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Change in the Lagrangian mean PVΒΆ

The time rate of change of Lagrangian mean PV is plotted in Fig. 1a in terms of a velocity (it is divided by the magnitude of the horizontal gradient of the Lagrangian mean PV as the rest of the PV equation). It is weaker than the velocity across mean PV contours (Fig. 1b) but not negligible. When the two quantities are summed (Fig. 2b), it equals the velocity deduced from either the change of PV (Figs. 1c and 2c) or the action of dissipation (Figs. 1d and 2d) following water parcels. The equality is not perfect due to some noise from the estimate of the time rate of change of Lagrangian mean PV, but it is still pretty good.


Figure 1: (a) Time rate of change of Lagrangian-mean PV computed using two waves cycles, 530-630 days and 531-631 days. The quantity is divided by the amplitude of the horizontal gradient of the Lagrangian-mean PV to have the unit of a velocity; (b) Velocity across contours of Lagrangian-mean PV; (c) Velocity deduced from the change of PV following parcels; (d) Velocity deduced from dissipation following parcels.


Figure 2: Same as Fig. 1 except that panel (b) is the sum of panels (a) and (b) of Fig. 1.

See RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/160d_with1200s and RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/160d_with30s for exp4, and RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp8/160d_with30s for exp8. The PV test was made in each case with analysis_4_script.m located in each of these directories.