Nonlinear interactions between the zonal flow, topographically forced waves and free baroclinic waves are investigated by using the two-layer, quasi-geostrophic, low-order model constructed in Part I (Yoden, 1983). An idealized topography is given by a Fourier component with the largest scale permitted in the present model.
When the zonal flow is more unstable with respect to a free wave than to the forced wave, there appears a final steady state in which the finite amplitude free wave with a constant phase velocity balances with the marginally stable zonal flow and the forced wave decays out. On the other hand, when the flow is more unstable with respect to the wave component directly coupled with the topography, the flow system has both of the forced and free wave components.
All the wave components are coupled with the topography in least severely truncated case in this paper (two meridional modes and three zonal wavenumbers of n, 2n and 3n are permitted). Then the flow system has several types of time-dependent behavior depending on the external parameters such as the external thermal forcing, the frictional dissipation and the static stability: Steady flow with constant forced wave and propagating free wave, periodic or quasi-periodic oscillation and irregular fluctuation.
For the external parameters corresponding to the real atmosphere, there appears an irregular fluctuation with large-amplitude waves. Statistical relation between the zonal flow and waves in the irregular fluctuation is investigated over a long time-span. The flow pattern at each time step is classified into one of three categories in terms of the magnitude of the mean zonal flow. Composite fields in three categories are characterized by the zonality in the high-index state and the moderate state and by the meander of the flow in the low-index state. When the flow is in the low-index state, both of the mean value and vertical shear of the zonal flow are small, the stationary waves have larger amplitudes, and the transient waves have smaller amplitudes compared with the high-index and the moderate states. The structure of the stationary waves in the irregular fluctuation is different from that of the forced wave in the equilibrium solutions in Part I.
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