Lagrangian Surface Wave Motion and Stokes Drift Fluctuations

Herbers, T. H. C.; Janssen, T. T.

doi:10.1175/jpo-d-15-0129.1

Cited by 26 publications

(23 citation statements)

References 25 publications

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“…Furthermore, our experiments demonstrate the existence of a vertical component to the Stokes drift, which only exists for wave groups and results in a positive (temporary) vertical particle displacement underneath the centre of the group. This positive vertical displacement by the Stokes drift has been predicted by Herbers & Janssen (2016), who showed the set-down of the wave-averaged free surface in Eulerian records can appear as (significant) set-up in Lagrangian (buoy) records. Nevertheless, a vertical component to the Stokes drift (for groups) has been contentious in adaptations of the work by Craik & Leibovich (1976) in the context of ocean circulation and Langmuir circulation.…”

Section: Introductionsupporting

confidence: 73%

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

et al. 2019

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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.

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Section: Introductionsupporting

confidence: 73%

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

et al. 2019

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“…We point out that a model similar to the JS equation was proposed by Herbers and Janssen [27] (see their equation (20)). That model however is inaccurate since it neglects the denominator in equation (9).…”

Section: John-sclavounos Equationmentioning

confidence: 77%

Surface Waves Enhance Particle Dispersion

Farazmand

Sapsis

2019

Fluids

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We study the horizontal dispersion of passive tracer particles on the free surface of gravity waves in deep water. For random linear waves with the JONSWAP spectrum, the Lagrangian particle trajectories are computed using an exact nonlinear model known as the John-Sclavounos equation. We show that the single-particle dispersion exhibits an unusual super-diffusive behavior. In particular, for large times t, the variance of the tracer |X(t)| 2 increases as a quadratic function of time, i.e., |X(t)| 2 ∼ t 2 . This dispersion is markedly faster than Taylor's single-particle dispersion theory which predicts that the variance of passive tracers grows linearly with time for large t. Our results imply that the wave motion significantly enhances the dispersion of fluid particles. We show that this super-diffusive behavior is a result of the long-term correlation of the Lagrangian velocities of fluid parcels on the free surface. Summary of the main resultsAs we review in Section 1.2, this second-order statistics has also been studied extensively. However, previous studies either assume the velocity field as a linear superposition of the velocity induced by linear waves or use perturbation theory to approximate the velocity field. Here, however, Submitted to Fluids, pages 1 -12

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“…Furthermore, in shallow water, where the magnitude of the set-down is typically strongly amplified, the distortion in its Lagrangian records is only expected to be small. Analysing velocity data from buoys, Herbers & Janssen [81] find clear evidence of the second-order Eulerian 'frequency-difference' or 'infragravity waves' that form in response to fluctuations in the Stokes drift in 'groupy' signals, emphasizing that such infragravity waves have periods small compared to the Earth's inertial period and thus do not cancel the Stokes drift exactly as suggested for periodic waves in the presence of rotation (see §2c).…”

Section: Field Measurements (A) Buoys and Driftersmentioning

confidence: 95%

Stokes drift

Bremer

Breivik

2017

Phil. Trans. R. Soc. A.

136

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During its periodic motion, a particle floating at the free surface of a water wave experiences a net drift velocity in the direction of wave propagation, known as the Stokes drift (Stokes 1847 , 441-455). More generally, the Stokes drift velocity is the difference between the average Lagrangian flow velocity of a fluid parcel and the average Eulerian flow velocity of the fluid. This paper reviews progress in fundamental and applied research on the induced mean flow associated with surface gravity waves since the first description of the Stokes drift, now 170 years ago. After briefly reviewing the fundamental physical processes, most of which have been established for decades, the review addresses progress in laboratory and field observations of the Stokes drift. Despite more than a century of experimental studies, laboratory studies of the mean circulation set up by waves in a laboratory flume remain somewhat contentious. In the field, rapid advances are expected due to increasingly small and cheap sensors and transmitters, making widespread use of small surface-following drifters possible. We also discuss remote sensing of the Stokes drift from high-frequency radar. Finally, the paper discusses the three main areas of application of the Stokes drift: in the coastal zone, in Eulerian models of the upper ocean layer and in the modelling of tracer transport, such as oil and plastic pollution. Future climate models will probably involve full coupling of ocean and atmosphere systems, in which the wave model provides consistent forcing on the ocean surface boundary layer. Together with the advent of new space-borne instruments that can measure surface Stokes drift, such models hold the promise of quantifying the impact of wave effects on the global atmosphere-ocean system and hopefully contribute to improved climate projections.This article is part of the theme issue 'Nonlinear water waves'.

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Lagrangian Surface Wave Motion and Stokes Drift Fluctuations

Cited by 26 publications

References 25 publications

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

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

Surface Waves Enhance Particle Dispersion

Stokes drift

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