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Net Lagrangian PV change along one latitude for different periods in exp4 and exp6

The 80-day running mean of the velocity field appears the same in exp4 and exp6 (Fig. 1). The net PV change has been computed along one latitude for one zonal wave cycle (Fig. 2) in the two experiments and for three different periods covering that of Fig. 1. The change is about the same in both experiments but it decreases with time. This is in accord with the hypothesis that what causes these changes are due to the long-term change of wave amplitude of Fig. 1; because the later decreases with time (Fig. 1), then we expect the PV change due to that effect to decrease also with time, which is the case.

One can then wonder what would happen if the experiments were run long enough so that the wave amplitude becomes constant and the PV change due to long-term wave amplitude becomes negligible. I am in the process of running both experiments up to day 2560.

../../../../../_images/u_v_runm_exp4_exp6.png

Figure 1: 80-day running mean of U and V at the eastern edge of the domain and two different latitudes (where U and V reach their maximum value) in exp4 and exp6.

../../../../../_images/net_Lag_PV_change_3periods_onelat_exp4_exp6.png

Figure 2: Net Lagrangian PV change along one latitude (21N) in exp4 and exp6 for three different periods of each run. Lines: from Q; dots: from HOR, both computed with snapshots u and v. See analysis_3_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/.

Same analysis extended up to day 2560

We extended the simulations up to day 2560 and performed the same analysis as above. The running mean are shown in Fig. 3. We see that the mean flow is slowly decreasing to zero as we expected if the simulation has to reach a stationary state. However, the net PV change for later periods, although much weaker, has still the same periodic shape in x. Either we are wrong to think that this periodic pattern is linked to the variation of the wave amplitude and should disappear at some point or that effect still dominates the net PV change even when it is weak over the effect due to friction alone which should give a zonally-symmetric net PV change.

../../../../../_images/u_v_runm_exp4_exp6_uptod2560.png

Figure 3: 80-day running mean of U and V at the eastern edge of the domain and two different latitudes (where U and V reach their maximum value) in exp4 and exp6. See concat_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/.

../../../../../_images/net_Lag_PV_change_2periods_onelat_exp4_exp6.png

Figure 4: Net Lagrangian PV change along one latitude (21N) in exp4 and exp6 for two different periods of each run. Lines: from Q; dots: from HOR, both computed with snapshots u and v. See analysis_3_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/quarter_of_a_day_output.