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

PULIDO, M AND C. RODAS

JOURNAL OF THE ATMOSPHERIC SCIENCES

AMER METEOROLOGICAL SOC

Lugar: Boston ; Año: 2011 vol. 68 p. 48 - 60

0022-4928

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 we 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. Our analytical results show that this formulation is free of the singularities that arise in ray theory. We examine orographic gravity waves that propagate in a background wind that  turns with height--same conditions as in Shutts´ work--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 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.