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02.13.13: LPV analysis of exp2_l over 2 and 13 cycles – “light version”

In this note, I show the LPV analysis of exp2_l over several cycles. I also noticed that we could come up with a simple diagnostic that would be rapid to get in order to estimate how many cycles we need before we reach the balance between PV advection and PV dissipation. I wrote a lighter version of theory_test.m called theory_test_light.m that does not compute the time rate of change of QL, as well as other Eulerian-mean quantities. dQL/dt is obtained when we use theory_test_light.m over several cycles (see theory_test_light.m).

In Fig. 1, I compare dQL/dt and the advective term obtained from the “full” and “light” version of theory_test.m. The comparison is good, good enough that if we compute the standard deviation in space of the two terms and see how they evolve with the number of cycles used for the average, we can have an idea of how many cycles is needed before dQL/dt is negligible with respect to the advective term (Fig. 2); of course, in this example, all terms have to go to zero so we will never have that case.

../../../../../_images/comp_dQLdt_calculated_with_full_and_light_analysis.png

Figure 1: Comparison of the time rate of change of QL and of the advective term obtained using either 2 or 12 cycles with (upper) theory_test.m and (lower) theory_test_light.m.

../../../../../_images/std_dQLdt_VC_2_to_13_cycles_exp2_l_light.png

Figure 2: Diagnostic of the convergence toward a steady balance obtained with theory_test_light.m. This should be compared with Fig. 2 of this note.


Computed with theory_test_several_cycles_script.m in RESEARCH/MODELISATION/HIM/studies/diss_train_of_eddies/exp2/exp2_l/analysis_1d on the main disk on ipu1. The Matlab files is diag_VC_thirteen_cycles_100day_long_day4215_to_day4500_exp2_l.mat in that same directory.