Topographic Rossby waves in a polar basin
Approximate analytical expressions for the eigenfrequencies of freely propagating, divergent, barotropic topographic Rossby waves over a step shelf are derived. The amplitude equation, that incorporates axisymmetric topography while retaining full spherical geometry, is analysed by standard asymptot...
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ftunivtasecite:oai:ecite.utas.edu.au:144636 2023-05-15T15:08:54+02:00 Topographic Rossby waves in a polar basin Bassom, AP Willmott, AJ 2020 https://doi.org/10.1017/jfm.2020.437 http://ecite.utas.edu.au/144636 en eng Cambridge Univ Press http://dx.doi.org/10.1017/jfm.2020.437 Bassom, AP and Willmott, AJ, Topographic Rossby waves in a polar basin, Journal of Fluid Mechanics, 899 Article A9. ISSN 0022-1120 (2020) [Refereed Article] http://ecite.utas.edu.au/144636 Mathematical Sciences Applied mathematics Theoretical and applied mechanics Refereed Article PeerReviewed 2020 ftunivtasecite https://doi.org/10.1017/jfm.2020.437 2021-11-22T23:17:57Z Approximate analytical expressions for the eigenfrequencies of freely propagating, divergent, barotropic topographic Rossby waves over a step shelf are derived. The amplitude equation, that incorporates axisymmetric topography while retaining full spherical geometry, is analysed by standard asymptotic methods based on the limited latitudinal extent of the polar basin as the natural small parameter. The magnitude of the planetary potential vorticity field, Π P , increases poleward in the deep basin and over the shelf. However, everywhere over the shelf Π P exceeds its deep-basin value. Consequently, the polar basin waveguide supports two families of vorticity waves; here, our concern is restricted to the study of topographic Rossby (shelf) waves. The leading-order eigenfrequencies and cross-basin eigenfunctions of these modes are derived. Moreover, the spherical geometry allows an infinite number of azimuthally propagating modes. We also discuss the corrections to these leading-order eigenfrequencies. It is noted that these corrections can be associated with planetary waves that can propagate in the opposite direction to the shelf waves. For parameter values typical of the Arctic Ocean, planetary wave modes have periods of tens of days, significantly longer than the shelf wave periods of one to five days. We suggest that observations of vorticity waves in the Beaufort Gyre with periods of tens of days reported in the refereed literature could be associated with planetary, rather than topographic, Rossby waves. Article in Journal/Newspaper Arctic Arctic Ocean eCite UTAS (University of Tasmania) Arctic Arctic Ocean Journal of Fluid Mechanics 899 |
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Open Polar |
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eCite UTAS (University of Tasmania) |
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ftunivtasecite |
language |
English |
topic |
Mathematical Sciences Applied mathematics Theoretical and applied mechanics |
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Mathematical Sciences Applied mathematics Theoretical and applied mechanics Bassom, AP Willmott, AJ Topographic Rossby waves in a polar basin |
topic_facet |
Mathematical Sciences Applied mathematics Theoretical and applied mechanics |
description |
Approximate analytical expressions for the eigenfrequencies of freely propagating, divergent, barotropic topographic Rossby waves over a step shelf are derived. The amplitude equation, that incorporates axisymmetric topography while retaining full spherical geometry, is analysed by standard asymptotic methods based on the limited latitudinal extent of the polar basin as the natural small parameter. The magnitude of the planetary potential vorticity field, Π P , increases poleward in the deep basin and over the shelf. However, everywhere over the shelf Π P exceeds its deep-basin value. Consequently, the polar basin waveguide supports two families of vorticity waves; here, our concern is restricted to the study of topographic Rossby (shelf) waves. The leading-order eigenfrequencies and cross-basin eigenfunctions of these modes are derived. Moreover, the spherical geometry allows an infinite number of azimuthally propagating modes. We also discuss the corrections to these leading-order eigenfrequencies. It is noted that these corrections can be associated with planetary waves that can propagate in the opposite direction to the shelf waves. For parameter values typical of the Arctic Ocean, planetary wave modes have periods of tens of days, significantly longer than the shelf wave periods of one to five days. We suggest that observations of vorticity waves in the Beaufort Gyre with periods of tens of days reported in the refereed literature could be associated with planetary, rather than topographic, Rossby waves. |
format |
Article in Journal/Newspaper |
author |
Bassom, AP Willmott, AJ |
author_facet |
Bassom, AP Willmott, AJ |
author_sort |
Bassom, AP |
title |
Topographic Rossby waves in a polar basin |
title_short |
Topographic Rossby waves in a polar basin |
title_full |
Topographic Rossby waves in a polar basin |
title_fullStr |
Topographic Rossby waves in a polar basin |
title_full_unstemmed |
Topographic Rossby waves in a polar basin |
title_sort |
topographic rossby waves in a polar basin |
publisher |
Cambridge Univ Press |
publishDate |
2020 |
url |
https://doi.org/10.1017/jfm.2020.437 http://ecite.utas.edu.au/144636 |
geographic |
Arctic Arctic Ocean |
geographic_facet |
Arctic Arctic Ocean |
genre |
Arctic Arctic Ocean |
genre_facet |
Arctic Arctic Ocean |
op_relation |
http://dx.doi.org/10.1017/jfm.2020.437 Bassom, AP and Willmott, AJ, Topographic Rossby waves in a polar basin, Journal of Fluid Mechanics, 899 Article A9. ISSN 0022-1120 (2020) [Refereed Article] http://ecite.utas.edu.au/144636 |
op_doi |
https://doi.org/10.1017/jfm.2020.437 |
container_title |
Journal of Fluid Mechanics |
container_volume |
899 |
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1766340167778435072 |