Nonlinear Free Surface Condition Due to Wave Diffraction for a Pair of Cylinders

Computation of the non-homogeneous term arising in the nonlinear free surface condition due to the second-order wave diffraction for a pair of cylinders under the assumption of an incompressible, inviscid and irrotational fluid is presented. In the computations of the nonlinear loads on offshore structures, the most challenging task is the computation of the free surface integral. The main contribution to this integrand is due to the non-homogeneous term present in the free surface condition for the second-order diffracted potential. The combined first-order diffracted potential is obtained using Graf’s addition theorem for the Bessel functions. Since the free surface term for the second-order diffracted potential can be expressed in terms of the first-order potentials, the free surface term can be computed using the knowledge of only the first order potentials. Numerical results are presented for different parameters. It is found that the main contribution to the nonlinear free surface term comes from the first few individual terms, the contribution from all other individual terms is insignificant. The results obtained in this analysis indicate that the contribution to the individual free surface term fl(r/ a) is negligible for higher values of M. It is observed that the succesive difference decreases rapidly as M increases. The zeroth-order term mainly contributes to the total free surface term. Except the first few individual terms, the contribution from all other individual terms to the free surface term is negligible. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.