PERMEABILITY OF THE STRATOSPHERIC VORTEX EDGE - ON THE MEAN MASS FLUXDUE TO THERMALLY DISSIPATING, STEADY, NON-BREAKING ROSSBY WAVES

As part of an assessment of the flowing-processor hypothesis of Tuck e r al. (1993) and references-see also Rosenlof ed al. (1997)-this paper estimates possible contributions to flow through the edge of the stra tospheric polar Vortex due solely to distortion of the vortex by therm ally dissipating Rossby waves forced from below. To isolate such contr ibutions in a clear-cut way, and to eliminate questions about numerica l dissipation and truncation error, an idealized model is studied anal ytically It assumes steady conditions and non-breaking waves, the wave s being stationary in some rotating frame such as that of the earth. T he model is studied using two approaches: first via the generalized La grangian-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 avoidin g the use of any mean-and-deviation formalism. It is shown, in particu lar, that under quasi-geostrophic scaling the Lagrangian-mean meridion al velocity (v) over bar(L) is given correct to O(a(2)) by (v) over ba r(L) similar or equal to -(partial derivative theta(B)/partial derivat ive z)-1 <(H'partial derivative eta'/partial derivative z)over bar>, w here theta(B) is the basic-state potential temperature, z the altitude , eta' the meridional particle displacement and H' the wave-induced fl uctuation in the diabatic rate of change of potential temperature thet a. The formula for (v) over bar(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 radiativ e relaxation in the wintertime lower stratosphere, (v) over bar(L) may well be directed into rather than out of the vortex, though weak outw ard flow is possible in some cases. There is, in addition, a vertical mean flow (w) over bar(L) controlled by eddy dynamics above the altitu de under consideration. This is usually directed downward ((w) over ba r(L) < 0), and can therefore push mass out of the vortex if the vortex edge has its usual upward equatorward slope. However, under typical p arameter conditions for the winter stratosphere, the magnitudes are no where near large enough to be consistent, by themselves, with Tuck et al.'s statement that the vortex is 'flushed several times' during a si ngle winter.