411
wavelength of the topography and this wave then feeds back on the flow
by bottom form stress. Depending on the structural parameters (forcing
amplitude, friction, wavelength and height of topography) the system may
bifurcate (the mean flow and the Rossby wave are in resonance) and besides
an unstable state two stable states emerge one of which is dominated by
friction and the other one is in a balance dominated by bottom form stress.
For low forcing or high friction or low topography there is no bifurcation
and only the stable frictional state survives. The system has thus the
elements of the dynamical balance - forcing, friction and form stress -
which we have described above for the ACC. However, barotropic Rossby
waves have the same phase speeds in the atmosphere and the ocean and in
the later medium the mismatch of the sizes of mean currents and barotropic
phase speeds is even more severe: there is no way how such waves can
be locked into resonance by the much smaller observed mean flow. A
'barotropic ACC' is thus necessarily in a frictional state, in contrast to
high-resolution numerical experiments and - very likely - to reality. This
context is outlined in the next section.
We thus proceed to investigate the resonance mechanism in a baroclinic
generalization of the CdV system by considering the flow in a two layer
quasigeostrophic channel on a jj-plane. In contrast to previous baroclinic
models (e. g. Charney and Straus 1980) studied in atmospheric context
the oceanic parameter range allows simplifications for planetary scale dynamics. The simplest of the low-order models which we have derived has
nine degrees of freedom (compared to three in the CdV model or six in
the model of Charney and Straus). The model is nonlinear, it includes
wave-wave interactions, there is form stress arising from the barotropic
and baroclinic waves, but despite of these complexities the model can still
be completely solved by analytical means. We are thus able to determine
the equilibria and analyse in detail the momentum balance of these states
as well as the resonance mechanism of the zonal flow with the baroclinic
Rossby waves. We find that the system may have up to three steady states
which in certain parts of the parameter domain may all become unstable
and generate quite complex temporal behavior. Finally, we compare the
structural and temporal features of the low-order model with a more realistic model of zonal channel flow, an eddy resolving quasigeostrophic jjplane model.
wavelength of the topography and this wave then feeds back on the flow
by bottom form stress. Depending on the structural parameters (forcing
amplitude, friction, wavelength and height of topography) the system may
bifurcate (the mean flow and the Rossby wave are in resonance) and besides
an unstable state two stable states emerge one of which is dominated by
friction and the other one is in a balance dominated by bottom form stress.
For low forcing or high friction or low topography there is no bifurcation
and only the stable frictional state survives. The system has thus the
elements of the dynamical balance - forcing, friction and form stress -
which we have described above for the ACC. However, barotropic Rossby
waves have the same phase speeds in the atmosphere and the ocean and in
the later medium the mismatch of the sizes of mean currents and barotropic
phase speeds is even more severe: there is no way how such waves can
be locked into resonance by the much smaller observed mean flow. A
'barotropic ACC' is thus necessarily in a frictional state, in contrast to
high-resolution numerical experiments and - very likely - to reality. This
context is outlined in the next section.
We thus proceed to investigate the resonance mechanism in a baroclinic
generalization of the CdV system by considering the flow in a two layer
quasigeostrophic channel on a jj-plane. In contrast to previous baroclinic
models (e. g. Charney and Straus 1980) studied in atmospheric context
the oceanic parameter range allows simplifications for planetary scale dynamics. The simplest of the low-order models which we have derived has
nine degrees of freedom (compared to three in the CdV model or six in
the model of Charney and Straus). The model is nonlinear, it includes
wave-wave interactions, there is form stress arising from the barotropic
and baroclinic waves, but despite of these complexities the model can still
be completely solved by analytical means. We are thus able to determine
the equilibria and analyse in detail the momentum balance of these states
as well as the resonance mechanism of the zonal flow with the baroclinic
Rossby waves. We find that the system may have up to three steady states
which in certain parts of the parameter domain may all become unstable
and generate quite complex temporal behavior. Finally, we compare the
structural and temporal features of the low-order model with a more realistic model of zonal channel flow, an eddy resolving quasigeostrophic jjplane model.