Notes on obtaining the eigenvalues of Laplace's tidal equation

Details Notes on obtaining the eigenvalues of Laplace's tidal equation Notes on obtaining the eigenvalues of Laplace's tidal equation

Dec 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981p%26ss...29.1339g&link_type=abstract

Planetary and Space Science, vol. 29, Dec. 1981, p. 1339-1344.

Other

4

Atmospheric Tides, Earth Tides, Eigenvalues, Laplace Equation, Rotating Spheres, Traveling Waves, Earth Rotation, Eigenvectors, Iterative Solution, Legendre Functions, Periodic Variations, Spherical Harmonics, Stream Functions (Fluids), Tidal Waves

Scientific paper

The various forms that have been obtained for the recurrence relation from which the eigenvalues of Laplace's tidal equation may be obtained are reviewed. The forms are shown to be analytically consistent and are discussed in relation to their subsequent numerical evaluation. It is noted that, by determining eigenvalues of equivalent depth for a given frequency of oscillation instead of the other way around, the problem becomes a straightforward one of matrix diagonalization. The matrix is symmetric if solutions are based on normalized Legendre functions. A method is described of evaluating the related wind functions.

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