Inertial instability on an asymmetric low‐latitude flow

Abstract

AbstractBoth satellite data and numerical model simulations have suggested a link between propagation of planetary waves into the low‐latitude middle atmosphere and the occurrence of dynamical structures with small vertical scale similar to those predicted by the theory of symmetric inertial instability. It is here argued that existing theories that consider the growth of disturbances to a basic flow that is independent of longitude are unlikely to be directly relevant to such observations. A theory is presented that takes account of longitudinal variations in the structure of the basic flow, using WKB methods and the notion of absolute instability to find localized unstable modes. In the limit of large vertical wavenumber it is demonstrated analytically that the flow is absolutely unstable. For finite vertical wavenumber the calculation is based on numerical derivation of the dispersion relation. The growth rates and the spatial structure of the unstable modes relative to the variation of the basic flow are predicted. The results are compared to those from numerical solution of the linear stability problem and with full numerical simulation in a three‐dimensional primitive‐equation model.It is found that under some circumstances the longitudinal variation causes the maximum growth rate to occur at finite vertical wavenumber, rather than at infinite vertical wavenumber as is the case when the basic flow is independent of longitude.