Planetary and Inertia-Gravity Waves in an Equatorial Channel on a Sphere

Abstract

Some of the issues encountered in the preceding chapter in the development of wave theory in a channel on the equatorial β-plane might be resolved when the β-plane approximation is relaxed and the same problem is studied in an equatorial channel on a sphere. This problem will not suffer from the limitation associated with the linear expansion of Coriolis frequency, $\sin \phi$, but the price we should expect to pay for the more general approach is the much more complex form of the shallow water equations in spherical geometry in which the GRAD and DIV differential operators contain latitude-dependent coefficients. Another reason for studying the problem of an equatorial channel on a sphere is that this setup is an intermediate step that should be studied prior to studying the shallow water equations on the entire rotating sphere.