Ray techniques are a promising tool for developing orographic gravity wave drag schemes. However, the modeling of the propagation of orographic waves using standard ray theory in realistic background wind conditions usually encounters several regions, called caustics, where the first-order ray approximation breaks down. In this work the authors develop a higher-order approximation than standard ray theory, named the Gaussian beam approximation, for orographic gravity waves in a background wind that depends on height. The analytical results show that this formulation is free of the singularities that arise in ray theory. Orographic gravity waves that propagate in a background wind that turns with height-the same conditions as in the work of Shutts-are examined under the Gaussian beam approximation. The evolution of the amplitude is well defined in this approximation even at caustics and at the forcing level. When comparing results from the Gaussian beam approximation with high-resolution numerical simulations that compute the exact solution, there is good agreement of the amplitude and phase fields. Realistic orography is represented by means of a superposition of multiple Gaussians in wavenumber space that fit the spectrum of the orography. The technique appears to give a good representation of the disturbances generated by flow over realistic orography.

ABSTRACT:The propagation of transient gravity waves in a shear flow towards their critical levels is examined using a ray tracing approximation and a higher-degree (quasi-optic) approximation. Because of its transient forcing, the amplitude of transient waves decays to zero in the neighbourhood of the critical region so that it is not clear whether transient gravity waves will reach the convective instability threshold or not. The analysis shows that the horizontal perturbation decays asymptotically as the inverse of the square root of time, while the vertical wavenumber depends linearly on time, thus transient gravity waves attain convective instability for long times. The theoretical results are compared with numerical simulations. The ray path approximation is not able to reproduce the maximum amplitude, but the quasi-optic approximation gives a reasonable agreement at short and long times. There are three breaking regimes for transient gravity waves. For wave packets with a narrow frequency spectrum (quasi-steady waves) and large enough initial wave amplitude, the wave breaking is similar to the abrupt monochromatic wave overturning. On the other hand, highly transient wave packets will dissipate near the critical region for very long times with small wave amplitudes and high vertical wavenumber. The third regime is a transition between the two extremes; in this case both wave amplitude and vertical wavenumber are important to produce the convective threshold. The dependencies of the convective instability height (a quantity that may be useful for gravity wave parametrizations) on the Richardson number and the frequency spectral width are obtained.

The impact of gravity wave drag on the Antarctic sudden stratospheric warming (SSW) in 2002 is examined through a mechanistic middle atmosphere model combined with a variational data assimilation system. Significant differences in the SSW representation are found between a model integration that uses reference gravity wave parameters and one that uses parameters estimated using data assimilation. Upon identical wave forcings at 100 hPa, the vortex breakdown may arise as either a vortex splitting event or a displacement vortex event depending on gravity wave parameters. A local enhancement of Rossby waves is found in the integration with estimated parameters, leading to a split SSW. The changes in the vortex breakdown are associated with changes in the vortex geometry caused entirely by modifying the gravity wave parameters. Gravity wave drag proved to play an instrumental role in preconditioning the stratosphere near a resonant excitation point that triggers the split SSW.

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The propagation of transient inertio-gravity waves in a shear flow is examined using the Gaussian beam formulation. This formulation assumes Gaussian wavepackets in the spectral space and uses a second-order Taylor expansion of the phase of the wave field. In this sense, the Gaussian beam formulation is also an asymptotic approximation like spatial ray tracing; however, the first one is free of the singularities found in spatial ray tracing at caustics. Therefore, the Gaussian beam formulation permits the examination of the evolution of transient inertio-gravity wavepackets from the initial time up to the destabilization of the flow close to the critical levels. We show that the transience favours the development of the dynamical instability relative to the convective instability. In particular, there is a well-defined threshold for which small initial amplitude transient inertio-gravity waves never reach the convective instability criterion. This threshold does not exist for steady-state inertio-gravity waves for which the wave amplitude increases indefinitely towards the critical level. The Gaussian beam formulation is shown to be a powerful tool to treat analytically several aspects of inertio-gravity waves in simple shear flows. In more realistic shear flows, its numerical implementation is readily available and the required numerical calculations have a low computational cost.