Based on the proper description of the condition at infinity for nonlinear surface wave diffraction In physical sense, the high order asymptotic solution as well as the Inhomogeneous boundary condition at infinity for second order surface wave diffraction are obtained. It contributes a complete and rational mathematical model towards the problem, and clarifies the controversy rising among a lot of works about it.


Stokes perturbation expansion has been recognized as an effective method valid for the solution of mild nonlinear sun-ace wave diffraction. The first order wave diffraction theory, i.e., the linear diffraction theory, based on the expansion, is complete and rational in Its mathematical formulation. However, for the diffraction problems of second order and higher orders, the free surface boundary condition is inhomogeneous. The right-hand side inhomogeneous term is recognized as pressure disturbance distributed infinitely on the free surface. Consequently, the question is how to properly define the boundary condition at infinity for the surface wave diffraction problems of second order and higher orders to be consistent with this kind of pressure disturbance. In the context of second order problem, a lot of papers have been published previously [1-5, 7-13]. However, even for the wave diffraction against a vertical cylinder, many solutions of second order problem obtained by different authors exhibit obvious differences, which are partly affected by distinct forms of boundary condition at infinity presented In those papers.


Essentially, the surface wave diffraction phenomenon is the wave motion generated by some active disturbance at infinity and existing in the flow field where some structures of large scale is located. For the nonlinear surface wave diffraction problem, we can't define the physical condition at infinity of assuming an active disturbance source at Infinity.

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