Scattering of Kelvin and Yanai waves at the eastern boundary of an Equatorial Basin

The theory of linear equatorial waves shows that there is an intermediate frequency band between the highest frequency equatorial Rossby wave and the lowest frequency equatorial gravity waves. The only equatorial waves with real east-west wave number in this band are the equatorial Kelvin wave, and the Yanai wave ( also known as the mixed Rossby - gravity wave ). Both of these wave modes have group velocity toward the east. When either of these modes runs into an eastern boundary, the energy is scattered away from the equator as a coastally trapped Kelvin wave, with some energy going to the south, and some to the north. If there is a single incoming wave (either Kelvin or Yanai), and the eastern boundary is perpendicular to the equator, half of the scattered energy goes north, and half goes south. If there is a single Kelvin wave and the eastern boundary is not perpendicular to the equator, a larger share of the Kelvin wave energy goes poleward in the direction which is less than a right angle from the equator, and a smaller fraction goes poleward in the other hemisphere. However, if the incident wave is a single Yanai wave, the opposite is true, with more than half the energy turning through a larger angle. Furthermore, if these two waves are at the same frequency, the fraction of Kelvin wave energy turning through the smaller angle is the same as the fraction of the Yanai wave energy turning through the larger angle.

We prove that this is always the case for this intermediate frequency band.