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Charney Problem with a Generic Stratosphere

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  • 1 Department of Atmospheric Sciences, University of Illinois at Urbana–Champaign, Champaign, Illinois
  • 2 School of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia
  • 3 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, Los Angeles, California
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Abstract

This paper reports a comprehensive instability analysis of a 3D Charney-like model with an observationally compatible generic stratosphere. It is found that the values of a single nondimensional parameter Γ=λfo2/(βDN12) (detailed definition in text), in conjunction with representative values of four other nondimensional parameters, would dictate the existence of multiple branches of unstable modes as a function of the zonal wavenumber. Prototype Charney mode, Green mode, and two additional structurally distinct modes (Charney+ mode and tropopause mode) are identified. The latter result from the additional strong influence of the tropopause. The dynamical nature of all modes is delineated in terms of their meridional fluxes of heat and potential vorticity. The three-dimensional structure of the ageostrophic velocity field in each mode is presented to identify its potential of inducing frontogenesis. Optimal-mode analyses are also performed to ascertain how a disturbance with a predisposed structure would explosively develop toward each type of normal mode. In view of the pivotal role of Γ in baroclinic instability and for historical reason, we name it the Charney number. It is most instructive to think of Γ as a ratio of the meridional gradient of PV associated with the basic flow in the troposphere, λfo2/(DN12), to that associated with Earth’s rotation, β.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mankin Mak, m-mak@illinois.edu

Abstract

This paper reports a comprehensive instability analysis of a 3D Charney-like model with an observationally compatible generic stratosphere. It is found that the values of a single nondimensional parameter Γ=λfo2/(βDN12) (detailed definition in text), in conjunction with representative values of four other nondimensional parameters, would dictate the existence of multiple branches of unstable modes as a function of the zonal wavenumber. Prototype Charney mode, Green mode, and two additional structurally distinct modes (Charney+ mode and tropopause mode) are identified. The latter result from the additional strong influence of the tropopause. The dynamical nature of all modes is delineated in terms of their meridional fluxes of heat and potential vorticity. The three-dimensional structure of the ageostrophic velocity field in each mode is presented to identify its potential of inducing frontogenesis. Optimal-mode analyses are also performed to ascertain how a disturbance with a predisposed structure would explosively develop toward each type of normal mode. In view of the pivotal role of Γ in baroclinic instability and for historical reason, we name it the Charney number. It is most instructive to think of Γ as a ratio of the meridional gradient of PV associated with the basic flow in the troposphere, λfo2/(DN12), to that associated with Earth’s rotation, β.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Mankin Mak, m-mak@illinois.edu
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