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Eulerian-mean flow, Stokes drift and Lagrangian-mean flow in exp2_wΒΆ

The Eulerian-mean flow (UE,VE), the Stokes drift (US,VS) and the Lagrangian-mean flow (UL,VL) are plotted in Figs. 1 (zonal) and 2 (meridional). The Lagrangian-mean flow has been deduced from the net displacement of parcels after one wave cycle (panels d) and from the sum of the Eulerian-mean flow and the Stokes drift (panels c). The two estimates agree well for the zonal component (Figs. 1c and d), less so for the meridional component (Figs. 2c and d). The agreement in the zonal direction confirms that the calculation of the Lagrangian-mean flow based on the net displacement of parcels is sound but it is not clear to me yet why there is such difference in the meridional component. Notice that when I add supposedly the next higher-order (third-order) term in the calculation of the Stokes drift, the comparisons are worse (not shown).


Figure 1: (a) Zonal Eulerian-mean flow (UE), (b) zonal Stokes drift (US), (c) UE+Us, and (d) zonal Lagrangian-mean flow (UL) over a wave cycle in the middle layer of exp2_w.


Figure 2: (a) Meridional Eulerian-mean flow (VE), (b) meridional Stokes drift (VS), (c) VE+Vs, and (d) meridional Lagrangian-mean flow (VL) over a wave cycle in the middle layer of exp2_w.

Finally, the Lagrangian-mean flow (the true one, deduced from parcel displacement) is nearly horizontally non-divergent (Fig. 3), which is a nice property to have and is consistent with the idea that the wave amplitude at a specific point does not change with time. This is not true, however, with the Lagrangian-mean flow deduced from UE and US (not shown).


Figure 3: (a) +ULx and (b) -VLy.