Experimental study of particle trajectories below deep-water surface gravity wave groups

Abstract

Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.

Laboratory study of the wave-induced mean flow and set-down in unidirectional surface gravity wave packets on finite water depth

“…We also carry out new particle tracking velocimetry (PTV) experiments for wavepackets in a laboratory wave flume in the finite-depth regime, in which the effect of set-down on Lagrangian particle displacement becomes significant. We thus extend results for deep-water for which the set-down can be ignored, obtained by van den Bremer et al [43], to finite depth for which it cannot. We measure the set-down, take into account the effect of error waves, extract the Lagrangian displacement and compare results with our theoretical predictions, finding good agreement.…”

“…In addition to the solutions to the irrotational water wave equations [35,36], streaming in the boundary layers [33,37,38], convection of vorticity from the ends of the tank into the interior of the fluid [37,39] (or conduction from the free surface and bottom boundary layers [40]) or enhanced transport for particles on the surface in breaking waves may play a role [34,41,42]. Recently, van den Bremer et al [43] have demonstrated experimentally that Lagrangian transport by the combination of Stokes drift and the Eulerian return flow underneath uni-directional, deep-water surface gravity wavepackets is in good agreement with leading-order solutions to the irrotational water wave equations. This paper derives solutions for the mean flow and the wave-averaged free surface using the multiple-scales method, which are valid in arbitrary depths relative to the scale of the packet and the Eulerian return flow.…”

Stokes drift: theory and experiments

“…The results in van den Bremer et al (2019) may not be the last word on this topic. In 1802 Gerstner used the Lagrangian momentum equations to derive an exact solution to the inviscid water wave problem valid up to and including the deformed free surface (Gerstner 1802).…”

“…Given that the theory behind the Stokes drift is 172 years old, it is striking that the recent paper by van den Bremer et al (2019) is the first definitive, quantitative and unambiguous demonstration that the mean Lagrangian velocity in the absence of other flows can be accurately calculated from the lowest-order irrotational wave velocity field.…”

Laboratory Measurements of the Wave‐Induced Motion of Plastic Particles: Influence of Wave Period, Plastic Size and Plastic Density

“…The wave‐induced particle drift has been studied experimentally in different works (i.e., Calvert et al., 2019; Grue & Koolas, 2017; Lenain et al., 2019; Paprota et al, 2016; van den Bremer et al., 2019) although there is still some confusion about the experimental measurement of the net wave‐induced drift at the interior of the fluid (Monismith et al., 2007; van den Bremer & Breivik, 2017). In a closed tank, the Stokes drift of a periodic wave train must be accompanied by a Eulerian return current so that the steady‐state depth‐integrated Lagrangian drift is zero.…”