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On the Forcing of Time-Mean Flows by Transient, Small-Amplitude Eddies

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  • 1 Meteorological Office Unit, Hooke Institute, Clarendon Laboratory, Oxford, United Kingdom
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Abstract

Small-amplitude, transient disturbances to a steady, zonally asymmetric basic state are considered, for barotropic (or baroclinic, quasi-geostrophic) flow on a beta-plane. An explicit expression is derived for the eddy vorticity (or potential vorticity) flux in terms of the basic velocity and basic vorticity (or potential vorticity), and transient and nonconservative eddy effects, plus an identically nondivergent term. The divergence of the time mean of this flux provides the forcing of the time-mean flow. The theory generalizes a “nonacceleration” result due to Plumb. In the case of conservative flow, the relevant expressions can be obtained in Eulerian form; however, for nonconservative flow it appears to be necessary to introduce the Lagrangian fluid particle displacements. Possible applications of the theory to the interpretation of atmospheric and model data are mentioned.

Abstract

Small-amplitude, transient disturbances to a steady, zonally asymmetric basic state are considered, for barotropic (or baroclinic, quasi-geostrophic) flow on a beta-plane. An explicit expression is derived for the eddy vorticity (or potential vorticity) flux in terms of the basic velocity and basic vorticity (or potential vorticity), and transient and nonconservative eddy effects, plus an identically nondivergent term. The divergence of the time mean of this flux provides the forcing of the time-mean flow. The theory generalizes a “nonacceleration” result due to Plumb. In the case of conservative flow, the relevant expressions can be obtained in Eulerian form; however, for nonconservative flow it appears to be necessary to introduce the Lagrangian fluid particle displacements. Possible applications of the theory to the interpretation of atmospheric and model data are mentioned.

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