Modelling topographic waves in a polar basin
This study is concerned with properties of freely propagating barotropic Rossby waves in a circular polar cap, a prototype model for the Arctic Ocean. The linearised shallow-water equations are used to derive an amplitude equation for the waves in which full spherical geometry is retained. Almost by...
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ftunivtasecite:oai:ecite.utas.edu.au:154908 2023-05-15T14:29:14+02:00 Modelling topographic waves in a polar basin Cockerill, M Bassom, AP Willmott, AJ 2022 https://doi.org/10.1080/03091929.2021.1954631 http://ecite.utas.edu.au/154908 en eng Taylor & Francis http://dx.doi.org/10.1080/03091929.2021.1954631 Cockerill, M and Bassom, AP and Willmott, AJ, Modelling topographic waves in a polar basin, Geophysical and Astrophysical Fluid Dynamics, 116 pp. 1-19. ISSN 1029-0419 (2022) [Refereed Article] http://ecite.utas.edu.au/154908 Mathematical Sciences Applied mathematics Theoretical and applied mechanics Refereed Article PeerReviewed 2022 ftunivtasecite https://doi.org/10.1080/03091929.2021.1954631 2023-02-13T23:17:07Z This study is concerned with properties of freely propagating barotropic Rossby waves in a circular polar cap, a prototype model for the Arctic Ocean. The linearised shallow-water equations are used to derive an amplitude equation for the waves in which full spherical geometry is retained. Almost by definition, polar basin dynamics are confined to regions of limited latitudinal extent and this provides a natural small scale which can underpin a rational asymptotic analysis of the amplitude equation. The coefficients of this equation depend on the topography of the basin and, as a simple model of the Arctic basin, we assume that the basin interior is characterised by a constant depth, surrounded by a continental shelf-slope the depth of which has algebraic dependence on co-latitude. Isobaths are therefore a family of concentric circles with centre at the pole. On the shelf and slope regions the leading order amplitude equation is of straightforward Euler type. Asymptotic values of the wave frequencies are derived and these are compared to values computed directly from the full amplitude equation. It is shown that the analytic results are in very good accord with the numerical predictions. Further simulations show that the properties of the waves are not particularly sensitive to the precise details of the underlying topography; this is reassuring as it is difficult to faithfully represent the shelf topography using simple mathematical functions. Article in Journal/Newspaper Arctic Basin Arctic Arctic Ocean eCite UTAS (University of Tasmania) Arctic Arctic Ocean Geophysical & Astrophysical Fluid Dynamics 116 1 1 19 |
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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 Cockerill, M Bassom, AP Willmott, AJ Modelling topographic waves in a polar basin |
topic_facet |
Mathematical Sciences Applied mathematics Theoretical and applied mechanics |
description |
This study is concerned with properties of freely propagating barotropic Rossby waves in a circular polar cap, a prototype model for the Arctic Ocean. The linearised shallow-water equations are used to derive an amplitude equation for the waves in which full spherical geometry is retained. Almost by definition, polar basin dynamics are confined to regions of limited latitudinal extent and this provides a natural small scale which can underpin a rational asymptotic analysis of the amplitude equation. The coefficients of this equation depend on the topography of the basin and, as a simple model of the Arctic basin, we assume that the basin interior is characterised by a constant depth, surrounded by a continental shelf-slope the depth of which has algebraic dependence on co-latitude. Isobaths are therefore a family of concentric circles with centre at the pole. On the shelf and slope regions the leading order amplitude equation is of straightforward Euler type. Asymptotic values of the wave frequencies are derived and these are compared to values computed directly from the full amplitude equation. It is shown that the analytic results are in very good accord with the numerical predictions. Further simulations show that the properties of the waves are not particularly sensitive to the precise details of the underlying topography; this is reassuring as it is difficult to faithfully represent the shelf topography using simple mathematical functions. |
format |
Article in Journal/Newspaper |
author |
Cockerill, M Bassom, AP Willmott, AJ |
author_facet |
Cockerill, M Bassom, AP Willmott, AJ |
author_sort |
Cockerill, M |
title |
Modelling topographic waves in a polar basin |
title_short |
Modelling topographic waves in a polar basin |
title_full |
Modelling topographic waves in a polar basin |
title_fullStr |
Modelling topographic waves in a polar basin |
title_full_unstemmed |
Modelling topographic waves in a polar basin |
title_sort |
modelling topographic waves in a polar basin |
publisher |
Taylor & Francis |
publishDate |
2022 |
url |
https://doi.org/10.1080/03091929.2021.1954631 http://ecite.utas.edu.au/154908 |
geographic |
Arctic Arctic Ocean |
geographic_facet |
Arctic Arctic Ocean |
genre |
Arctic Basin Arctic Arctic Ocean |
genre_facet |
Arctic Basin Arctic Arctic Ocean |
op_relation |
http://dx.doi.org/10.1080/03091929.2021.1954631 Cockerill, M and Bassom, AP and Willmott, AJ, Modelling topographic waves in a polar basin, Geophysical and Astrophysical Fluid Dynamics, 116 pp. 1-19. ISSN 1029-0419 (2022) [Refereed Article] http://ecite.utas.edu.au/154908 |
op_doi |
https://doi.org/10.1080/03091929.2021.1954631 |
container_title |
Geophysical & Astrophysical Fluid Dynamics |
container_volume |
116 |
container_issue |
1 |
container_start_page |
1 |
op_container_end_page |
19 |
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1766303299565256704 |