Standing waves on water of uniform depth: On their resonances and matching with short-crested waves

Makoto Okamura, M. Ioualalen, C. Kharif

研究成果: ジャーナルへの寄稿記事

7 引用 (Scopus)

抄録

Numerical calculations of the resonant interactions of three-dimensional short-crested waves very near their two-dimensional standing wave limit are performed for water of uniform depth. A detailed study of the properties of the solutions indicates that both classes of waves admit multiple solutions that are connected to each other through turning points. It is also shown that the solutions match each other at the limit. Then a study on the superharmonic instabilities (resonant interactions) of short-crested waves was performed in the vicinity of the standing wave limit. The matching allowed extrapolation of the short-crested wave stability results to standing waves. The results are that for resonant waves, superharmonic instabilities associated with harmonic resonance are dominant. The possible jumps from one solution to another may lead to a drastic change of the wave itself. Since the superharmonic instability enhances this property one may conclude that this class of waves can be considered non-stationary. By contrast, non-resonant waves are weakly unstable or stable and are the only waves that are likely to exist. Thus, this class of waves can be considered as quasi-permanent.

元の言語英語
ページ(範囲)145-156
ページ数12
ジャーナルJournal of Fluid Mechanics
発行部数495
DOI
出版物ステータス出版済み - 11 25 2003

Fingerprint

standing waves
water
superharmonics
Water
extrapolation
Convergence of numerical methods
Extrapolation
interactions
harmonics

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

これを引用

Standing waves on water of uniform depth : On their resonances and matching with short-crested waves. / Okamura, Makoto; Ioualalen, M.; Kharif, C.

:: Journal of Fluid Mechanics, 番号 495, 25.11.2003, p. 145-156.

研究成果: ジャーナルへの寄稿記事

@article{f1c50746b9784457b189ddc20c640b00,
title = "Standing waves on water of uniform depth: On their resonances and matching with short-crested waves",
abstract = "Numerical calculations of the resonant interactions of three-dimensional short-crested waves very near their two-dimensional standing wave limit are performed for water of uniform depth. A detailed study of the properties of the solutions indicates that both classes of waves admit multiple solutions that are connected to each other through turning points. It is also shown that the solutions match each other at the limit. Then a study on the superharmonic instabilities (resonant interactions) of short-crested waves was performed in the vicinity of the standing wave limit. The matching allowed extrapolation of the short-crested wave stability results to standing waves. The results are that for resonant waves, superharmonic instabilities associated with harmonic resonance are dominant. The possible jumps from one solution to another may lead to a drastic change of the wave itself. Since the superharmonic instability enhances this property one may conclude that this class of waves can be considered non-stationary. By contrast, non-resonant waves are weakly unstable or stable and are the only waves that are likely to exist. Thus, this class of waves can be considered as quasi-permanent.",
author = "Makoto Okamura and M. Ioualalen and C. Kharif",
year = "2003",
month = "11",
day = "25",
doi = "10.1017/S0022112003006037",
language = "English",
pages = "145--156",
journal = "Journal of Fluid Mechanics",
issn = "0022-1120",
publisher = "Cambridge University Press",
number = "495",

}

TY - JOUR

T1 - Standing waves on water of uniform depth

T2 - On their resonances and matching with short-crested waves

AU - Okamura, Makoto

AU - Ioualalen, M.

AU - Kharif, C.

PY - 2003/11/25

Y1 - 2003/11/25

N2 - Numerical calculations of the resonant interactions of three-dimensional short-crested waves very near their two-dimensional standing wave limit are performed for water of uniform depth. A detailed study of the properties of the solutions indicates that both classes of waves admit multiple solutions that are connected to each other through turning points. It is also shown that the solutions match each other at the limit. Then a study on the superharmonic instabilities (resonant interactions) of short-crested waves was performed in the vicinity of the standing wave limit. The matching allowed extrapolation of the short-crested wave stability results to standing waves. The results are that for resonant waves, superharmonic instabilities associated with harmonic resonance are dominant. The possible jumps from one solution to another may lead to a drastic change of the wave itself. Since the superharmonic instability enhances this property one may conclude that this class of waves can be considered non-stationary. By contrast, non-resonant waves are weakly unstable or stable and are the only waves that are likely to exist. Thus, this class of waves can be considered as quasi-permanent.

AB - Numerical calculations of the resonant interactions of three-dimensional short-crested waves very near their two-dimensional standing wave limit are performed for water of uniform depth. A detailed study of the properties of the solutions indicates that both classes of waves admit multiple solutions that are connected to each other through turning points. It is also shown that the solutions match each other at the limit. Then a study on the superharmonic instabilities (resonant interactions) of short-crested waves was performed in the vicinity of the standing wave limit. The matching allowed extrapolation of the short-crested wave stability results to standing waves. The results are that for resonant waves, superharmonic instabilities associated with harmonic resonance are dominant. The possible jumps from one solution to another may lead to a drastic change of the wave itself. Since the superharmonic instability enhances this property one may conclude that this class of waves can be considered non-stationary. By contrast, non-resonant waves are weakly unstable or stable and are the only waves that are likely to exist. Thus, this class of waves can be considered as quasi-permanent.

UR - http://www.scopus.com/inward/record.url?scp=0346401376&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346401376&partnerID=8YFLogxK

U2 - 10.1017/S0022112003006037

DO - 10.1017/S0022112003006037

M3 - Article

AN - SCOPUS:0346401376

SP - 145

EP - 156

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 495

ER -