# 02.19.13: LPV analysis of exp32 using 38 cycles over 1850 daysΒΆ

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:

1. 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.
2. 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).
3. 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.

Figure 1: Test of convergence toward the steady balance (balance between the advective and dissipative terms) using up to 38 cycles over 1850 days for exp32 (38 100-day long cycles were used that are 50 days apart between day 2015 and day 3865).

Figure 2: LPV analysis using 38 cycles over 1850 days in exp32.

Figure 3: Lagrangian-mean flow using 37 cycles in exp32.

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.