On divergent barotropic and inertial instability in zonal-mean flow profiles

Impacts of atmospheric mean zonal flows on equatorial and subequatorial waves are examined using the generalized Laplace tidal equation, a horizontal structure equation that explicitly includes the effect of horizontal divergence on disturbances via the Lamb parameter epsilon = (2 Omega a)(2)/(gh(e)). Two important consequences of the mean zonal flow profile are the excitation of barotropically unstable waves associated with a reversed meridional gradient of potential vorticity and the excitation of inertially unstable waves related to anomalous potential vorticity values. Investigations show that both types of instabilities occur in realistic wind fields of the upper troposphere around 200 hPa. The barotropically unstable waves are divided into weakly divergent waves located in the middle latitudes and the more important class of strongly divergent waves located at the equatorward flank of the jet stream in the subtropics. The strongly divergent inertially unstable waves are identified by equatorially trapped waves showing horizontal structures of Kelvin waves, Rossby-gravity waves, and gravity waves. For large values of the Lamb parameter epsilon, that is, small values of the equivalent depth h(e), it is possible to obtain barotropically unstable perturbations located in the subtropics with an additional secondary maximum penetrating into equatorial regions. The secondary maximum resembles Kelvin wavelike structures, and it is related to the weak inertial instability caused by a nonvanishing cross-equatorial hear. This shear usually occurs for barotropically unstable flow profiles with corresponding unstable regions in the subtropics. For inertially unstable flow profiles it is also possible to excite equatorially trapped Kelvin wavelike perturbations with an additional secondary maximum in the subtropics showing Rossby-like gyres. When the underlying mean flow profile is barotropically and inertially unstable, the structure of subtropical barotropic perturbations and equatorial inertial perturbations are "fused" forming a new class of strongly divergent modes. This class may be interpreted as a generalization of inertially unstable perturbations for linear wind shear profiles on the equatorial beta plane. The coupling of barotropic and inertial instabilities is discussed for the equatorial middle atmosphere where inertial stability is influenced by the occurrence of subtropical Rossby waves, and for the tropical troposphere where the intraseasonal oscillation may be affected by barotropically unstable waves and their influence on equatorially trapped Kelvin wavelike structures.