Kinematic and thermal properties of a large-amplitude wave in the westerlies

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Abstract
The characteristics of a large-amplitude long wave, with superimposed short-wave disturbances, are described with emphasis on the deviations between the real and geostrophic winds, and between the corresponding vorticity fields. In the long-wave trough and ridge, the maximum wind speed differed from the geostrophic wind by a factor of about two. Correspondingly large differences were observed between the thermal shear and the vertical shear of the real wind. Consistent with this, the slope of the polar front was much steeper in the trough, and shallower in the ridge, than is indicated by Margules' formula for straight flow. The vertical shear was also influenced by the change of trajectory curvature with height, which is shown to be systematically related in part to the vertical motion field. The regions of strongest divergence and convergence in the upper troposphere lay very nearly on the jet-stream axis, and local maximum values were an order of magnitude larger than the mean divergence over the region between trough and ridge of the long wave. Kinematically computed vertical motions indicate descent west and ascent east of the trough, in the warm air; in the cold air mass, however, there was ascent west and descent east of the trough line. The differential adiabatic heating or cooling associated with this distribution of vertical motions contributes to strengthening of the horizontal temperature gradient in air approaching the trough, and a weakening in the air streaming eastward from the trough. The indicated redistributions of potential energy are qualitatively in accord with kinetic energy variations along the current, on the west and east sides of the trough where marked deceleration and acceleration are observed in the upper troposphere. DOI: 10.1111/j.2153-3490.1963.tb01370.x

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