04.24.2013: LPV analysis of exp33_sponge (PV balance along trajectories)ΒΆ
Here, I look at the LPV analysis in exp33_sponge [NOTA: Until now, I was calling the GLM analysis, the LPV analysis. From now on, I will call the LPV analysis the study of the PV balance along parcel trajectories and the GLM analysis, the additional step of looking at the Lagrangian-mean PV balance broken down into different terms as described by Andrews and MacIntyre 1978].
Fig. 1 shows a bunch of trajectories and Fig. 2 shows the LPV analysis for the 5 trajectories highlighted in Fig. 1. We see that the PV is not balanced. Furthermore, because we obtain the same result with snapshot (plain) or 1-day averages (dash), I conclude that the problem does not come from a lack of temporal resolution [although I would like to check this using, for instance, half-a-day output] or a sensitivity to the way terms are being computed [In the 1-day averaged calculation, some terms are directly from the model output]. If this is indeed correct, that means that the PV is not well balanced in exp33_sponge, which is an interested result in itself [The model characteristics needed to assure that PV is balanced over a certain amount of time depend on the regime]. To confirm this, we could run the model with higher spatial resolution [assuming that this is the issue].
Figure 1: Trajectories over 200 days in exp33_sponge. The averaged Lagrangian mean flow is shown in Fig. 4 in this note [NOTA: Note that the Lagrangian-mean flow varies significantly form one cycle to another so that the trajectories obtained over this particular 200-day-long period are not necessarily consistent with the averaged Lagrangian-mean flow shown in Fig. 4 of the note. I want to add, however, that the way I obtain the Lagrangian-mean flow is maybe a nice way to estimate what is the average transport by eddies, even in a flow that is not purely periodic].
Figure 2: 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_exp33_sponge.mat, all in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp33_sponge/ on the main disk on ipu1.