On the Distribution of Angular Velocity in Gaseous Envelopes Under the Influence of Large-Scale Horizontal Mixing Processes*

Abstract

An attempt is made to determine the limiting zonal wind distribution in the atmosphere which would result from intense, thermally driven, lateral mixing processes. The total thickness of that portion of the atmosphere which effectively participates in the perturbations responsible for the large-scale lateral exchange has a thickness of the order of magnitude of 20 km, while the distance between pole and equator is about 10,000 km. In view of the small value (1/500) of the ratio between these dimensions the atmosphere is considered as a thin shell in which the vertical dimension may be neglected. It is assumed that the mixing process is associated with a tendency towards equalization of the vertical component of the absolute vorticity. On this basis it is possible to account for some of the more striking features of the zonal wind distribution at the tropopause level. Assuming a similar type of lateral mixing to occur in the surface layers of the sun it is possible to account for the observed distribution of its rotation, and in particular for its “equatorial acceleration.” The velocity profiles obtained through lateral mixing in such thin atmospheric shells are analyzed from the point of view of shearing instability. It is found that shearing instability would limit the zone of constant absolute vertical vorticity within each hemisphere to a polar cap, the equatorial boundary of which would be 30° to 35° polewards from the equator. This result agrees well with the apparent break in the law for solar rotation at about 30° heliographic latitude and with the occurrence of a sharp maximum in the zonal west wind at the tropopause level at the same latitude during the season of maximum lateral mixing (winter season).