In Fig. 1, I show the test of convergence toward the steady balance for `exp32` (same as `exp25` except that KH = 50 m2/s). This test needs to be compared with the same test for `exp25` (Fig. 1 in *this note*). We see that it converges less rapidly in `exp32` than in `exp25` but it does converge at least.

A look at the wave field shows that the wave field is not more periodic; in `exp25`, there was at least a 600-day period, but this is not the case for `exp32`. That probably explains why the convergence is much slower and we may need more cycles to get the steady balance.

Two questions have to be answered: 1) Does the balance and is convergence differ in `exp25` when using a sponge layer? and 2) How many cycles we need to get a satisfactory steady balance in `exp32` (at the look at Fig. 1, we may need up to 70 cycles)?

Fig. 2 shows the balance we get with 37 cycles. It needs to be compared with the same calculation for `exp25` (Fig. 2 in *this note*). Several remarks:

- The overall balance is not as great as before but I am hoping that is due to the fact I am using the “light” version of the analysis and the “full” version will be better.
- The upper middle and upper right panels are not as equal as before; this is probably due to the absence of periodicity and that can be a problem as I use the second term to define the component of the Lagrangian-mean flow that is across Lagrangian-mean PV contours (I do not know if this gets better with more cycles included).
- The pattern of the dissipative term is actually a bit more regular than in
`exp25`.

Fig. 3 shows the Lagrangian-mean flow using 37 cycles. The patterns are similar to what we get in `exp25`.

Computed with `theory_test_light_several_cycles_script.m` in `RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp32` on the main disk on `ipu1`. The Matlab file is `diag_VC_38_cycles_100day_long_50day_apart_day2015to3865_exp32_light.mat` in that same directory. Fig. 1 was produced using `LPV_steady_balance_test_conv.m` in that same directory.