### Abstract

The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation. The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time, which imply that the entire solution is uniformly-valid. The explicit parametric solution highlights the trajectory of a water particle and 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 water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.

Original language | English |
---|---|

Pages (from-to) | 89-98 |

Number of pages | 10 |

Journal | Acta Oceanologica Sinica |

Volume | 28 |

Issue number | 1 |

Publication status | Published - 2009 Apr 30 |

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### All Science Journal Classification (ASJC) codes

- Oceanography
- Aquatic Science

### Cite this

*Acta Oceanologica Sinica*,

*28*(1), 89-98.

}

*Acta Oceanologica Sinica*, vol. 28, no. 1, pp. 89-98.

**Interactions of nonlinear gravity waves and uniform current in Lagrangian system.** / Hsu, Hung Chu; Chen, Yang Yih; Li, Meng Syue; Tseng, Wen Jer.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Interactions of nonlinear gravity waves and uniform current in Lagrangian system

AU - Hsu, Hung Chu

AU - Chen, Yang Yih

AU - Li, Meng Syue

AU - Tseng, Wen Jer

PY - 2009/4/30

Y1 - 2009/4/30

N2 - The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation. The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time, which imply that the entire solution is uniformly-valid. The explicit parametric solution highlights the trajectory of a water particle and 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 water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.

AB - The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation. The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time, which imply that the entire solution is uniformly-valid. The explicit parametric solution highlights the trajectory of a water particle and 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 water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.

UR - http://www.scopus.com/inward/record.url?scp=65349188869&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65349188869&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:65349188869

VL - 28

SP - 89

EP - 98

JO - Acta Oceanologica Sinica

JF - Acta Oceanologica Sinica

SN - 0253-505X

IS - 1

ER -