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

Christopher Higgins, Ton Van Den Bremer, Jacques Vanneste

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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 stratisfaction affect this mass transport for an isolated nondissipating 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 (2D) seas, but zero for spanwise-localised packets representing
directionally-spread seas (3D). We resolve this 2D-3D difference by demonstrating that a transition between 2D-like (finite) and 3D-like (zero) displacement occurs on a time scale inversely proportional to the degree of directional spreading. For a stratified ocean, we show that in 2D 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 3D, the net displacement remains zero in the presence of stratification, but finite-time displacements may be appreciably altered.
Original languageEnglish
Number of pages18
JournalJournal of Fluid Mechanics
Early online date28 Nov 2019
Publication statusPublished - 25 Jan 2020

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