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The Structure of Idealized Upper-Tropospheric Shear Lines

Martin JuckesMeteorologisches Institut der Universität München, Munich, Germany

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Abstract

The structure of idealized two-dimensional shear lines has been calculated for specified tropopause potential temperature anomalies. A cold anomaly corresponds to an intrusion of stratospheric air into the troposphere. A balanced hydrostatic primitive equation structure is derived using an iterative technique. The resulting wind and vertical displacement of the tropopause are compared with a recent result extending quasigeostrophic theory to situations where the variation of potential vorticity along an isentrope or isobar is large, as is the case, for instance, when the isosurface intersects the tropopause. The formulation of the theory is clarified by analyzing the relation between quasigeostrophic potential vorticity and Ertel’s potential vorticity. The comparison between the low–Rossby number theoretical approximation and primitive equation structures confirms the theoretical prediction that the relative error is proportional to the Rossby number. The constant of proportionality is close to unity. The effect of the lower boundary condition on the shear line structure is analyzed. For a shear line consisting of an upper-tropospheric potential vorticity anomaly in the absence of a surface temperature anomaly it is found that the horizontal extent of the wind is not limited, as might have been expected, by the Rossby deformation radius, but rather by the largest scale of the shear line, which may be somewhat greater.

Corresponding author address: Dr. Martin Juckes, Department of Atmospheric, Oceanic, and Planetary Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom.

Email: juckes@atm.ox.ac.uk

Abstract

The structure of idealized two-dimensional shear lines has been calculated for specified tropopause potential temperature anomalies. A cold anomaly corresponds to an intrusion of stratospheric air into the troposphere. A balanced hydrostatic primitive equation structure is derived using an iterative technique. The resulting wind and vertical displacement of the tropopause are compared with a recent result extending quasigeostrophic theory to situations where the variation of potential vorticity along an isentrope or isobar is large, as is the case, for instance, when the isosurface intersects the tropopause. The formulation of the theory is clarified by analyzing the relation between quasigeostrophic potential vorticity and Ertel’s potential vorticity. The comparison between the low–Rossby number theoretical approximation and primitive equation structures confirms the theoretical prediction that the relative error is proportional to the Rossby number. The constant of proportionality is close to unity. The effect of the lower boundary condition on the shear line structure is analyzed. For a shear line consisting of an upper-tropospheric potential vorticity anomaly in the absence of a surface temperature anomaly it is found that the horizontal extent of the wind is not limited, as might have been expected, by the Rossby deformation radius, but rather by the largest scale of the shear line, which may be somewhat greater.

Corresponding author address: Dr. Martin Juckes, Department of Atmospheric, Oceanic, and Planetary Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom.

Email: juckes@atm.ox.ac.uk

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