INERTIAL INSTABILITY ON AN ASYMMETRIC LOW-LATITUDE FLOW

Both satellite data and numerical model simulations have suggested a l ink between propagation of planetary waves into the low-latitude middl e atmosphere and the occurrence of dynamical structures with small ver tical scale similar to those predicted by the theory of symmetric iner tial instability. It is here argued that existing theories that consid er the growth of disturbances to a basic flow that is independent of l ongitude are unlikely to be directly relevant to such observations. A theory is presented that takes account of longitudinal variations in t he structure of the basic flow, using WKB methods and the notion of ab solute instability to find localized unstable modes. In the limit of l arge vertical wavenumber it is demonstrated analytically that the flow is absolutely unstable. For finite vertical wavenumber the calculatio n is based on numerical derivation of the dispersion relation. The gro wth rates and the spatial structure of the unstable modes relative to the variation of the basic flow are predicted. The results are compare d to those from numerical solution of the linear stability problem and with full numerical simulation in a three-dimensional primitive-equat ion model. It is found that under some circumstances the longitudinal variation causes the maximum growth rate to occur at finite vertical w avenumber, rather than at infinite vertical wavenumber as is the case when the basic flow is independent of longitude.