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02.13.13: LPV analysis of exp25 using 12 cycles over 600days

Fig. 1 first shows the PDf in time of the zonal velocity U west of the forcing area and around the central latitude in the middle layer. We see that an instability occurred with a low-frequency wave of period about 600 days has been generated. This wave interacts with the initial wave to generate multiple peaks around the frequency peak of the initial wave. A similar feature appears around each harmonic of the initial wave frequency.


Figure 1: PDf in time of U in the middle layer of exp25.

Fig. 2 shows the LPV analysis using 12 cycles separated by 50 days each (over a total of 600 days). We can compare this with the analysis made over two cycles only (Fig. 4 in this note). As expected, the time rate of change is much weaker and we almost have a the steady balance between the advective term and the dissipative term.

Fig. 3 shows how the rms of each term varies with a greater number of cycles included. We see that the rms of the time rate of change keeps decreasing while the rms of the advective and dissipative terms stabilize and become equal. We may need, however, 4 or 6 more cycles to maybe get the rms as low as 5% of the rms of the advective and dissipative term.

The only thing I am a bit disappointed is the structure of the Lagrangian-mean flow. Unfortunately, I did a mistake in writing the output of theory_test_light_several_cycles_script.m (now corrected) so I do not have the Lagrangian-mean flow averaged over all these cycles. But the advective and dissipative terms shown in Fig. 2 should now be close to the meridional component of the Lagrangian-mean flow. If that is true then the structure of Lagrangian-mean flow becomes very complicated.


Figure 2: LPV analysis using 12 cycles over 600 days in exp25.


Figure 3: Test of convergence toward the steady balance (balance between the advective and dissipative terms) using up to 12 cycles over 600 days (exp25).

Computed with theory_test_light_several_cycles_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp25 on the main disk on ipu1. The Matlab file is diag_VC_twenty_cycles_100day_long_day2015_to_day2300_exp25_light.mat in that same directory. Fig. 3 was produced using LPV_steady_balance_test_conv.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp25.