Horizontal wave propagation in the equatorial waveguide

Abstract

The dispersive (i.e. non-Kelvin) linear wave field on the equatorial β-plane, in a single vertical mode, is fully described by a single potential φ. Long Rossby waves, which are weakly dispersive, are represented in this field. This description is free from the problem of the ‘spurious solution’ encountered when working with an evolution equation for the meridional velocity; addition of this unwanted solution represents a gauge transformation that leaves the physical fields unaltered.The general solution of the ray equations is found, including trajectories, and the amplitudes and phase fields. This solution is asymptotically valid for either high or low frequencies. The ray paths are identical in both limits, but the phase field is not, reflecting the isotropy of Poincaré waves, in one case, and the zonal anisotropy of Rossby waves, in the other.Two examples are studied by ray theory: meridional normal modes and wave radiation from a point source in the equator. In the first case, the exact dispersion relation is obtained. In the second one, northern and southern caustics bend towards the equator, meeting there at focal points. The full solution is the superposition of many leaves and has a structure that would be hard to find in a normal modes expansion.