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05.10.2013: LPV analysis of exp35_spongeΒΆ

exp35_sponge is like exp33_sponge (KH=10 m2/s) except that there 400x400 points instead of 200x200.

Fig. 1 shows how the kinetic energy averaged within the middle layer evolved with time. We see that after day 3000, the system has reached a statistically steady state. We can also compare this to the same graph from exp33_sponge in this note. We see that there is almost 3 more times energy in exp35_sponge than in exp33_sponge.

../../../../../_images/statistically_stationary_test1.png

Figure 1: Evolution of the kinetic energy in the intermediate layer in exp35_sponge.

Fig. 2 shows the trajectory of 5 parcels in exp35_sponge (right) and in exp33_sponge (left). Because the system is chaotic in both experiments, it is normal not to expect the same trajectories even if they started at the same place and same time.

Finally, Fig. 3 shows the LP analysis for these 5 parcels in exp35_sponge. As in exp33_sponge, it is not balanced (see 04.29.2013: LPV analysis of exp33_sponge with reduced time step) although we might argue that it is better. We would need to perform another simulation with even higher resolution to see when we get the LPV balance, if we even get it.

../../../../../_images/LPV_analysis_alltime_d4015d4215_8E11E_30N_mid_exp33_sponge_exp35_sponge_traj.png

Figure 2: Trajectories over 175 days in exp35_sponge.

../../../../../_images/LPV_analysis_alltime_d4015d4215_8E11E_30N_mid_exp35_sponge.png

Figure 3: LPV analysis for the 5 trajectories highlighted in Fig. 1 using snapshots (plain) or 1-day averages (dash).


The LPV analysis was done with LPV_analysis_all_time_script.m producing the Matlab file LPV_analysis_alltime_d4015d4215_8E11E_30N_mid_delta_tday_0_5_reduced_timestep_exp35_sponge.mat, all in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp35_sponge/ on the main disk on ipu1.