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

Abstract

The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modelling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wavepackets that is valid for all water depths, both relative to the length of the wave and the length of the wavepacket. To validate this solution, we carry out Particle Tracking Velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wavepackets, finding good agreement. The extraction technique is able to deal with small background motion and sub-harmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wavepacket scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.

Surface wavepackets subject to an abrupt depth change. Part 1. Second-order theory

“…1989; Calvert et al. 2019). After the step ( figure 3 e – h ), both the superharmonic bound wavepacket and the subharmonic bound set-down have increased in magnitude.…”

“…1989; Calvert et al. 2019) where () is the maximum wavenumber of the packet resulting from the assumption of narrow bandwidth, is the phase velocity and is the group velocity of the wavepacket on the deeper side.…”

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

“…Calvert et al. (2019) extended this work to analytically solve the Eulerian and Stokes drift for various values of kh and wave group length to water depth ratios showing good match with experimental measurements.…”

“…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.…”

On the Estimation of the Surface Elevation of Regular and Irregular Waves Using the Velocity Field of Bubbles

“…Later, [30,31] performed simultaneous measurements of topography and velocity fields on FSEW and [32] analyzed a refracted image and a reference image to measure the FSEW. Other research studies measured the deformation of the FSEW with a modification to the optical profilometry technique [33] and measured the flow fields beneath the free surface of the waves with PTV [34,35]; [36,37] also used PTV to measure wave-induced mean flow and particle trajectories for linear wave packets. In turn, [38] used PIV methods to evaluate mass transport velocity based on measured vector fields.…”