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01.24.13: Comparison of Eulerian and Lagrangian PDf for uΒΆ

We compare here the PDf of zonal velocity calculated either at a fixed point (Eulerian) or along a parcel’s trajectory (Lagrangian). The map of the time rate of change of Q_L (computed over one wave cycle) is shown in Fig. 1 together with the location chosen for computing the Eulerian PDf and the parcel’s trajectory to compute the Lagrangian PDf. In both cases, we are in a region where the time rate of change does not exactly cancel to zero.

Fig. 2 shows the two PDf. We see that the energy in the Eulerian PDf is well discretized over multiple of the forcing frequency (100 day period) while the energy in the Lagrangian PDf is spread over surrounding frequencies. That does explain why we should not expect the time rate of change of Q_L to cancel.

../../../../../_images/PDf_Eul_Lag_map.png

Figure 1: Map of the time rate of change of Q_L (one 100-day cycle used). The blue dot shows the location chosen to compute the Eulerian PDf. The black line shows the 4900-day trajectory of the parcel used to compute the Lagrangian PDf.

../../../../../_images/PDf_Eul_Lag.png

Figure 2: Eulerian (blue) and Lagrangian (red) PDf of zonal velocity.


computed with PDf_Eul_Lag_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp20 on the main ipu1 disk.