# 02.19.13: LPV analysis of exp2_6 and exp2_w6_sponge using 17 cycles over 800 daysΒΆ

I, here, look at how the steady balance in the LPV equation converges in exp2_w6 and exp2_w6_sponge (both have KH = 10 m2/s and MAG=500; see this note).

Not only the balance has not converged yet even after using 17 cycles but I do not even get a very nice PV balance between all terms using the light version of the LPV analysis. It would be nice to see if I recover the LPV balance using the full version of the analysis.

Another comment is that I use segments translated by 50 days. What I should have done before the calculation is looking at how the wave field varies. Does it have a 600-day periodicity as in exp25 (see this note) or something else? I just did that and the answer is that there is no obvious periodicity. Time series of 1-day U between day 2000 and 3000 looks like that from a realistic eddy field; a dominant period of about 100 day but no obvious periodicity. By curiosity, I looked also at the wave field in exp2_l, a simulation that has a weaker wave field but zero dissipation. According to this note or this note, the LPV balance converges quite rapidly toward the steady balance (in this case, zero equals zero). Not surprising, the wave field is actually perfectly periodic in exp2_l, suggesting that it should be more difficult (that is, more cycles are needed) to get the steady balance in any non-periodic case such as in exp2_w6 and exp2_w6_sponge.

Figure 1: Test of convergence toward the steady balance (balance between the advective and dissipative terms) using up to 17 cycles over 800 days for exp2_w6.

Figure 2: Same as Fig. 1 but for exp2_w6_sponge.

Computed with theory_test_light_several_cycles_script.m and LPV_steady_balance_test_conv.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/diss_train_of_eddies/exp2/exp2_w6/analysis_1d and RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/diss_train_of_eddies/exp2/exp2_w6_sponge/analysis_1d on the main disk on ipu1. The Matlab files are diag_VC_17_cycles_100day_long_50day_apart_day2015to2815_exp2_w6_light.mat and diag_VC_17_cycles_100day_long_50day_apart_day2015to2815_exp2_w6_sponge_light.mat in that same directory.