Long solitary internal waves in stable stratifications
International audience 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 t...
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ftccsdartic:oai:HAL:hal-00302313v1 2023-11-12T04:06:19+01:00 Long solitary internal waves in stable stratifications Zimmerman, W. B. Rees, J. M. Department of Chemical and Process Engineering Department of Applied Mathematics Sheffield University of Sheffield Sheffield 2004-04-14 https://hal.science/hal-00302313 https://hal.science/hal-00302313/document https://hal.science/hal-00302313/file/npg-11-165-2004.pdf en eng HAL CCSD European Geosciences Union (EGU) hal-00302313 https://hal.science/hal-00302313 https://hal.science/hal-00302313/document https://hal.science/hal-00302313/file/npg-11-165-2004.pdf info:eu-repo/semantics/OpenAccess ISSN: 1023-5809 EISSN: 1607-7946 Nonlinear Processes in Geophysics https://hal.science/hal-00302313 Nonlinear Processes in Geophysics, 2004, 11 (2), pp.165-180 [PHYS.ASTR.CO]Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO] [SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph] [SDU.STU]Sciences of the Universe [physics]/Earth Sciences info:eu-repo/semantics/article Journal articles 2004 ftccsdartic 2023-10-21T23:12:29Z International audience 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 Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) Antarctic |
institution |
Open Polar |
collection |
Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
op_collection_id |
ftccsdartic |
language |
English |
topic |
[PHYS.ASTR.CO]Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO] [SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph] [SDU.STU]Sciences of the Universe [physics]/Earth Sciences |
spellingShingle |
[PHYS.ASTR.CO]Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO] [SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph] [SDU.STU]Sciences of the Universe [physics]/Earth Sciences Zimmerman, W. B. Rees, J. M. Long solitary internal waves in stable stratifications |
topic_facet |
[PHYS.ASTR.CO]Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO] [SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph] [SDU.STU]Sciences of the Universe [physics]/Earth Sciences |
description |
International audience 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. |
author2 |
Department of Chemical and Process Engineering Department of Applied Mathematics Sheffield University of Sheffield Sheffield |
format |
Article in Journal/Newspaper |
author |
Zimmerman, W. B. Rees, J. M. |
author_facet |
Zimmerman, W. B. Rees, J. M. |
author_sort |
Zimmerman, W. B. |
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 |
HAL CCSD |
publishDate |
2004 |
url |
https://hal.science/hal-00302313 https://hal.science/hal-00302313/document https://hal.science/hal-00302313/file/npg-11-165-2004.pdf |
geographic |
Antarctic |
geographic_facet |
Antarctic |
genre |
Antarc* Antarctic Ice Shelf |
genre_facet |
Antarc* Antarctic Ice Shelf |
op_source |
ISSN: 1023-5809 EISSN: 1607-7946 Nonlinear Processes in Geophysics https://hal.science/hal-00302313 Nonlinear Processes in Geophysics, 2004, 11 (2), pp.165-180 |
op_relation |
hal-00302313 https://hal.science/hal-00302313 https://hal.science/hal-00302313/document https://hal.science/hal-00302313/file/npg-11-165-2004.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1782327405107478528 |