### Abstract

A set of fully-dispersive nonlinear wave equations is derived by introducing a velocity expression with a few vertical-dependence functions and then applying the Galerkin method, which provides an optimum combination of the vertical-dependence functions to express an arbitrary velocity field under wave motion. The obtained equations can describe nonlinear non-breaking waves under general conditions, such as nonlinear random waves with a wide-banded spectrum at an arbitrary depth including very shallow and far deep water depths. The single component forms of the new wave equations, one of which is referred to here as 'time-dependent nonlinear mild-slope equation', are shown to produce various existing wave equations such as Boussinesq and mild-slope equations as their degenerate forms. Numerical examples with comparison to experimental data are given to demonstrate the validity of the present wave equations and their high performance in expressing not only wave profiles but also velocity fields.

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

Pages (from-to) | 427-441 |

Number of pages | 15 |

Journal | Proceedings of the Coastal Engineering Conference |

Volume | 1 |

Publication status | Published - Jan 1 1995 |

Externally published | Yes |

Event | Proceedings of the 24th International Conference on Coastal Engineering. Part 1 (of 3) - Kobe, Jpn Duration: Oct 23 1994 → Oct 28 1994 |

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### All Science Journal Classification (ASJC) codes

- Ocean Engineering

### Cite this

*Proceedings of the Coastal Engineering Conference*,

*1*, 427-441.

**Fully-dispersive nonlinear wave model and its numerical solutions.** / Nadaoka, Kazuo; Beji, Serdar; Nakagawa, Yasuyuki.

Research output: Contribution to journal › Conference article

*Proceedings of the Coastal Engineering Conference*, vol. 1, pp. 427-441.

}

TY - JOUR

T1 - Fully-dispersive nonlinear wave model and its numerical solutions

AU - Nadaoka, Kazuo

AU - Beji, Serdar

AU - Nakagawa, Yasuyuki

PY - 1995/1/1

Y1 - 1995/1/1

N2 - A set of fully-dispersive nonlinear wave equations is derived by introducing a velocity expression with a few vertical-dependence functions and then applying the Galerkin method, which provides an optimum combination of the vertical-dependence functions to express an arbitrary velocity field under wave motion. The obtained equations can describe nonlinear non-breaking waves under general conditions, such as nonlinear random waves with a wide-banded spectrum at an arbitrary depth including very shallow and far deep water depths. The single component forms of the new wave equations, one of which is referred to here as 'time-dependent nonlinear mild-slope equation', are shown to produce various existing wave equations such as Boussinesq and mild-slope equations as their degenerate forms. Numerical examples with comparison to experimental data are given to demonstrate the validity of the present wave equations and their high performance in expressing not only wave profiles but also velocity fields.

AB - A set of fully-dispersive nonlinear wave equations is derived by introducing a velocity expression with a few vertical-dependence functions and then applying the Galerkin method, which provides an optimum combination of the vertical-dependence functions to express an arbitrary velocity field under wave motion. The obtained equations can describe nonlinear non-breaking waves under general conditions, such as nonlinear random waves with a wide-banded spectrum at an arbitrary depth including very shallow and far deep water depths. The single component forms of the new wave equations, one of which is referred to here as 'time-dependent nonlinear mild-slope equation', are shown to produce various existing wave equations such as Boussinesq and mild-slope equations as their degenerate forms. Numerical examples with comparison to experimental data are given to demonstrate the validity of the present wave equations and their high performance in expressing not only wave profiles but also velocity fields.

UR - http://www.scopus.com/inward/record.url?scp=0029228539&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029228539&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0029228539

VL - 1

SP - 427

EP - 441

JO - Proceedings of the Coastal Engineering Conference

JF - Proceedings of the Coastal Engineering Conference

SN - 0893-8717

ER -