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PV balance in exp13 and exp14 (basin case)ΒΆ

We are now back to the basin case –for which a mean meridional Lagrangian circulation is possible. exp13 is like exp6 (especially, NO SPLIT, short time step of 30 s) except that the domain is now a basin and the surface forcing is the same as in diss_train_of_eddies/exp2/exp2_w (100-day oscillating patch of wind in the middle of the basin with no basin-averaged curl –see this note and the ones that follow). exp14 is like exp13 except that the horizontal Laplacian diffusion is reduced by a factor of 10 from 500 to 50 m2/s. exp13 and exp14 have 0.1 deg. resolution in both x and y (while exp6, the zonal channel case, had 0.21 deg. and 0.06 deg. resolution in x and y, respectively).

In exp13, the potential vorticity (PV) balance for 6 parcels seems to be satisfied (Fig. 3). This is an improvement compared to exp2_w that was run with time step fo 1200 s instead of 30 s (see this note). This shows again that the time setp is important for the PV test to be satisfied or not.

In exp14, however, the PV balance is less well satisfied. Does this mean we need to run the experiment with a time step smaller than 30 s? Strangely, the time series of the PV is “jumpy” in time; this is true for both estimates of the PV (using either the output PV or the output u and v), not from estimates of PV from the horizontal diffusion term. Notice that these jumps do not come from jumps in the trajectories (Fig. 4).

Finally, notice that, compared to the simulations in the zonal channel case, the displacements and, thus, the advection are large (Fig. 1). Notice also that the trajectories change a lot between the two simulations. We might want to run a simulation with weaker amplitude in order to be in a regime where trajectories change smoothly with dissipation. The large advection may, finally, be another reason for the lack of PV balance in exp14.

The next step is to see if I can start exp14 with a smaller time step from the RESTART file or from rest. To do that, I will use exp4 for which the PV balance was not satisfied due to a too large time step (exp6).

../../../../../_images/traj_6parcels_exp13_exp14.png

Figure 1: Trajectories of 6 parcels in exp13 (red) and exp14 (black). Notice how 1) the parcel displacements are relatively large and 2) how different the trajectories are between the two experiments.

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Figure 2: Parcel trajectories in exp13.

../../../../../_images/PV_bal_6parcels_exp13.png

Figure 3: PV balance in exp13 for 6 parcels, the trajectory of which are shown in Fig. 2.

../../../../../_images/traj_6parcels_exp14.png

Figure 4: Parcel trajectories in exp14.

../../../../../_images/PV_bal_6parcels_exp14.png

Figure 5: PV balance in exp14 for 6 parcels, the trajectory of which are shown in Fig. 4.