A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography
An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for m...
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ftmdpi:oai:mdpi.com:/2311-5521/1/2/17/ 2023-08-20T04:00:59+02:00 A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography David Marshall 2016-05-27 application/pdf https://doi.org/10.3390/fluids1020017 EN eng Multidisciplinary Digital Publishing Institute Geophysical and Environmental Fluid Mechanics https://dx.doi.org/10.3390/fluids1020017 https://creativecommons.org/licenses/by/4.0/ Fluids; Volume 1; Issue 2; Pages: 17 Rossby waves ocean circulation Southern Ocean Antarctic Circumpolar Current bottom topography topographic steering Doppler shift planetary geostrophic equations Text 2016 ftmdpi https://doi.org/10.3390/fluids1020017 2023-07-31T20:53:43Z An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for material conservation of buoyancy along the sea surface and the sea floor. The mean, steady-state surface circulation follows characteristics that are intermediate to f and f / H contours, where f is the Coriolis parameter and H is the ocean depth; for realistic stratification and weak bottom currents, these characteristics are mostly zonal with weak deflections over the major topographic features. Equations are derived for linear long Rossby waves about this mean state. These are qualitatively similar to the long Rossby wave equations for a two-layer ocean, linearised about a state of rest, except that the surface characteristics in the wave equation, which dominate the propagation, follow precisely the same path as the mean surface flow. In addition to this topographic steering, it is shown that a weighted integral of the Rossby propagation term vanishes over any area enclosed by an f / H contour, which has been shown in the two-layer model to lead to Rossby waves “jumping” across the f / H contour. Finally, a nonlinear Rossby wave equation is derived as a specialisation of the result previously obtained by Rick Salmon. This consists of intrinsic westward propagation at the classical long Rossby speed, modified to account for the finite ocean depth, and a Doppler shift by the depth-mean flow. The latter dominates within the Antarctic Circumpolar Current, consistent with observed eastward propagation of sea surface height anomalies. Text Antarc* Antarctic Southern Ocean MDPI Open Access Publishing Antarctic Southern Ocean The Antarctic Fluids 1 2 17 |
institution |
Open Polar |
collection |
MDPI Open Access Publishing |
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ftmdpi |
language |
English |
topic |
Rossby waves ocean circulation Southern Ocean Antarctic Circumpolar Current bottom topography topographic steering Doppler shift planetary geostrophic equations |
spellingShingle |
Rossby waves ocean circulation Southern Ocean Antarctic Circumpolar Current bottom topography topographic steering Doppler shift planetary geostrophic equations David Marshall A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography |
topic_facet |
Rossby waves ocean circulation Southern Ocean Antarctic Circumpolar Current bottom topography topographic steering Doppler shift planetary geostrophic equations |
description |
An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for material conservation of buoyancy along the sea surface and the sea floor. The mean, steady-state surface circulation follows characteristics that are intermediate to f and f / H contours, where f is the Coriolis parameter and H is the ocean depth; for realistic stratification and weak bottom currents, these characteristics are mostly zonal with weak deflections over the major topographic features. Equations are derived for linear long Rossby waves about this mean state. These are qualitatively similar to the long Rossby wave equations for a two-layer ocean, linearised about a state of rest, except that the surface characteristics in the wave equation, which dominate the propagation, follow precisely the same path as the mean surface flow. In addition to this topographic steering, it is shown that a weighted integral of the Rossby propagation term vanishes over any area enclosed by an f / H contour, which has been shown in the two-layer model to lead to Rossby waves “jumping” across the f / H contour. Finally, a nonlinear Rossby wave equation is derived as a specialisation of the result previously obtained by Rick Salmon. This consists of intrinsic westward propagation at the classical long Rossby speed, modified to account for the finite ocean depth, and a Doppler shift by the depth-mean flow. The latter dominates within the Antarctic Circumpolar Current, consistent with observed eastward propagation of sea surface height anomalies. |
format |
Text |
author |
David Marshall |
author_facet |
David Marshall |
author_sort |
David Marshall |
title |
A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography |
title_short |
A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography |
title_full |
A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography |
title_fullStr |
A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography |
title_full_unstemmed |
A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography |
title_sort |
theoretical model of long rossby waves in the southern ocean and their interaction with bottom topography |
publisher |
Multidisciplinary Digital Publishing Institute |
publishDate |
2016 |
url |
https://doi.org/10.3390/fluids1020017 |
geographic |
Antarctic Southern Ocean The Antarctic |
geographic_facet |
Antarctic Southern Ocean The Antarctic |
genre |
Antarc* Antarctic Southern Ocean |
genre_facet |
Antarc* Antarctic Southern Ocean |
op_source |
Fluids; Volume 1; Issue 2; Pages: 17 |
op_relation |
Geophysical and Environmental Fluid Mechanics https://dx.doi.org/10.3390/fluids1020017 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.3390/fluids1020017 |
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Fluids |
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1 |
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2 |
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17 |
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1774721881425838080 |