Long solitary internal waves in stable stratifications
Observations of internal solitary waves over an antarctic ice shelf (Rees and Rottman, 1994) demonstrate that even large amplitude disturbances have wavelengths that are bounded by simple heuristic arguments following from the Scorer parameter based on linear theory for wave trapping. Classical weak...
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ftdoajarticles:oai:doaj.org/article:e22611c471714875aeec1493afeb6a3b 2023-05-15T13:48:51+02:00 Long solitary internal waves in stable stratifications W. B. Zimmerman J. M. Rees 2004-01-01T00:00:00Z https://doaj.org/article/e22611c471714875aeec1493afeb6a3b EN eng Copernicus Publications http://www.nonlin-processes-geophys.net/11/165/2004/npg-11-165-2004.pdf https://doaj.org/toc/1023-5809 https://doaj.org/toc/1607-7946 1023-5809 1607-7946 https://doaj.org/article/e22611c471714875aeec1493afeb6a3b Nonlinear Processes in Geophysics, Vol 11, Iss 2, Pp 165-180 (2004) Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 article 2004 ftdoajarticles 2022-12-31T12:39:19Z Observations of internal solitary waves over an antarctic ice shelf (Rees and Rottman, 1994) demonstrate that even large amplitude disturbances have wavelengths that are bounded by simple heuristic arguments following from the Scorer parameter based on linear theory for wave trapping. Classical weak nonlinear theories that have been applied to stable stratifications all begin with perturbations of simple long waves, with corrections for weak nonlinearity and dispersion resulting in nonlinear wave equations (Korteweg-deVries (KdV) or Benjamin-Davis-Ono) that admit localized propagating solutions. It is shown that these theories are apparently inappropriate when the Scorer parameter, which gives the lowest wavenumber that does not radiate vertically, is positive. In this paper, a new nonlinear evolution equation is derived for an arbitrary wave packet thus including one bounded below by the Scorer parameter. The new theory shows that solitary internal waves excited in high Richardson number waveguides are predicted to have a halfwidth inversely proportional to the Scorer parameter, in agreement with atmospheric observations. A localized analytic solution for the new wave equation is demonstrated, and its soliton-like properties are demonstrated by numerical simulation. Article in Journal/Newspaper Antarc* Antarctic Ice Shelf Directory of Open Access Journals: DOAJ Articles Antarctic |
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Open Polar |
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Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 |
spellingShingle |
Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 W. B. Zimmerman J. M. Rees Long solitary internal waves in stable stratifications |
topic_facet |
Science Q Physics QC1-999 Geophysics. Cosmic physics QC801-809 |
description |
Observations of internal solitary waves over an antarctic ice shelf (Rees and Rottman, 1994) demonstrate that even large amplitude disturbances have wavelengths that are bounded by simple heuristic arguments following from the Scorer parameter based on linear theory for wave trapping. Classical weak nonlinear theories that have been applied to stable stratifications all begin with perturbations of simple long waves, with corrections for weak nonlinearity and dispersion resulting in nonlinear wave equations (Korteweg-deVries (KdV) or Benjamin-Davis-Ono) that admit localized propagating solutions. It is shown that these theories are apparently inappropriate when the Scorer parameter, which gives the lowest wavenumber that does not radiate vertically, is positive. In this paper, a new nonlinear evolution equation is derived for an arbitrary wave packet thus including one bounded below by the Scorer parameter. The new theory shows that solitary internal waves excited in high Richardson number waveguides are predicted to have a halfwidth inversely proportional to the Scorer parameter, in agreement with atmospheric observations. A localized analytic solution for the new wave equation is demonstrated, and its soliton-like properties are demonstrated by numerical simulation. |
format |
Article in Journal/Newspaper |
author |
W. B. Zimmerman J. M. Rees |
author_facet |
W. B. Zimmerman J. M. Rees |
author_sort |
W. B. Zimmerman |
title |
Long solitary internal waves in stable stratifications |
title_short |
Long solitary internal waves in stable stratifications |
title_full |
Long solitary internal waves in stable stratifications |
title_fullStr |
Long solitary internal waves in stable stratifications |
title_full_unstemmed |
Long solitary internal waves in stable stratifications |
title_sort |
long solitary internal waves in stable stratifications |
publisher |
Copernicus Publications |
publishDate |
2004 |
url |
https://doaj.org/article/e22611c471714875aeec1493afeb6a3b |
geographic |
Antarctic |
geographic_facet |
Antarctic |
genre |
Antarc* Antarctic Ice Shelf |
genre_facet |
Antarc* Antarctic Ice Shelf |
op_source |
Nonlinear Processes in Geophysics, Vol 11, Iss 2, Pp 165-180 (2004) |
op_relation |
http://www.nonlin-processes-geophys.net/11/165/2004/npg-11-165-2004.pdf https://doaj.org/toc/1023-5809 https://doaj.org/toc/1607-7946 1023-5809 1607-7946 https://doaj.org/article/e22611c471714875aeec1493afeb6a3b |
_version_ |
1766249853315186688 |