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Lagrangian transport by breaking surface waves

Published online by Cambridge University Press:  19 September 2017

Luc Deike Open the ORCID record for Luc Deike [Opens in a new window] ,
Nick Pizzo Open the ORCID record for Nick Pizzo [Opens in a new window]  and
W. Kendall Melville
Luc Deike*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, NJ 08540, USA Princeton Environmental Institute, Princeton University, NJ 08544, USA Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92037, USA
Nick Pizzo
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92037, USA
W. Kendall Melville*
Affiliation:
Scripps Institution of Oceanography, University of California San Diego, La Jolla, CA 92037, USA
*
†Email addresses for correspondence: ldeike@princeton.edu, kmelville@ucsd.edu
†Email addresses for correspondence: ldeike@princeton.edu, kmelville@ucsd.edu
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Abstract

The Lagrangian transport due to non-breaking and breaking focusing wave packets is examined. We present direct numerical simulations of the two-phase air–water Navier–Stokes equations describing focusing wave packets, investigating the Lagrangian drift by tracking tracer particles in the water before, during and after the breaking event. The net horizontal transport for non-breaking focusing packets is well described by the classical Stokes drift, both at the surface and in the bulk of the fluid, where the e-folding scale of the evanescent vertical profile is given by the characteristic wavenumber. For focusing wave packets that lead to breaking, we observe an added drift that can be ten times larger than the classical Stokes drift for a non-breaking packet at the surface, while the initial depth of the broken fluid scales with the wave height at breaking. We find that the breaking induced Lagrangian transport scales with the breaking strength. A simple scaling argument is proposed to describe this added drift and is found to be consistent with the direct numerical simulations. Applications to upper ocean processes are discussed.

JFM classification

Geophysical and Geological Flows: Air/sea interactions Geophysical and Geological Flows: Ocean processes Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 829 , 25 October 2017 , pp. 364 - 391
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Copyright
© 2017 Cambridge University Press 

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