A Non-Dispersive Eastward Propagating Mode on the Sphere: A Kelvin Wave, or the N=0 Inertial Gravity Mode?

There is strong observational evidence for the existence of a non-dispersive eastward propagating mode on the sphere whose maximum is at the equator. This mode is typically identified as a Kelvin wave, whose  classical theories were developed by Matsuno, 1966 and Longuet Higgins, 1968. Recently, a Schroedinger eigenvalue problem for zonally propagating modes on the sphere has been formulated which yields highly accurate experessions for the dispersion relations of the western propagating Rossby and the eastward and westward propagating inertial gravity waves.  These latter wave solutions form a complete set for the linearized shallow water system.  We will discuss the implications of these results for the existence of Kelvin waves, and show that on a sphere the eastward propagating n=0 inertial gravity mode is indistinguishable from a Kelvin wave.