On azimuthal eigenwavenumbers associated with Laplace's tidal equations

Laplace's tidal equations for the case of an ocean of constant depth bounded by meridians were considered by two authors at a specific frequency as an eigenvalue problem in the azimuthal wavenumber. A finite spectrum of eigenwavenumbers was found. That eigenvalue problem is re-examined by means of asymptotic techniques and numerical integration of the governing equation of the problem. At low frequencies a formula connecting the frequency and the number of eigensolutions is established. It is shown that at a given frequency the spectrum of eigenwavenumbers is wider than that reported, but (for this type of solution) the meridional boundary conditions are satisfied approximately only for the case of very low frequencies.