The linearized Shallow Water Equations (LSWE) on a tangent (x, y) plane to the rotating spherical Earth with Coriolis parameter f(y) that depends arbitrarily on the northward coordinate y is considered as a spectral problem of a selfadjoint operator. This operator is associated with a linear second-order equation in x - y plane that yields all the known exact and approximate solutions of the LSWE including those that arise from different boundary conditions, vanishing of some small terms (e.g. the β-term and frequency) and certain forms of the Coriolis parameter f(y) on the equator or in mid-latitudes. The operator formulation is used to show that all solutions of of the LSWE are stable. In some limiting cases these solutions reduce to the well-known plane waves of geophysical fluid dynamics: Inertia-gravity (Poincaré) waves, Planetary (Rossby) waves and Kelvin waves. In addition, the unified theory yields the non-harmonic analogs of these waves as well as the more general propagating solutions and solutions in closed basins. © 2008 Springer.
CITATION STYLE
Paldor, N., & Sigalov, A. (2008). A unified linear wave theory of the Shallow Water Equations on a rotating plane. In Solid Mechanics and its Applications (Vol. 6, pp. 403–413). Springer Verlag. https://doi.org/10.1007/978-1-4020-6744-0_36
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