Theoretical and experimental study of particle trajectories for nonlinear water waves propagating on a sloping bottom

Yang Yih Chen, Meng Syue Li, Hung Chu Hsu, Chiu On Ng

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

A third-order asymptotic solution in Lagrangian description for nonlinear water waves propagating over a sloping beach is derived. The particle trajectories are obtained as a function of the nonlinear ordering parameter 3 and the bottom slope a to the third order of perturbation. A new relationship between the wave velocity and the motions of particles at the free surface profile in the waves propagating on the sloping bottom is also determined directly in the complete Lagrangian framework. This solution enables the description of wave shoaling in the direction of wave propagation from deep to shallow water, as well as the successive deformation of wave profiles and water particle trajectories prior to breaking. A series of experiments are conducted to investigate the particle trajectories of nonlinear water waves propagating over a sloping bottom. It is shown that the present third-order asymptotic solution agrees very well with the experiments.

Original languageEnglish
Pages (from-to)1543-1571
Number of pages29
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume370
Issue number1964
DOIs
Publication statusPublished - 2012 Apr 13
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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