Abstract
The objectives of present paper are to formulate the nonlinear diffraction problem for the long waves induced by a short wave groups using the multiple scales perturbation method and to find the effect of 2 nd-order long waves on the ocean structures.The governing equation for the 1 st-order zeroth harmonic potential is obtained by using the solvability condition of the boundary value problem for 3 rd-order zeroth harmonic potential. The formulas for the surface elevation of the 2 nd-order long waves induced by modulated short wave groups are derived analytically.Numerical results are presented for the case where the envelope of incident waves-train is a sine function and the influences of the long waves around a huge circular cylinder are considered.
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