# 09.06.2013: 10-year ensemble of annual mean Lagrangian flow, mean Eulerian flow, Stokes drift and bolus velocity in a two-layer simulation forced by an annual forcing¶

Shown here are the Eulerian mean flow (Fig. 1), the Lagrangian mean flow (Fig. 2), the Stokes drift calculated as the difference between the Lagrangian mean and the Eulerian mean (Fig. 3) and the bolus velocity (Fig. 4). Several observations:

1. The Lagrangian-mean flow is of the same order of magnitude as the Eulerian mean flow except near the equator.
2. The Stokes drift cancels the Eulerian mean flow at almost all latitudes (Fig. 5).
3. The bolus velocity is surprising low.
4. The Stokes drift approximated at the second and third order (Lighthill’s formulation) does not resemble the Stokes drift of Fig. 3 (not shown), suggesting that the flow is too nonlinear for the approximation to work. A rapid look at velocity amplitude (in u) and phase speed near 12.5°N gives about 30 cm/s in amplitude and 1° per day in phase speed (about 120 cm/s), suggesting that the simulation is indeed moderately nonlinear (30/120 = 0.25 is not much lower than 1).

Update: In Fig. 6, I show the meridional averages of the different quantities (first, just the Eulerian mean and the bolus velocity, then, in the lower panel, all quantities). As in Marshall et al. (2013), the bolus velocity exactly cancels the Eulerian mean flow. This suggests that my calculation of the bolus velocity should be OK. The lower panel, however, shows, I think, the noise level of the Lagrangian calculation. After all, the order of the meridional average is 1 cm/s which is an order of magnitude smaller than the strongest Lagrangian mean flow obtained in Fig. 5). Hence, the meridional averages of the Lagrangian mean flow and the Stokes drift should not be trusted and no meaningful conclusion should be drawn.

Figure 1: 10-year ensemble of annual mean (upper) zonal and (lower) meridional Eulerian flow in the upper layer of one of Eric’s simulation (save_08)

Figure 2: 10-year ensemble of annual mean (upper) zonal and (lower) meridional Lagrangian flow in the upper layer of one of Eric’s simulation (save_08)

Figure 3: 10-year ensemble of annual mean (upper) zonal and (lower) meridional Stokes drift in the upper layer of one of Eric’s simulation (save_08)

Figure 4: 10-year ensemble of annual mean (upper) zonal and (lower) meridional bolus velocity in the upper layer of one of Eric’s simulation (save_08)

Figure 5: Zonal averages of the 10-year ensemble of annual means in the upper layer of one of Eric’s simulation (save_08)

Figure 6: Meridional averages of the 10-year ensemble of annual means in the upper layer of one of Eric’s simulation (save_08)

These plots were made with plot_UE_VE_day7201_10years.py, plot_UL_VL_day7201_10years.py, plot_US_VS_day7201_10years.py, plot_Ub_Vb_day7201_10years.py and plot_zonal_averages_day7201_10years.py in RESEARCH/PROJECTS/EDDY_DRIVEN_MEAN_FLOWS/MID-LATITUDE-ZONAL-JETS/HIM-analysis