INERTIAL INSTABILITY OF NONPARALLEL FLOW ON AN EQUATORIAL BETA-PLANE

A simple theoretical model was developed to investigate the inertial i nstability of zonally nonuniform, non-parallel flow near the equator. The basic state was independent of height and time but included cross- equatorial shear with longitudinal variation, as observed in the tropi cal mesosphere and elsewhere. Numerical solutions were obtained for th e most unstable modes. It is shown that, in addition to previously kno wn ''global'' (symmetric and nonsymmetric) modes of inertial instabili ty, there exist ''local'' modes within regions of anomalous potential vorticity. Local modes may be exactly stationary or display zonal phas e propagation, but are distinguished from global modes by their zero g roup velocity and concentration of amplitude within, or downstream fro m, the region of most unstable flow. Local stationary instability has the largest growth rate and occurs in strong inhomogeneous shear when the in situ mean flow is near zero, that is, quasi-stationary with res pect to the (stationary) basic-state pattern. This situation is expect ed in an equatorial Rossby wave critical layer. The local mode has pro perties similar to those of ''absolute'' instability of nonparallel fl ow as discussed elsewhere in fluid dynamics.