The PV test has been reperformed for `exp2_t` which has a 200x200 domain and it has been performed for `exp2_v` that has a 400x400 domain. In the second case, the PV test has been performed using the full and half the spatial resolution. The trajectories used in each case are shown in Fig. 1. Because the advection is significative, we could say that the experiments are quite nonlinear. Furthermore, the differences due to different spatial resolution in the initial domain are not too significative, which suggests that the results are relatively insensitive to spatial resolution. The trajectories in the 400x400 case compuated with the full resolution (red) are nearly similar with those computed with half the resolution suggesting also that the computation of the trajectories are not sensitive to the resolution.

Similarly, the PV tests are quite similar in every case (Figs. 2, 3 and 4). Differences between plain and dashed lines are due to the difference in the choice of the output (either snapshot or time averages). Differences between blue and red lines should arise because of the violation of the PV equation in the model. Because all these differences are comparable and are all smaller in most cases relative to the net PV change during a cycle, we could conclude that the model does respect the PV equation. If this is true then we could use the 200x200 domain to check that the Lagrangian-mean should fall to zero for infinitively small and large values of dissipation; we started it but we have seen only so far a decrease of the Lagrangian-mean flow with increasing dissipation. In the meantime, I am a bit disappointed that even with the 400x400 domain, neither the test nor the model are more “perfect”. Maybe the differences will disappear with an output more frequent than every day?