Generalization of the Effect of Vertical Shear of Mean Zonal Flow on Tropical CISK-Wave Excitation

Abstract

This paper investigates the effects of vertical shear of the mean zonal flow on CISK waves in a spherical geometry. A linearized primitive equation model, including mean zonal flow, on a sphere is designed to generalize the previous results about the effects of the vertical shear of the mean zonal flow on the excitation of fast tropical waves with periods shorter than 20 days. In the case of linear CISK heating, the eastward propagating Kelvin waves are most unstable when the vertical shear of the mean zonal flow is easterly with height, and the westward propagating gravity waves (not mixed Rossby?gravity waves) are preferentially excited when the vertical shear of the mean zonal flow is westerly. The vertical structure of these unstable waves is in agreement with the previous results. In the troposphere, both the temperature and vertical velocity fields of the unstable waves tilt backward with height, and the tilt is smaller for the vertical velocity field than for the temperature field. In contrast, forward phase tilts are found above the troposphere, consistent with upward propagation of wave energy. In the case of positive-only (nonlinear) CISK heating, antisymmetric waves (with zonal wind antisymmetric about the equator) are suppressed, and an eastward propagating symmetric nondispersive wave packet with negligible meridional wind is excited. This unstable wave packet not only has zonally asymmetric structure but also has a change of zonal scale with height. Unlike in the linear case, the vertical shear of the mean zonal flow is unable to excite westward propagating gravity waves, but it does affect the instability of the wave packet in the same way as in the linear heating case. As was found for a single wave in the linear heating case, the unstable wave packet is shown to have a backward phase tilt with height in the troposphere. However, the effect of the vertical shear of the mean zonal flow on the wave packet works not by changing its phase tilt but by changing its zonal scale.