I repeat the calculation made in *this note*, except that I use now up to 38 cycles. The criterion for the convergence toward the steady balance is shown in Fig. 1. We see, somewhat as expected, that after a quick decrease, the time rate of change only decreases very slowly. Fig. 2 shows the balance of terms using an average over the 38 cycles; it is not too different from what we had with 12 cycles (Fig. 2 in *this note*). Again, this should not be surprising because when we used 12 cycles, we already cover the main domain of variability of the wave field. Anything that varies at a time scale longer than 600 days is expected to vary only slowly suggesting it will take time to reach the final balance.

In any case, in the same time, we should not expect much change from the balance we have already obtained. Fig. 3 shows the Lagrangian-mean flow. After all, the zonal component does not have a spatial structure as complex as we could have thought by just looking at the meridional component. Yet, when we compare the zonal average of the zonal component with the same quantity from `exp24` (which uses a KH of 250 m2/s instead of 100 m2/s and does not exhibit much variability between cycles so that calculation using 2 cycles have already converged), we see that there is a sudden change in the meridional profile with high asymmetry in the simulation with the lowest KH (Fig. 4).

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_38_cycles_100day_long_50day_apart_day2015to3865_exp25_light.mat` in that same directory. Fig. 1 was produced using `LPV_steady_balance_test_conv.m` in that same directory.