I show here the relationship between the Lagrangian mean and Eulerian mean velocity, Stokes drift and the coefficient of Laplacian dissipation. Figs. 1 and 2 show the typical pattern of the Lagrangian-mean, Eulerian-mean velocities and Stokes drift in one experiment. The Stokes drift always cancel the Eulerian-mean flow so that the Lagrangian-mean flow, that has the same pattern as the Eulerian-mean flow, is nonetheless weaker than the latter.

Figs. 3 and 4 show the evolution of some measure of each of these mean velocity components to the coefficient of Laplacian dissipation. Although all components vary, the evolution of the Eulerian-mean flow is qualitatively the same as that of the Lagrangian-mean flow, as long as the coefficient of dissipation (and dissipation) is not too small. Thus, although for weaker coefficient, both the Stokes drift and the Eulerian-mean flow increases, the increase of the latter is still larger than the increase in the former so that the difference, the Lagrangian-mean flow, evolves in the same direction as the Eulerian-mean flow.

Finally, notice that the theoretical prediction of the Stokes drift –valid at the third order in wave amplitude (the dashed red lines)– is not good for the meridional component but is relatively good for the zonal component. This is important as it means we could *a priori* estimate the zonal Lagrangian flow in observations from Eulerian time series alone.

computed with `theory_test_script.m` in the respective directories of `RESEARCH/MODELISATION/HIM/studies/diss_train_of_eddies/exp2/*/analysis_1d/` and `RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/`. The matlab routine to produce Figs. 3 and 4 is `plot_synthesis_Eulerian_Lagrangian_Stokes_diss.m` in `RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp15`.