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

Published online by Cambridge University Press:  20 September 2019

T. S. van den Bremer Open the ORCID record for T. S. van den Bremer [Opens in a new window] ,
C. Whittaker ,
R. Calvert ,
A. Raby  and
P. H. Taylor
T. S. van den Bremer*
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
C. Whittaker
Affiliation:
Department of Civil and Environmental Engineering, University of Auckland, Auckland 1010, New Zealand
R. Calvert
Affiliation:
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK
A. Raby
Affiliation:
School of Engineering, University of Plymouth, Plymouth PL4 8AA, UK
P. H. Taylor
Affiliation:
Faculty of Engineering and Mathematical Sciences, University of Western Australia, Crawley, WA 6009, Australia
*
†Email address for correspondence: ton.vandenbremer@eng.ox.ac.uk
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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.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: Ocean processes

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 168 - 186
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Copyright
© 2019 Cambridge University Press 

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