Optimal Perturbations to Inertia-Gravity-Wave Packets

Using a hierarchy of three models of increasing complexity optimal perturbations to inertia-gravity-wave (IGW) packets are studied under typical mesospheric conditions. While for statically stable IGW no significant normal-mode (NM) instability is found, the energy in singular vectors (SV) can grow within one Brunt-Vaisala period by nearly two orders of magnitude. Many of their properties can already be understood within the framework of a stratified constant-shear layer approximating the IGW conditions at its statically least stable location. Within the analytic treatment one finds reduced static stability in concerted action with the vertical gradient in the horizontal IGW wind component transverse to its propagation direction to be the controlling parameters. SV propagating parallel to the IGW grow most vigorously over short time scales, extracting their energy from the IGW via a statically amplified tilting mechanism, while transverse SV, gaining in importance with increasing optimization time, are controlled by a statically modified Orr mechanism, both relate to corresponding mechanisms discussed by Farrell and Ioannou (1993) and Bakas et al. (2001). In both cases optimal growth can be traced back to an increasingly constructive interference between two or three contributing NM. An alternative interpretation of the favoured optimal growth in comparison to that of NM is the observation that besides exponential growth or decay NM are structurally fixed, while SV can adjust their dynamical structure flexibly, thereby admitting over finite time a more efficient energy exchange with the IGW packet. This also holds in an approximation of the IGW packet by a vertical one-dimensional profile at the statically least stable horizontal location, within which the longer-term development of the SV can be studied. While parallel SV from short optimization times are small-scale features of wavelengths down to a few 100 m which are closely confined via a typical wave duct to the statically least stable wave phase, their wavelength increases in proportion with optimization time, finally admitting gravity-wave radiation into altitude regions not affected by the IGW packet. The same also holds for obliquely propagating SV, while the transverse perturbations, typically of largest scale, are always prevented from radiating by the formation of critical layers near the zero line of transverse wind in the IGW. At optimization times of the order of the IGW period oblique SV are found to amplify most strongly. A determination of SV in the complete IGW packet further supports our assumption that the vertical IGW gradients are decisive for the SV dynamics. The horizontal structure of the IGW leads to a localization of optimal growth to the horizontal locations where static stability is most strongly reduced, suggesting a certain patchiness in the turbulence onset in IGW packets propagating upwards through the mesosphere.