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3. The meridional circulation in a zonally symmetric model

We now investigate to what extent the meridional circulations produced in the wave-one model of the previous section can be reproduced in a zonally symmetric model using an applied zonal momentum force that is derived from the wave-induced momentum forcing of the wave-one model. Three sets of experiments are described. In the first, Z1, the radiative forcing is the same as that of the perpetual winter cases, W1, of Section 2 above and the zonal momentum force is the steady state wave induced zonal momentum force per unit mass produced by h₀=240m, that is

where is the Eliassen-Palm flux from W1 (eg. Andrews et al., 1987). In the second, Z2, the radiative forcing is the same as that of the seasonally varying cases, W1, of §2 above and the zonal momentum force is the seasonally varying wave induced zonal momentum force per unit mass produced by h₀=240m. In the third, Z3, both the radiative forcing and the zonal momentum force are constant in time and equal to the annual average of the values used in Z2.

The results are shown in Figure 2. We see that the zonal model produces similar upwelling responses in both the steady state and in the seasonally varying cases (Figure 2a,b solid and dashed lines). This is despite having smoothed the zonal force in both space and time, verifying that it is the broad scale structure that is important in determining the response. Figure 2b also shows the response to Z3 (dotted line), the steady state calculation forced with the time averaged values of the seasonally varying Z2. We see that there is a slight decrease in magnitude of the upwelling response, of about 20%, from that of Z3. Since linear theory predicts that the two responses should be the same, this suggests that there may be some nonlinear interaction taking place between the zonal momentum forcing and the seasonal cycle in radiative basic state. This will be considered more fully below.

Figure 2: As Figure 1 but for a zonally symmetric model forced with the wave induced zonal momentum force per unit mass output from W1 and W2 with h₀=240 (solid), together with the associated W1/W2 reponse (dashed): (a) steady state response; (b) annually averaged, seasonally varying response. The dotted line in (b) is Z3 (see text).