Journal of Nonlinear Mathematical Physics

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Volume 16, Issue 1, March 2009, Pages 47 - 61

Nonlinear Water Waves on Uniform Current in Lagrangian Coordinates

Authors
Hung-Chu Hsu*, §, Yang-Yih Chen†, , John R. C. Hsu†, ‖, Wen-Jer Tseng‡, **
*Tainan Hydraulics Laboratory, National Cheng Kung University, Tainan 709, Taiwan
†Department of Marine Environment and Engineering, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
‡Department of Civil Engineering, Cheng Shiu University, Kaohsiung 804, Taiwan
Received 28 January 2008, Accepted 2 March 2008, Available Online 7 January 2021.
DOI
10.1142/S1402925109000054How to use a DOI?
Keywords
Nonlinear water waves; current; Lagrangian; trajectory; Lagrangian wave frequency; Lagrangian mean level
Abstract

This paper presents a new third-order trajectory solution in Lagrangian form for the water particles in a wave-current interaction flow based on an Euler–Lagrange transformation. The explicit parametric solution highlights the trajectory of a water particle and the wave kinematics above the mean water level and within a vertical water column, which were calculated previously by an approximation method using Eulerian approach. Mass transport associated with a particle displacement can now be obtained directly in Lagrangian form. The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian. The variations in the wave profile and the water particle orbits resulting from the interaction with a steady uniform current of different magnitudes are also investigated. Comparison on the wave profiles given by the Eulerian and Lagrangian solution to a third-order reveals that the latter is more accurate than the former in describing the shape of the wave profile. Moreover, the influence of a following current is found to increase the relative horizontal distance traveled by a water particle, while the converse is true in the case of an opposing current.

Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
16 - 1
Pages
47 - 61
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925109000054How to use a DOI?
Copyright
© 2009 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Hung-Chu Hsu
AU  - Yang-Yih Chen
AU  - John R. C. Hsu
AU  - Wen-Jer Tseng
PY  - 2021
DA  - 2021/01/07
TI  - Nonlinear Water Waves on Uniform Current in Lagrangian Coordinates
JO  - Journal of Nonlinear Mathematical Physics
SP  - 47
EP  - 61
VL  - 16
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925109000054
DO  - 10.1142/S1402925109000054
ID  - Hsu2021
ER  -