The atmospheric Kelvin wave is modeled with nonlinear terms included. Forcing from below leads to a Kelvin wave similar to that observed. The nonlinear terms lead to an asymmetry in the wave, producing a zone of strong vertical shear in association with the westerly shear zone. Dissipation was not included in the model to limit the degree of asymmetry or buildup of vertical shear. Observational evidence indicates that clear-air turbulence (CAT) eventually breaks out, thus causing the waves to suddenly dissipate. It is inferred that, at the time of dissipation, large amounts of westerly momentum are supplied to the mean flow and that this is responsible for the downward propagation of the westerly shear zone.