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03.08.11: Test of the GLM theory over 475 days

In Fig. 1, I show the test of the GLM theory over 4 and 3/4 of a cycle (475 days) and over a small portion of the domain in order to see if we would reach a quasi-steady state (the change of Lagrangian-mean PV with time is negligible, panel (a), compared to other quantities) if we perform the average over a length of time that is not exactly a multiple of the wave period. We see (Fig. 1a) that even after 4 cycles there is still a large value for the change of the Lagrangian-mean PV with time and many more cycles would be needed to make that term negligible.

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Figure 1: (a): Time rate of change the Lagrangian-mean PV.(b): Lagrangian mean velocity across the Lagrangian-mean PV contours. (c); Sum of (a) and (b). (d): Lagrangian-mean velocity across mean PV contours deduced from the change of PV following water parcels. (e) Lagrangian-mean velocity across mean PV contours deduced from dissipation along parcel trajectories. All quantities have been computed for the days 2002-2477 and for simulation exp15 (KH=1000 m2/s).