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Topographic Rossby waves in a polar basin

Bassom, AP ORCID: 0000-0003-3275-7801 and Willmott, AJ 2020 , 'Topographic Rossby waves in a polar basin' , Journal of Fluid Mechanics, vol. 899 , pp. 1-12 , doi: 10.1017/jfm.2020.437.

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Abstract

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, ΠP , increases poleward in the deep basin and over the shelf. However, everywhere over the shelf ΠP 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.

Item Type: Article
Authors/Creators:Bassom, AP and Willmott, AJ
Keywords: topographic effects, waves in rotating fluids
Journal or Publication Title: Journal of Fluid Mechanics
Publisher: Cambridge Univ Press
ISSN: 0022-1120
DOI / ID Number: 10.1017/jfm.2020.437
Copyright Information:

Copyright 2020 The Authors

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