Lagrangian transport for two-dimensional deep-water surface gravity wave groups

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13 Citations (Scopus)

Abstract

The Lagrangian trajectories of neutrally buoyant particles underneath surface gravity wave groups are dictated by two physical phenomena: the Stokes drift results in a net displacement of particles in the direction of propagation of the group, whereas the Eulerian return flow, as described by the multi-chromatic wave theory of Longuet-Higgins & Stewart (1962 J. Fluid Mech. 13, 481-504. (doi:10.1017/S0022112062000877)), transports such particles in the opposite direction. By pursuing a separation of scales expansion, we develop simple closed-form expressions for the net Lagrangian displacement of particles. By comparing the results from the separation of scales expansion at different orders in bandwidth, we study the effect of frequency dispersion on the local Lagrangian transport, which we show can be ignored for realistic sea states.

Original languageEnglish
Article number20160159
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume472
Issue number2192
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Lagrangian dynamics
  • Stokes drift
  • Surface gravity waves
  • Wave groups

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