Kelvin and Rossby Waves Trapped at Boundaries under the Full Coriolis Force

It is shown that there are two types of wave solutions trapped at the boundaries which owe to the Coriolis force proportional to the meridional component of the earth's rotation vector (hereafter referred to as the f(H) force) under the nontraditional approximation (non-TA). One is a type of Kelvin waves (non-TA Kelvin waves) trapped on the eastern and western boundaries. Unlike traditional Kelvin waves (TA Kelvin waves), non-TA Kelvin waves trapped on the western (eastern) boundary can have northward (southward) phase and group velocities in the Northern Hemisphere (NH). The other is a type of Rossby waves trapped on the ground. The external Rossby waves can have wave structure in the vertical and amplitudes decaying with height. Moreover, the f(H) force modifies even the characteristics of TA Kelvin waves trapped on the southern and northern boundaries: In the NH, the Kelvin waves trapped on the southern boundary have an upper limit (k(c)) to the zonal wavenumber (k), and those with large k (>k(c)) trapped on the northern boundary have eastward phase velocity in the NH. The latter is regarded as the third type of edge waves unique to non-TA.