On stability of jetstreams

A. WIIN NIELSEN

Abstract

The quasi-geostrophic, baroclinic stability problem is solved using vertical structure functions corresponding to a vertical variation of the static stability parameter which is inversely proportional to the square of the pressure. Due to this assumption it is necessary to apply the upper boundary condition at a pressure level different from the outer limit of the atmosphere. While this technique has been used earlier, the emphasis in this paper is on the stability of jet profiles. Various jet-like profiles of the zonal wind are defined mathematically, and they are used to investigate how the stability depends on the maximum wind, the position of the jet maximum, the sharpness of the jet, and also the position of the upper boundary. A comparison is made with the stability of the advective model for which the stability may be obtained analytically. From the general, quasi-geostrophic model it is found that a short-wave cut-off exists, while instability exists for all wavelenghts larger than the cut-off wavelength, i.e. no long-wave cut-off exists. Smaller instabilities occurs when the maximum wind is around 300 hPa, when the top level is located at 30 hPa, and when the jet profiles are well rounded. A wind profile with "stratospheric easterlies" has about the same stability for Rossby waves of a few thousand kilometers as a profile with westerlies at all levels. However, for very long waves the profile with easterlies is more unstable.

 

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