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On “A Consistent Theory for Linear Waves of the Shallow-Water Equations on a Rotating Plane in Midlatitudes”

Francis J. PoulinDepartment of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada

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Kristopher RoweDepartment of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada

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Abstract

Recently, Paldor et al. provided a consistent and unified theory for Kelvin, Poincaré (inertial–gravity), and Rossby waves in the rotating shallow-water equations (SWE). Unfortunately, the article has some errors, and the effort is made to correct them in this note. Also, the eigenvalue problem is rewritten in a dimensional form and then nondimensionalized in terms of more traditional nondimensional parameters and compared to the dispersion relations of the old and new theories. The errors in Paldor et al. are only quantitative in nature and do not alter their major results: Rossby waves can have larger phase speeds than what is predicted from the classical theory, and Rossby and Poincaré waves can be trapped near the equatorward boundary.

Corresponding author address: Francis Poulin, Department of Applied Mathematics, University of Waterloo, Ontario N2L 3G1, Canada. Email: fpoulin@uwaterloo.ca

Abstract

Recently, Paldor et al. provided a consistent and unified theory for Kelvin, Poincaré (inertial–gravity), and Rossby waves in the rotating shallow-water equations (SWE). Unfortunately, the article has some errors, and the effort is made to correct them in this note. Also, the eigenvalue problem is rewritten in a dimensional form and then nondimensionalized in terms of more traditional nondimensional parameters and compared to the dispersion relations of the old and new theories. The errors in Paldor et al. are only quantitative in nature and do not alter their major results: Rossby waves can have larger phase speeds than what is predicted from the classical theory, and Rossby and Poincaré waves can be trapped near the equatorward boundary.

Corresponding author address: Francis Poulin, Department of Applied Mathematics, University of Waterloo, Ontario N2L 3G1, Canada. Email: fpoulin@uwaterloo.ca

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