Figure 6: Modelled fluid particle trajectories at the fluid surface perturbed by waves.

(a,b) Fluid particle motions (red curves) in a 2D linear wave propagating from left to right (blue and green dashed lines). (a) At order L in the particle displacement (see equations (8 and 10)), the instantaneous Lagrangian and Eulerian velocities are identical, the particle paths are closed loops. The period average velocity of the five trajectories shown is null. (b) Same linear wave, the fluid motion is now described (at order L²) in the Lagrangian frame: a particle follows a trochoidal curve, which illustrates the period-averaged Stokes drift velocity U_d. (c,d) Modelled surface particle trajectories in 3D linear standing waves for φ=π/2. This modelling corresponds to the experimental data shown in Fig. 3c,d. Surface particle drifts are tracked for ≈50T, the parameters are f=ω/2π=3.9 Hz (λ=104 mm), H=2.5 mm in (c) and f=3.9 Hz, H=1 mm in (d). These Lagrangian particle trajectories computed by numerical integration of the Eulerian equation (8) exhibit small-radius gyrations at frequency ω superimposed with a circulatory drift about the unit cell at a much lower frequency. The black dots signal the initial positions of the particles. The direction of the simulated drift alternates in adjacent unit cells.