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On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System

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

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.

Suggested Citation

  • Chi-Min Liu & Hwung-Hweng Hwung & Ray-Yeng Yang, 2013. "On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-12, May.
    • Handle: RePEc:hin:jnlmpe:253401
    DOI: 10.1155/2013/253401
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