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Wentzel–Kramers–Brillouin approximation for atmospheric waves

Published online by Cambridge University Press:  16 July 2015

Oleg A. Godin
Oleg A. Godin*
Affiliation:
Cooperative Institute for Research in Environmental Sciences, University of Colorado at Boulder, Boulder, CO 80309-0216, USA NOAA/Earth System Research Laboratory, Physical Sciences Division, Boulder, CO 80305-3328, USA
*
†Email address for correspondence: [email protected]
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Abstract

Ray and Wentzel–Kramers–Brillouin (WKB) approximations have long been important tools in understanding and modelling propagation of atmospheric waves. However, contradictory claims regarding the applicability and uniqueness of the WKB approximation persist in the literature. Here, we consider linear acoustic–gravity waves (AGWs) in a layered atmosphere with horizontal winds. A self-consistent version of the WKB approximation is systematically derived from first principles and compared to ad hoc approximations proposed earlier. The parameters of the problem are identified that need to be small to ensure the validity of the WKB approximation. Properties of low-order WKB approximations are discussed in some detail. Contrary to the better-studied cases of acoustic waves and internal gravity waves in the Boussinesq approximation, the WKB solution contains the geometric, or Berry, phase. The Berry phase is generally non-negligible for AGWs in a moving atmosphere. In other words, knowledge of the AGW dispersion relation is not sufficient for calculation of the wave phase.

JFM classification

Compressible Flows: Compressible Flows Waves/Free-surface Flows: Elastic waves Geophysical and Geological Flows: Internal waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 260 - 290
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© 2015 Cambridge University Press 

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