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.

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.