initial solitary wave. Interacting packets may either pass through one another, or merge to form a longer packet. The packets appear to be modulated, fully-nonlinear versions of the steadily translating quasi-cnoidal waves.
Author Posting. © The Author, 2007. This is the author's version of the work. It is posted here by permission of American Institute of Physics for personal use, not for redistribution. The definitive version was published in Physics of Fluids 19 (2007): 026601, doi:10.1063/1.2472509.
Suggested CitationPreprint: Helfrich, Karl R., "Decay and return of internal solitary waves with rotation", 2006-12-18, https://doi.org/10.1063/1.2472509, https://hdl.handle.net/1912/1553
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Grimshaw, Roger H. J.; Guo, Chuncheng; Helfrich, Karl R.; Vlasenko, Vasiliy (American Meteorological Society, 2014-04)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 ...
Ostrovsky, Lev A.; Helfrich, Karl R. (American Meteorological Society, 2019-06-13)Using a recently developed asymptotic theory of internal solitary wave propagation over a sloping bottom in a rotating ocean, some new qualitative and quantitative features of this process are analyzed for internal waves ...
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 ...