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

Abstract EN

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.