Modal and nonmodal perturbations of monochromatic inertia-gravity waves: Linear and primary nonlinear dynamics

The stability of monochromatic inertia-gravity waves (IGWs) is examined using singular-vector (SV) or normal-mode (NM) analysis. The breaking of an IGW, initiated by its leading NMs or SVs, and the resulting small-scale eddies are investigated by means of direct numerical simulations (DNS) of a Boussinesq fluid characterizing the upper mesosphere. There the focus is on the primary nonlinear dynamics, neglecting the effect of secondary instabilities. The stability analyses show considerable growth of SVs for IGWs without any static or dynamic instability. In the DNS it is found that the structures with the strongest impact on the IGW and also the largest turbulence amplitudes are the NM (for a statically unstable IGW) or short-term SV (statically and dynamically stable IGW) propagating horizontally transversely with respect to the IGW, possibly in agreement with observations of airglow ripples in conjunction with statically unstable IGWs. In both cases these leading structures reduce the IGW amplitude well below the static and dynamic instability thresholds. The resulting turbulent dissipation rates are within the range of available estimates from rocket soundings, even for IGWs at amplitudes low enough precluding NM instabilities. SVs thus can help explain turbulence occurring under conditions not amenable for the classic interpretation via static and dynamic instability. Due to an important role of the statically enhanced roll mechanism in the energy exchange between IGW and eddies the turbulent velocity fields are often conspicuously anisotropic. In contrast to the behavior in a Kelvin-Helmholtz instability, the spatial turbulence distribution is determined to a large degree by the elliptically polarized horizontal velocity field of the IGW. The results also indicate the potential necessity of an incorporation of the possibility of subcritical IGW breaking into gravity-wave parameterization schemes for general circulation models.