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arXiv · 2006.12596

Improved Asymptotic Expressions for the Eigenvalues of Laplace's Tidal Equations

R. H. D. Townsend
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Abstract

Laplace's tidal equations govern the angular dependence of oscillations in stars when uniform rotation is treated within the so-called traditional approximation. Using a perturbation expansion approach, I derive improved expressions for the eigenvalue associated with these equations, valid in the asymptotic limit of large spin parameter $q$. These expressions have a relative accuracy of order $q^{-3}$ for gravito-inertial modes, and $q^{-1}$ for Rossby and Kelvin modes; the corresponding absolute accuracy is of order $q^{-1}$ for all three mode types. I validate my analysis against numerical calculations, and demonstrate how it can be applied to derive formulae for the periods and eigenfunctions of Rossby modes.

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R. H. D. Townsend. 2020-07-21. Improved Asymptotic Expressions for the Eigenvalues of Laplace's Tidal Equations. https://doi.org/10.1093/mnras%2Fstaa2159

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