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Lagrangian transport by deep-water surface gravity wavepackets: effects of directional spreading and stratification

Published online by Cambridge University Press:  28 November 2019

C. Higgins Open the ORCID record for C. Higgins [Opens in a new window] ,
T. S. van den Bremer Open the ORCID record for T. S. van den Bremer [Opens in a new window]  and
J. Vanneste Open the ORCID record for J. Vanneste [Opens in a new window]
C. Higgins*
Affiliation:
Department of Engineering Science, University of Oxford, OxfordOX1 3PJ, UK
T. S. van den Bremer
Affiliation:
Department of Engineering Science, University of Oxford, OxfordOX1 3PJ, UK
J. Vanneste
Affiliation:
School of Mathematics and Maxwell Institute for Mathematical Sciences, University of Edinburgh, EdinburghEH9 3FD, UK
*
†Email address for correspondence: [email protected]
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Abstract

The Lagrangian mass transport by non-dissipating surface gravity wavepackets consists of the Stokes drift and the wave-induced return flow. We examine how directional spreading and density stratification affect this mass transport for an isolated non-dissipating wavepacket in deep water using a perturbation expansion. For an unstratified ocean, we show that the net displacement by the return flow is finite, negative, the same at all vertical levels and inversely proportional to the depth for spanwise-infinite packets representing unidirectional (two-dimensional) seas, but zero for spanwise-localised packets representing directionally spread seas (three-dimensional). We resolve this difference by demonstrating that a transition between two-dimensional-like (finite) and three-dimensional-like (zero) displacement occurs on a time scale inversely proportional to the degree of directional spreading. For a stratified ocean, we show that in two dimensions the net displacement profile by the return flow oscillates slowly with depth, with a wavelength dependent on the ratio of buoyancy frequency to the surface wave group velocity, and infinite displacements are predicted when the surface wavepacket resonantly excites internal waves. In three dimensions, the net displacement remains zero in the presence of stratification, but finite-time displacements may be appreciably altered.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A42
Copyright
© 2019 Cambridge University Press

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