Large-Amplitude Coherent Anomalies in Baroclinic Zonal Flows

Abstract

In a previous paper the authors developed an asymptotic time-dependent theory for coherent structures on a marginally stable baroclinic flow. It was shown that solitary waves, as well as other more general disturbances of sufficient amplitude, could be explosively unstable and that the asymptotic theory provided no mechanism for equilibration. The asymptotic theory is reexamined and shows that the instability can be interpreted as a problem in local instability. A discussion of the appropriate boundary conditions for localized instability problems is also given. Direct numerical integration of the full quasigeostrophic equations is then undertaken to determine the ultimate fate of the explosive instability. The instability equilibrates as a locally steady, zonally uniform O(1) alteration of the original zonal flow that expands slowly in time. This region is connected to the original flow by narrow regions of strong meridional flow. The finite-amplitude region develops both closed streamlines and uniform potential vorticity. The ultimate state is a finite-amplitude attractor; it is independent of the initial disturbance and depends only on the original zonal flow. A simple model demonstrates that the finite-amplitude state is a conjugate solution of the original zonal potential-vorticity-streamfunction relation. The model solution is described and compared with the numerical calculations. It is suggested that this transition from a weakly nonlinear to finite-amplitude modonlike state is a possible mechanism for the generation of atmosphere blocking events that requires neither forcing nor dissipation.