# The mean flow and waves in exp2_w¶

The mean flow and thickness anomaly in the middle layer of exp2_w and over a wave cycle are shown in Fig. 1. There is a westward flow centered at the central latitude of the forcing with eastward flows on both sides. Because the wave field is present everywhere to the west of the forcing area, it is not clear how much the Eulerian-mean flow shown in Fig. 1 is representative of the Lagrangian-mean flow. We have followed six parcels during a wave cycle (Fig. 2); the initial position of each is shown in Fig. 1. The net Lagrangian-mean zonal velocity (UL) of the three parcels to the west of the forcing area is in the same direction but is weaker than the Eulerian-mean zonal velocity (UE) at their initial position: UL=+0.072 cm/s and UE=+0.070 cm.s for the parcel to the north, UL=-0.03 cm/s and UE = -0.07 cm/s for the middle parcel and UL=+0.06 cm/s and UE=+0.07 cm/s for the parcel to the south. The same is true for the middle parcel to the east, located within the forcing area: UL=-0.063 cm/s and UE=-0.3 cm/s. Notice for this parcel that we would overestimate by a factor of 5 the Lagrangian-mean velocity based on the Eulerian-mean velocity. The fact that UL is much closer to UE for the parcels to the west is consistent with the fact that the wave amplitude is weaker there (Fig. 3).

Although weak, the Lagrangian-mean meridional flow of the parcel initially at 5°E and 33°N is southward, that of the parcel initially at 5°E and 27°N is northward. Based on this and the above, we could speculate that there are two zonal Lagrangian circulations between the forcing area and the western boundary, a clockwise one to the north of 30°N and an anti-clockwise one to the south of 30°N. If true then the Lagrangian-mean meridional flow is divergent along the western boundary and convergent everywhere else, especially within the forcing area.

Figure 1: Averaged quantities in the middle layer of exp2_w over a wave cycle: (upper) U, (middle) V and (lower) thickness anomaly. The red dots show the initial positions of 6 parcels followed during one wave cycle (see Fig. 2).

Figure 2: Trajectory (thin line) of six parcels and their net displacement (thick line) over a wave cycle. The initial position of the parcels is shown with a red dot in Fig. 1 and 2.

Figure 3: Standard deviation (STD) of quantities in the middle layer of exp2_w over a wave cycle: (upper) U, (middle) V and (lower) thickness anomaly.

The waves are in the order of 1-5 cm/s and appears to be stronger within and slightly to the west of the forcing area (Figs. 3 and 4). The fact that the wave amplitude weakens to the west is consistent with the idea that the waves are damped while propagating westward.

Figure 4: U and V in the middle layer and at 6 locations during a wave cycle.