A fully dispersive weakly nonlinear model for water waves

K. Nadaoka; S. Beji; Yasuyuki Nakagawa

doi:10.1098/rspa.1997.0017

A fully dispersive weakly nonlinear model for water waves

K. Nadaoka, S. Beji, Yasuyuki Nakagawa

Research output: Contribution to journal › Article › peer-review

40 Citations (Scopus)

Abstract

A fully dispersive weakly nonlinear water wave model is developed via a new approach named the multiterm-coupling technique, in which the velocity field is represented by a few vertical-dependence functions having different wave-numbers. This expression of velocity, which is approximately irrotational for variable depth, is used to satisfy the continuity and momentum equations. The Galerkin method is invoked to obtain a solvable set of coupled equations for the horizontal velocity components and shown to provide an optimum combination of the prescribed depth-dependence functions to represent a random wave-field with diversely varying wave-numbers.

Original language	English
Pages (from-to)	303-318
Number of pages	16
Journal	Proceedings - Royal Society of London, A
Volume	453
Issue number	1957
DOIs	https://doi.org/10.1098/rspa.1997.0017
Publication status	Published - Jan 1 1997
Externally published	Yes

All Science Journal Classification (ASJC) codes

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

Access to Document

10.1098/rspa.1997.0017

Fingerprint Dive into the research topics of 'A fully dispersive weakly nonlinear model for water waves'. Together they form a unique fingerprint.

Cite this

@article{d1c9114afbb24a09bc7fe705eae2f786,

title = "A fully dispersive weakly nonlinear model for water waves",

abstract = "A fully dispersive weakly nonlinear water wave model is developed via a new approach named the multiterm-coupling technique, in which the velocity field is represented by a few vertical-dependence functions having different wave-numbers. This expression of velocity, which is approximately irrotational for variable depth, is used to satisfy the continuity and momentum equations. The Galerkin method is invoked to obtain a solvable set of coupled equations for the horizontal velocity components and shown to provide an optimum combination of the prescribed depth-dependence functions to represent a random wave-field with diversely varying wave-numbers.",

author = "K. Nadaoka and S. Beji and Yasuyuki Nakagawa",

year = "1997",

month = jan,

day = "1",

doi = "10.1098/rspa.1997.0017",

language = "English",

volume = "453",

pages = "303--318",

journal = "Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences",

issn = "0080-4630",

publisher = "Royal Society of London",

number = "1957",

}

TY - JOUR

T1 - A fully dispersive weakly nonlinear model for water waves

AU - Nadaoka, K.

AU - Beji, S.

AU - Nakagawa, Yasuyuki

PY - 1997/1/1

Y1 - 1997/1/1

N2 - A fully dispersive weakly nonlinear water wave model is developed via a new approach named the multiterm-coupling technique, in which the velocity field is represented by a few vertical-dependence functions having different wave-numbers. This expression of velocity, which is approximately irrotational for variable depth, is used to satisfy the continuity and momentum equations. The Galerkin method is invoked to obtain a solvable set of coupled equations for the horizontal velocity components and shown to provide an optimum combination of the prescribed depth-dependence functions to represent a random wave-field with diversely varying wave-numbers.

AB - A fully dispersive weakly nonlinear water wave model is developed via a new approach named the multiterm-coupling technique, in which the velocity field is represented by a few vertical-dependence functions having different wave-numbers. This expression of velocity, which is approximately irrotational for variable depth, is used to satisfy the continuity and momentum equations. The Galerkin method is invoked to obtain a solvable set of coupled equations for the horizontal velocity components and shown to provide an optimum combination of the prescribed depth-dependence functions to represent a random wave-field with diversely varying wave-numbers.

UR - http://www.scopus.com/inward/record.url?scp=0030917608&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030917608&partnerID=8YFLogxK

U2 - 10.1098/rspa.1997.0017

DO - 10.1098/rspa.1997.0017

M3 - Article

AN - SCOPUS:0030917608

VL - 453

SP - 303

EP - 318

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 1957

ER -