Some aspects of the nonlinear behavior of mid-latitude baroclinic waves are investigated by means of a series of integrations of the primitive equations with spherical geometry. Each integration has as initial conditions a balanced zonal flow perturbed by a small-amplitude disturbance of normal-mode form. Results are presented in detail for several zonal flows and perturbations which are confined initially to either zonal wavenumber 6 or zonal wavenumber 9.
In each case a disturbance grows by baroclinic instability and develops a structure in some agreement with the usual synoptic picture of an occluding system. Its growth rate at low levels decreases more rapidly than that at higher levels, as found by Gall using a more severely truncated model, and upper-level amplitudes become larger relative to surface values than in the initial linear mode. This is more marked for wavenumber 6 than for wavenumber 9, and differences in linear structure are thus enhanced in the nonlinear regime.
Barotropic processes become important during the occlusion of the disturbance as the forcing of vertical motion by thermal advection decreases in importance, although the vorticity actually changes at about half the rate that would occur in a barotropic fluid. In these examples the barotropic effects bring about a decay of the wave at a rate similar to that of its earlier baroclinic growth, and a well-defined life cycle exists.
Large-scale eddy fluxes of heat and momentum averaged over this life cycle have a structure that is substantially different from that given by linear stability analyses, and agreement with observation is improved. Net changes to the zonal-mean temperature gradient are largely confined to the lower troposphere and, to a lesser extent, the lower stratosphere. The change in surface zonal-mean flow is much as suggested by linear theory but at upper levels the westerly jet is strengthened as the disturbance decays.
Additional barotropic integrations have been performed to examine the changes in structure of longer wavelength disturbances at upper levels. Predominantly poleward momentum fluxes result from latitudinal variations in phase speed, and movement at a particular latitude is found to be governed largely by the zonal-mean velocity and vorticity gradient at that latitude. Additional baroclinic experiments provide an example of interactions involving a slower growing, longer wavelength component, and examples of some truncation errors that may result from use of lower resolution models. The sensitivity of results to the inclusion of dissipative processes is also examined.