On the study of second-order wave theory and its convergence for a two-fluid system

Chi Min Liu, Hwung Hweng Hwung, Ray-Yeng Yang

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Second-order solutions of internal and surface waves in a two-fluid system are theoretically analyzed in this study. Using the perturbation technique, the derivation of second-order solutions for internal waves is revisited, and the results are expressed in one-by-one forms instead of a matrix form. Second-order solutions arising from the interactions of two arbitrary linear waves of different frequencies contain the sum-frequency (superharmonic) and the difference-frequency (subharmonic) components, which are separately examined. Internal Stokes wave being a special case of present solutions is firstly investigated. Next, the convergence of second-order theory and the second-order effects on wave profiles are analyzed. For general cases, the effects of the thickness ratio of two fluids and the ratio of wavenumbers of two first-order waves on second-order wave characteristics, which include transfer functions and particle velocities, are also examined. Moreover, most existing theories for the one-fluid and two-fluid systems can be deduced from present solutions.

Original languageEnglish
Article number253401
JournalMathematical Problems in Engineering
Volume2013
DOIs
Publication statusPublished - 2013 May 27

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Fluid
Fluids
Internal Waves
Perturbation techniques
Subharmonics
Perturbation Technique
Surface Waves
Stokes
Surface waves
Transfer Function
Transfer functions
First-order
Internal
Arbitrary
Interaction
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

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abstract = "Second-order solutions of internal and surface waves in a two-fluid system are theoretically analyzed in this study. Using the perturbation technique, the derivation of second-order solutions for internal waves is revisited, and the results are expressed in one-by-one forms instead of a matrix form. Second-order solutions arising from the interactions of two arbitrary linear waves of different frequencies contain the sum-frequency (superharmonic) and the difference-frequency (subharmonic) components, which are separately examined. Internal Stokes wave being a special case of present solutions is firstly investigated. Next, the convergence of second-order theory and the second-order effects on wave profiles are analyzed. For general cases, the effects of the thickness ratio of two fluids and the ratio of wavenumbers of two first-order waves on second-order wave characteristics, which include transfer functions and particle velocities, are also examined. Moreover, most existing theories for the one-fluid and two-fluid systems can be deduced from present solutions.",
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On the study of second-order wave theory and its convergence for a two-fluid system. / Liu, Chi Min; Hwung, Hwung Hweng; Yang, Ray-Yeng.

In: Mathematical Problems in Engineering, Vol. 2013, 253401, 27.05.2013.

Research output: Contribution to journalArticle

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