Notes on 3-layer zonal channel simulations: exp4

For the first time, I study 3-layer model in a zonal channel forced by a zonally periodic wind stress (Fig. 1). These experiments start with exp4 in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/.

exp4 was run with the same level of friction and resolution than exp2_w in RESEARCH/MODELISATION/HIM/studies/diss_train_of_eddies/exp2/exp2_w for which the PV test appeared to be successful (see this note).

Figure 1: Snapshot of the (a) zonal and (b) meridional wind stress.

Snapshots of zonal (U) and meridional (V) velocity for the three layers are shown in Figs. 2 and 3, respectively. Although the fields are zonally periodic, the meridional structure is not symmetric as the wind stress. One possible reason is the presence of friction, horizontal but especially bottom friction, that modifies enough the wave field to loss its symmetry in the meridional direction. Fig. 4 shows the time series of U and V for the same location in the middle layer. It appears that the fields are not perfectly periodic.

Figure 2: Snapshot of the zonal velocity field U in the three layers.

Figure 3: Snapshot of the meridional velocity field V in the three layers.

Figure 4: Time series of U and V at 12.65E and 22.53N.

Although the potential vorticity (PV) equation is not satisfied during one wave cycle (see PV balance in Fig. 7 for 4 parcels, the trajectories of which are shown in Fig. 6 and the initial positions in Fig. 5), the net PV change after one wave cycle is. Notice also that, contrary to expectation, the net PV change is not zonally symmetric. Finally, notice that the displacement of parcels (Fig. 6) are much smaller than the model resolution, which might explain why the PV balance is not satisfied.

Figure 5: Net PV change (during the wave cycle of days 550-630) using (a) PV output and (b) horizontal friction (HOR) output. The black dots show the initial position of 4 parcels, the trajectories and PV balance are show in Figs. 6 and 7. See analysis_1_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4.

Figure 6: Trajectories of the parcels shown in Fig. 5. The numbers at the top of each panel give the maximum zonal and meridional displacements of each parcel, numbers that can be compared to the zonal and meridional resolution in the simulation given in the middle.

Figure 7: PV balance of the 4 parcels of Figs. 5 and 6.

Things to do:

• Understand why the net PV change is satisfied but not the PV balance with time
• Understand why the net PV change is not zonally symmetric
• Increase the magnitude so that the model resolve the trajectories
• Study the effect of having different ratio zonal/meridional resolution (see exp5)
• Study the effect of model time step (DT)
• Study the effect of SPLIT (see exp6)