SHEAR INSTABILITY OF INTERNAL INERTIA-GRAVITY WAVES

Local shear and convective instabilities of internal inertia-gravity w aves (IGW) are examined assuming a steady, plane-parallel Bow with ver tical profiles of horizontal velocity and static stability resembling an IGW packet in a basic state at rest, without mean vertical shear. T he eigenproblem can be described in terms of a nondimensional rotation rate R = fr omega(0) <, where f is the Coriolis parameter, is IGW int rinsic frequency, and IGW amplitude is a, such that a = 1 for convecti vely neutral waves. In the nonrotating case, shear instability is poss ible only for convectively supercritical waves, with horizontal waveve ctor aligned parallel or nearly parallel to the plane of IGW propagati on. Transverse convection, with wavevector aligned perpendicular to th e plane of IGW propagation, displays faster growth than parallel shear or convective instability at any horizontal wavenumber, For intermedi ate R, eigenmodes in supercritical IGW are characterized at small hori zontal wavenumber k by a transverse mode of convective instability and a parallel mode of shear instability. The transverse mode again has l arger growth rate at small k but is suppressed at high wavenumbers whe re parallel convection prevails. Shear production of perturbation kine tic energy in transverse instability is positive (negative) at interme diate or large (small) R. For R approaching unity, shear instability t akes precedence over convective instability at all azimuths regardless of a. In this limit, growth of the most unstable mode is almost indep endent of azimuth. It is shown that the parallel shear instabilities o f an IGW art analogous to the unstable modes of a stratified jet.