Nonlinear Processes in Geophysics
Abstract. 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. Clas...
Main Authors: | , |
---|---|
Other Authors: | |
Format: | Text |
Language: | English |
Published: |
2003
|
Subjects: | |
Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.371.981 http://hal.archives-ouvertes.fr/docs/00/30/23/13/PDF/npg-11-165-2004.pdf |
id |
ftciteseerx:oai:CiteSeerX.psu:10.1.1.371.981 |
---|---|
record_format |
openpolar |
spelling |
ftciteseerx:oai:CiteSeerX.psu:10.1.1.371.981 2023-05-15T14:01:15+02:00 Nonlinear Processes in Geophysics W. B. Zimmerman J. M. Rees The Pennsylvania State University CiteSeerX Archives 2003 application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.371.981 http://hal.archives-ouvertes.fr/docs/00/30/23/13/PDF/npg-11-165-2004.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.371.981 http://hal.archives-ouvertes.fr/docs/00/30/23/13/PDF/npg-11-165-2004.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://hal.archives-ouvertes.fr/docs/00/30/23/13/PDF/npg-11-165-2004.pdf text 2003 ftciteseerx 2016-01-08T01:21:17Z Abstract. 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. 1 Text Antarc* Antarctic Ice Shelf Unknown Antarctic |
institution |
Open Polar |
collection |
Unknown |
op_collection_id |
ftciteseerx |
language |
English |
description |
Abstract. 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. 1 |
author2 |
The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
W. B. Zimmerman J. M. Rees |
spellingShingle |
W. B. Zimmerman J. M. Rees Nonlinear Processes in Geophysics |
author_facet |
W. B. Zimmerman J. M. Rees |
author_sort |
W. B. Zimmerman |
title |
Nonlinear Processes in Geophysics |
title_short |
Nonlinear Processes in Geophysics |
title_full |
Nonlinear Processes in Geophysics |
title_fullStr |
Nonlinear Processes in Geophysics |
title_full_unstemmed |
Nonlinear Processes in Geophysics |
title_sort |
nonlinear processes in geophysics |
publishDate |
2003 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.371.981 http://hal.archives-ouvertes.fr/docs/00/30/23/13/PDF/npg-11-165-2004.pdf |
geographic |
Antarctic |
geographic_facet |
Antarctic |
genre |
Antarc* Antarctic Ice Shelf |
genre_facet |
Antarc* Antarctic Ice Shelf |
op_source |
http://hal.archives-ouvertes.fr/docs/00/30/23/13/PDF/npg-11-165-2004.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.371.981 http://hal.archives-ouvertes.fr/docs/00/30/23/13/PDF/npg-11-165-2004.pdf |
op_rights |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
_version_ |
1766270845427122176 |