Editorial Type:
Article
Article Type:
Research Article

Planetary and Gravity Waves in a Polar Basin

Andrew J. Willmott Newcastle University, Newcastle upon Tyne, United Kingdom

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Estanislao Gavilan Pascual-Ahuir Newcastle University, Newcastle upon Tyne, United Kingdom

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Print Publication:
01 Jun 2017
DOI:
https://doi.org/10.1175/JPO-D-16-0253.1
Page(s):
1433–1440
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Abstract

The eigenfrequencies of freely propagating barotropic, divergent, planetary waves and gravity waves in a spherical polar cap are presented using an approximation in which full spherical geometry is retained in the derivation of the wave amplitude equation. Subsequently, the colatitude angle in the coefficients of the wave amplitude equation is fixed, thereby allowing the eigenvalue problem to be solved using analytical methods. The planetary wave frequencies are compared with published results that adopt the polar-plane approximation to solve the equivalent free-wave problem. Low-order planetary wave frequencies calculated in this study agree well with the polar-plane approximation results. The sensitivity of the wave frequencies to the choice of the fixed colatitude in the coefficients of the wave amplitude equation is discussed.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andrew J. Willmott, andrew.willmott@newcastle.ac.uk

Abstract

The eigenfrequencies of freely propagating barotropic, divergent, planetary waves and gravity waves in a spherical polar cap are presented using an approximation in which full spherical geometry is retained in the derivation of the wave amplitude equation. Subsequently, the colatitude angle in the coefficients of the wave amplitude equation is fixed, thereby allowing the eigenvalue problem to be solved using analytical methods. The planetary wave frequencies are compared with published results that adopt the polar-plane approximation to solve the equivalent free-wave problem. Low-order planetary wave frequencies calculated in this study agree well with the polar-plane approximation results. The sensitivity of the wave frequencies to the choice of the fixed colatitude in the coefficients of the wave amplitude equation is discussed.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Andrew J. Willmott, andrew.willmott@newcastle.ac.uk
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