03.02.11: GLM theory over a period that is not a wave period

The Lagrangian-mean PV equation is computed over 100 days (one wave cycle; Fig. 1) and 133 days (Fig. 2). As expected, it does not matter that the mean is not over a wave cycle; the change of PV following parcel (either calculated directly like in panels d or by adding the time rate of change of PV –panels a– to the Lagrangian-mean advection –panels b– as in panels c) is always balanced by the Lagrangian-mean dissipation (panels e).

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 a wave cycle (days 2125-2225).

Figure 2: Same as Fig. 1 except that the quantities were compute over 133 days (days 2125-2258).