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A Three-Dimensional Wave-Activity Relation for Pseudomomentum

Lingkun RanLaboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

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Shouting GaoLaboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

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Abstract

A three-dimensional, nonhydrostatic local wave-activity relation for pseudomomentum is derived from the nonhydrostatic primitive equations in Cartesian coordinates by using an extension of the momentum–Casimir method. The stationary and zonally symmetric basic states are chosen and a Casimir function, which is the single-valued function of potential vorticity and potential temperature, is introduced in the derivation.

The wave-activity density and wave-activity flux of the local wave-activity relation for pseudomomentum are expressed entirely in terms of Eulerian quantities so that they are easily calculated with atmospheric data and do not require the knowledge of particle placements. Constructed in the ageostrophic and nonhydrostatic dynamical framework, the local wave-activity relation for pseudomomentum is applicable to diagnosing the evolution and propagation of mesoscale weather systems.

Corresponding author address: Dr. Shouting Gao, Laboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China. Email: gst@lasg.iap.ac.cn

Abstract

A three-dimensional, nonhydrostatic local wave-activity relation for pseudomomentum is derived from the nonhydrostatic primitive equations in Cartesian coordinates by using an extension of the momentum–Casimir method. The stationary and zonally symmetric basic states are chosen and a Casimir function, which is the single-valued function of potential vorticity and potential temperature, is introduced in the derivation.

The wave-activity density and wave-activity flux of the local wave-activity relation for pseudomomentum are expressed entirely in terms of Eulerian quantities so that they are easily calculated with atmospheric data and do not require the knowledge of particle placements. Constructed in the ageostrophic and nonhydrostatic dynamical framework, the local wave-activity relation for pseudomomentum is applicable to diagnosing the evolution and propagation of mesoscale weather systems.

Corresponding author address: Dr. Shouting Gao, Laboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China. Email: gst@lasg.iap.ac.cn

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