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

Author:

Chen Yang-Yih12,Li Meng-Syue1,Hsu Hung-Chu3,Ng Chiu-On4

Affiliation:

1. Department of Marine Environment and Engineering, National Sun Yat-sen University, Kaohsiung 80424, Taiwan

2. Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 70955, Taiwan

3. Tainan Hydraulics Laboratory, National Cheng Kung University, Tainan 70101, Taiwan

4. Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, People's Republic of China

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 ε and the bottom slope α 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.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Reference44 articles.

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3. Biesel F.. 1952 Study of wave propagation in water of gradually varying depth. 521 Gravity waves. Circular pp. 243–253 US National Bureau of Standards.

4. Water waves of finite amplitude on a sloping beach

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