On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System. (2nd May 2013)

• Record Type: Journal Article
• Authors: Liu, Chi-Min; Hwung, Hwung-Hweng; Yang, Ray-Yeng
• Other Names: Vajravelu Kuppalapalle Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2013(2013)
• Publication Date: 2013-05-02
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2013/253401
• Languages: English
• ISSNs: 1024-123X

Abstract

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.