A new numerical model of the middle atmosphere is described. In addition to the equations governing the zonal mean state, the model includes a potential vorticity equation for a single planetary-scale Rossby wave. Nonlinearity associated with large-amplitude waves is represented by means of the planetary wave breaking parameterization of Garcia <1991>. The formulation of the zonal mean problem differs from our earlier work in that the momentum equation is solved directly to facilitate the study of tropical dynamics. The model also includes an infrared radiative transfer code for the stratosphere and lower mesosphere, which replaces the Newtonian cooling parameterization used previously. It is shown that explicit computation of the planetary-scale wave field yields a more realistic representation of the zonal mean dynamics and the distribution of trace chemical species. In particular, wave breaking produces a well-mixed ''surf zone'' equatorward of the polar night vortex and drives a meridional circulation with downwelling on the poleward side of the vortex. This combination of mixing and downwelling produces shallow meridional gradients of trace gases in the subtropics and middle latitudes, and very steep gradients at the edge of the polar vortex. Mixing ratios of trace gases of tropospheric origin are very low within the vortex in winter. Computed distributions of methane and nitrous oxide are shown to agree well with observations. ¿ American Geophysical Union 1992