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Topographic Rossby waves in a polar basin

Published online by Cambridge University Press:  15 July 2020

Andrew P. Bassom Open the ORCID record for Andrew P. Bassom [Opens in a new window]  and
Andrew J. Willmott
Andrew P. Bassom*
Affiliation:
School of Natural Sciences, University of Tasmania, Hobart, TAS7001, Australia
Andrew J. Willmott
Affiliation:
School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, Newcastle upon TyneNE1 7RU, UK
*
†Email address for correspondence: andrew.bassom@utas.edu.au
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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, $\Pi _P$, increases poleward in the deep basin and over the shelf. However, everywhere over the shelf $\Pi _P$ 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.

JFM classification

Geophysical and Geological Flows: Topographic effects Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A9
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

REFERENCES

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