A Modeling of Atmospheric Gravity Waves and Wave Drag Generated by Isotropic and Anisotropic Terrain

Colin O. Hines Arecibo Observatory, Arecibo, Puerto Rico 00613

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Abstract

Momentum deposition by orographically generated atmospheric gravity waves has been incorporated into a general circulation model of the troposphere and lower stratosphere by McFarlane, using a parameterization of real terrain and the waves that terrain would generate. Similar modeling will no doubt follow for extension to greater heights, where the effects of momentum deposition are expected to be greater. MeFarlane's parameterization treated an upward flux of momentum directed into a single azimuth (namely, that opposed to the surface wind) and tacitly assumed a Boussinesq approximation and horizontally isotropic terrain. These limitations are probed here and, to some extent, removed.

The analysis is generalized from the Boussinesq to the “incompressible” approximation, with consequences that can be important in some circumstances. It is found appropriate to represent the momentum flux from isotropic terrain by two azimuths rather than one, these two being at angles of 32.5° or more from the single azimuth previously chosen. On the other hand, it is found appropriate to represent the momentum flux from anisotropic terrain by a single azimuth, that opposing the wind component normal to the long axis of the terrain, the transition from “isotropic” to “anisotropic” occurring at a length/breadth ratio of about two. Anomalous effects introduced by plateaus are also examined, and arguments are presented for removing them somewhat arbitrarily because of associated blocking.

Abstract

Momentum deposition by orographically generated atmospheric gravity waves has been incorporated into a general circulation model of the troposphere and lower stratosphere by McFarlane, using a parameterization of real terrain and the waves that terrain would generate. Similar modeling will no doubt follow for extension to greater heights, where the effects of momentum deposition are expected to be greater. MeFarlane's parameterization treated an upward flux of momentum directed into a single azimuth (namely, that opposed to the surface wind) and tacitly assumed a Boussinesq approximation and horizontally isotropic terrain. These limitations are probed here and, to some extent, removed.

The analysis is generalized from the Boussinesq to the “incompressible” approximation, with consequences that can be important in some circumstances. It is found appropriate to represent the momentum flux from isotropic terrain by two azimuths rather than one, these two being at angles of 32.5° or more from the single azimuth previously chosen. On the other hand, it is found appropriate to represent the momentum flux from anisotropic terrain by a single azimuth, that opposing the wind component normal to the long axis of the terrain, the transition from “isotropic” to “anisotropic” occurring at a length/breadth ratio of about two. Anomalous effects introduced by plateaus are also examined, and arguments are presented for removing them somewhat arbitrarily because of associated blocking.

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