TY - JOUR A2 - Vajravelu, Kuppalapalle AU - Liu, Chi-Min AU - Hwung, Hwung-Hweng AU - Yang, Ray-Yeng PY - 2013 DA - 2013/05/02 TI - On the Study of Second-Order Wave Theory and Its Convergence for a Two-Fluid System SP - 253401 VL - 2013 AB - 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. SN - 1024-123X UR - https://doi.org/10.1155/2013/253401 DO - 10.1155/2013/253401 JF - Mathematical Problems in Engineering PB - Hindawi Publishing Corporation KW - ER -