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Permeability of the stratospheric vortex edge: On the mean mass flux due to thermally dissipating, steady, non‐breaking Rossby waves
Author(s) -
Mo Ruping,
Bühler Oliver,
McIntyre Michael E.
Publication year - 1998
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49712455015
Subject(s) - physics , rossby wave , potential vorticity , vortex , amplitude , vorticity , stratosphere , mechanics , mean flow , dissipation , zonal and meridional , breaking wave , classical mechanics , wave propagation , turbulence , meteorology , atmospheric sciences , quantum mechanics
As part of an assessment of the flowing‐processor hypothesis of Tuck et al. (1993) and references–see also Rosenlof et al. (1997)–this paper estimates possible contributions to flow through the edge of the stratospheric polar vortex due solely to distortion of the vortex by thermally dissipating Rossby waves forced from below. To isolate such contributions in a clear‐cut way, and to eliminate questions about numerical dissipation and truncation error, an idealized model is studied analytically. It assumes steady conditions and non‐breaking waves, the waves being stationary in some rotating frame such as that of the earth. The model is studied using two approaches: first via the generalized Lagrangian‐mean formalism of Andrews and McIntyre (1978), simplified by assuming small wave amplitude a; and second via a direct consideration of the three‐dimensional, finite‐amplitude undulations of the vortex edge, as defined by isentropic contours of potential vorticity, avoiding the use of any mean‐and‐deviation formalism. It is shown, in particular, that under quasi‐geostrophic scaling the Lagrangian‐mean meridional velocity V −L is given correct to O (a 2 ) by, where θ B is the basic‐state potential temperature, z the altitude, η′ the meridional particle displacement and the wave‐induced fluctuation in the diabatic rate of change of potential temperature θ. The formula for V −L is shown to be consistent with the independently derived finite‐amplitude result; and the implication of both results is that, for disturbances dissipated by infrared radiative relaxation in the wintertime lower stratosphere, V −L may well be directed into rather than out of the vortex, though weak outward flow is possible in some cases. There is, in addition, a vertical mean flow w −L controlled by eddy dynamics above the altitude under consideration. This is usually directed downward V −L < 0), and can therefore push mass out of the vortex if the vortex edge has its usual upward equatorward slope. However, under typical parameter conditions for the winter stratosphere, the magnitudes are nowhere near large enough to be consistent, by themselves, with Tuck et al.'s statement that the vortex is ‘flushed several times’ during a single winter.