A Higher-Order Ray Approximation Applied to Orographic Gravity Waves: Gaussian Beam Approximation

Abstract

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.

High gravity‐wave activity observed in Patagonia, Southern America: generation by a cyclone passage over the Andes mountain range

“…This asymmetric pattern is not found in simulations with a horizontally uniform background wind in the region (Pulido and Rodas, 2011). One explanation for this asymmetry is the non-uniformity in latitude of the background wind; in particular the height of the critical level changes with the latitude.…”

A stationary phase solution for mountain waves with application to mesospheric mountain waves generated by Auckland Island

“…The intrinsic group velocity vector is , where the subscripts k , l , m denote partial derivatives. The notation here is that the sign of m is chosen to be the opposite sign of for upward propagating waves with c g 3 >0, as in the Fourier formulations of Pulido and Rodas [] and Teixeira and Yu [].…”

“…Equations and are integrated forms of the ray equations [ Pulido and Rodas , , equation 7]: …”

“…A Fourier integral of the type (2) has been applied to mountain waves by Broutman et al [2002] and Eckermann et al [2006Eckermann et al [ , 2015aEckermann et al [ , 2016 and, in a Gaussian beam formulation, by Pulido and Rodas [2011]. The Fourier integral (2) contains a ray approximation for the vertical eigenfunctions, and so it is assumed that the background is slowly varying in the vertical.…”

Directional Absorption of Parameterized Mountain Waves and Its Influence on the Wave Momentum Transport in the Northern Hemisphere

“…Xu, Wang, et al () recently developed a new OGWD parameterization scheme (hereafter the X17 scheme) based on the Gaussian beam approximation (GBA) (see Pulido & Rodas, , hereafter PR11). This new scheme was used to study the impact of horizontal propagation on the mountain wave drag in the Northern Hemisphere (Xu, Shu, & Wang, ).…”