Shear and Static Instability of Inertia–Gravity Wave Packets: Short-Term Modal and Nonmodal Growth

Abstract

The problem of nonmodal instabilities of inertia–gravity waves (IGW) in the middle atmosphere is addressed, within the framework of a Boussinesq model with realistic molecular viscosity and thermal diffusion, by singular-vector analysis of horizontally homogeneous vertical profiles of wind and buoyancy obtained from IGW packets at their statically least stable or most unstable horizontal location. Nonmodal growth is always found to be significantly stronger than that of normal modes, most notably at wave amplitudes below the static instability limit where normal-mode instability is very weak, whereas the energy gain between the optimal perturbation and singular vector after one Brunt–Väisälä period can be as large as two orders of magnitude. Among a multitude of rapidly growing singular vectors for this optimization time, small-scale (wavelengths of a few 100 m) perturbations propagating in the horizontal parallel to the IGW are most prominent. These parallel optimal perturbations are amplified by a roll mechanism, while transverse perturbations (with horizontal scales of a few kilometers) are to a large part subject to an Orr mechanism, both controlled by the transverse wind shear in the IGW at its statically least stable altitude, but further enhanced by reduced static stability. The elliptic polarization of the IGW leaves its traces in an additional impact of the roll mechanism via the parallel wind shear on the leading transverse optimal perturbation.