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01.24.13: Results from averaging over 10 cycles, 90-day-long eachΒΆ

Here (Fig. 1), we show the result of a calculation where Lagrangian means have been computed over 90-day long cycles and these means have been then further averaged out over 10 of these cycles.

Good: The time rate of change has not blown out and the other terms are similar to what we get when we calculate the Lagrangian means over the actual wave cycles (100 days). Good: Also, the nonlinear term is nearly equal to the terms computed from the ensemble-averaged Lagrangian means. Bad (but not too bad): The time rate of change has not canceled (even if it does when the cycles are 100-day long).


Figure 1: Terms in the Lagrangian-mean PV equation. Terms are shown as an equivalent velocity. The Lagrangian averages have been performed over 90-day long cycles and these have been further averaged out over 10 cycles. The first cycle starts on day 2015 and all other nine cycles starts 45 days later than the previous one.

Fig. 2 shows that, actually, the time rate of change does get weaker and weaker, the more cycles are included in the average. Given the decay, we hope that it should get small relative to the other terms after including about 20 cycles. Actually, if we would have included 9, instead of 10 cycles, we would have already get the picture we want, with negligible time rate of change (Fig. 3).


Figure 2: Maximum absolute amplitude of the time rate of change (plotted as an equivalent velocity) over the region 5E-15E and 26N-34N.


Figure 3: Same as Fig. 1 except that the average shown is over the first 9 cycles.

computed with theory_test_several_cycles_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp20 on the main ipu1 disk. The Matlab file is diag_VC_ten_cycles_90day_long_exp20_2.mat in that same directory.