Lagrangian Moan Motion Induced by a Growing Baroclinic Wave

Abstract

Lagrangian mean motion induced by a growing baroclinic wave is discussed, based onthe solution of Eady type problem of baroclinic instability including non-geostrophic effect. It is shown that to the leading order of Rossby number, the Lagrangian mean meridional motion is convergent toward the center of the channel. This means that air particles are mixed horizontally as a consequence of the instability. It is also shown that to the second order, air particles move downward near the northern wall and upward near the southern wall, while in the central region they move southward in the upper layer and northward in the lower, except for weak reverse flows near the top and the bottom. This Lagrangian mean picture is completely different from the usual Eulerian mean picture, and agrees qualitatively well with the result of Kida's (1977) numerical experiment as far as the behaviors of tropospheric particles are concerned, and with the result by Riehl and Fultz (1957) obtained in a rotating annulus experiment as far as the distribution of Lagrangian mean vertical flow is concerned.
The result that the Lagrangian mean velocity field is convergent (divergent) even under Boussinesq assumption (cf. Andrews and McIntyre, 1978) is attributed mainly to horizontal mixing term and partly to a term of transverse-gradient transport. Eliminating the horizontal mixing term from the latitudinal component of Stokes drift and also a term of transversegradient transport from the vertical component, we can obtain the solenoidal part of Lagrangian mean meridional velocity field. This residual circulation is somewhat similar to the Eulerian mean meridional circulation, and it may be equivalent to the Lagrangian mean meridional circulation induced by a dissipating planetary wave (of. Matsuno and Nakamura, 1978).
It is shown that only a part of the second order field mentioned above can be responsible to the change in Lagrangian mean zonal flow. As a result, the direction of the mean zonal flow acceleration is reverse to that in the Eulerian mean problem.
Finally, we estimate the so-called eddy diffusivity, to obtain that KH=9.6×109cm2/sec and KV=8.1×103cm2/sec under the assumed condition of baroclinic wave which is chosen as a typical cyclone. It is further pointed out that latitudinal buoyancy (heat) flux consists of down-gradient transport (or particle mixing) term and transverse-gradient transport term, and that the latter is about 20% of the former in magnitude.