Barotropic and Baroclinic Ageostrophic Winds and Completeness of Solution for the Psi Equations

Qin Xu NOAA/ERL, National Severe Storms Laboratory and University of Oklahoma, CIMMS, Norman, Oklahoma

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Daniel Keyser Department of Atmospheric Science, State University of New York at Albany, Albany, New York

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Abstract

This paper examines the completeness of the solutions for three-dimensional ageostrophic circulations determined from the quasigeostrophic psi equations (or from the counterpart semigeostrophic psi equations in geostrophic-coordinate space). It is shown that a complete solution should contain two parts: a baroclinic part and a barotropic part. The solution of the psi equations with homogeneous (zero) upper and lower boundary conditions yields only the baroclinic part of the ageostrophic wind field, while the barotropic part can be recovered from the ageostrophic vorticity equation. The barotropic ageostrophic wind field is two-dimensional and nondivergent. It may be subdivided into rotational and harmonic pans, respectively forced by barotropic ageostrophic vorticity and by nonhomogeneous lateral boundary conditions (with nonzero cross-boundary mass flux). Methods for obtaining the complete solution are proposed and examples are given, showing the possible significance of the barotropic ageostrophic wind.

Abstract

This paper examines the completeness of the solutions for three-dimensional ageostrophic circulations determined from the quasigeostrophic psi equations (or from the counterpart semigeostrophic psi equations in geostrophic-coordinate space). It is shown that a complete solution should contain two parts: a baroclinic part and a barotropic part. The solution of the psi equations with homogeneous (zero) upper and lower boundary conditions yields only the baroclinic part of the ageostrophic wind field, while the barotropic part can be recovered from the ageostrophic vorticity equation. The barotropic ageostrophic wind field is two-dimensional and nondivergent. It may be subdivided into rotational and harmonic pans, respectively forced by barotropic ageostrophic vorticity and by nonhomogeneous lateral boundary conditions (with nonzero cross-boundary mass flux). Methods for obtaining the complete solution are proposed and examples are given, showing the possible significance of the barotropic ageostrophic wind.

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