Kr. Helfrich et J. Pedlosky, LARGE-AMPLITUDE COHERENT ANOMALIES IN BAROCLINIC ZONAL FLOWS, Journal of the atmospheric sciences, 52(10), 1995, pp. 1615-1629
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 dist
urbances of sufficient amplitude, could be explosively unstable and th
at 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 app
ropriate boundary conditions for localized instability problems is als
o given. Direct numerical integration of the full quasigeostrophic equ
ations is then undertaken to determine the ultimate fate of the explos
ive instability. The instability equilibrates as a locally steady, zon
ally uniform O(1) alteration of the original zonal flow that expands s
lowly in time. This region is connected to the original flow by narrow
regions of strong meridional flow. The finite-amplitude region develo
ps both closed streamlines and uniform potential vorticity. The ultima
te state is a finite-amplitude attractor; it is independent of the ini
tial disturbance and depends only on the original zonal dow. A simple
model demonstrates that the finite-amplitude state is a conjugate solu
tion of the original zonal potential-vorticity-streamfunction relation
. The model solution is described and compared with the numerical calc
ulations. It is suggested that this transition from a weakly nonlinear
to finite-amplitude modonlike state is a possible mechanism for the g
eneration of atmospheric blocking events that requires neither forcing
nor dissipation.