Optimal perturbations to monochromatic gravity waves and their possible role in the formation of thin turbulent layers in the mesosphere (formerly paper JP5.2)

The incipient linear phase of gravity-wave instability has so far exclusively been studied by way of normal-mode analyzes. Motivated by the useful new insights from optimal-perturbation theory into the onset of turbulence in other fields the singular vectors in stable and unstable monochromatic gravity waves have been determined. Both inertia-gravity waves and high-frequency gravity waves have been considered within the framework of the Boussinesq equations on an f plane. It is found that optimal growth within one Brunt-Vaisala period is always stronger than that of normal modes. Inertia-gravity waves admit rapid nonmodal growth even when no significantly unstable normal modes exist. High-frequent gravity waves show a dependence of optimal growth on the propagation direction of the perturbation with respect to the wave which is quite different from that of normal modes. The singular vectors have a preferentially transverse propagation direction with respect to the gravity wave, while in most cases the most unstable normal modes tend to propagate in the same plane as the gravity wave. The difference in the dynamics of the two types of modes is characterized by a time-invariance in the comparative role of the different possible exchange processes between normal mode and basic wave, while singular vectors can have a highly time-dependent structure allowing a more efficient energy exchange over a finite time. In the case of inertia-gravity waves the latter are located in the region of least static instability. Since even for statically stable waves their energy growth can cover two orders of magnitude, it might be possible that they directly lead the wave into a nonlinear stage before a normal mode has time to do so. Singular vectors in high-frequent gravity waves are sharply peaked pulses with negligible group velocity which are repeatedly excited as the rapidly propagating wave passes over them. In a transition to the leading normal mode they are gradually broadened and slowly transformed into the normal-mode structure until they finally move with the phase of the gravity wave. This process is however so slow that in many cases one can expect singular vectors to more appropriately describe the turbulence onset via local perturbations of a gravity wave. This might be of importance for the formation of thin turbulent layers as observed by others in mesospheric rocket soundings. Corresponding simulations are also discussed.