Shear Instability of Internal Inertia-Gravity Waves

Local shear and convective instabilities of internal inertia-gravity waves (IGW) are examined assuming a steady, plane-parallel flow with vertical profiles of horizontal velocity and static stability resembling an IGW packet in a basic state at rest, without mean vertical shear. The eigenproblem can be described in terms of a nondimensional rotation rate R = f/ω̂0 < 1, where f is the Coriolis parameter, ω̂0 is IGW intrinsic frequency, and IGW amplitude is a, such that a = 1 for convectively neutral waves. In the nonrotating case, shear instability is possible only for convectively supercritical waves, with horizontal wavevector aligned parallel or nearly parallel to the plane of IGW propagation. Transverse convection, with wavevector aligned perpendicular to the plane of IGW propagation, displays faster growth than parallel shear or convective instability at any horizontal wavenumber. For intermediate R, eigenmodes in supercritical IGW are characterized at small horizontal wavenumber k by a transverse mode of convective instability and a parallel mode of shear instability. The transverse mode again has larger growth rate at small k but is suppressed at high wavenumbers where parallel convection prevails. Shear production of perturbation kinetic energy in transverse instability is positive (negative) at intermediate or large (small) R. For R approaching unity, shear instability takes precedence over convective instability at all azimuths regardless of a. In this limit, growth of the most unstable mode is almost independent of azimuth. It is shown that the parallel shear instabilities of an IGW are analogous to the unstable modes of a stratified jet.