Radiating Instabilities of Internal Inertio-Gravity Waves

Abstract

The vertical radiation of local convective and shear instabilities of internal inertio-gravity waves is examined within linear stability theory. A steady, plane-parallel Boussinesq flow with vertical profiles of horizontal velocity and static stability resembling an internal inertio-gravity wave packet without mean vertical shear is used as the dynamical framework. The influence of primary wave frequency and amplitude, as well as orientation and horizontal wavenumber of the instability on vertical radiation, is discussed. Considerable radiation occurs at small to intermediate instability wavenumbers for basic-state gravity waves with high to intermediate frequencies and moderately convectively supercritical amplitudes. Radiation is then strongest when the horizontal wave vector of the instability is aligned parallel to the horizontal wave vector of the basic-state gravity wave. These radiating modes are essentially formed by shear instability. Convective instabilities, that occur at large instability wavenumbers or strongly convectively supercritical amplitudes, as well as shear instabilities of low-frequency basic-state gravity waves, are nonradiating, trapped in the region of instability. The radiation of an instability is found to be related to the existence of critical levels, a radiating mode being characterized by the absence of critical levels outside the region of instability of the primary wave.