Semi-Analytical Formulation for Second-Order Diffraction by a Vertical Cylinder in Bichromatic Waves

The analytic form of Green’s function in elliptic coordinates

“…In particular, for the low-frequency κa = 0.4, the location of the maximum value is evidently apparent for both the real and the imaginary parts, and for both angular locations that were selected to be investigated (Figs. 5,6,8,9). Also, the same figures show that Green's function decays away from the body for ρ > R. The decay here is smooth, as it was expected to be, due to the low wave frequency.…”

“…An appropriate form for the diffraction potential φ D 2 that satisfies the boundary conditions on the bottom and the free surface (see Eqs. [4][5] is [9][10][11][12][13]:…”

“…Chau and Eatock Taylor [8], Eatock Taylor and Huang [9], and Huang and Eatock Taylor [10,11] applied a different line of approach to derive the one-dimensional Green's function (depending only on the radial coordinate) for the second-order diffraction by cylinders in monochromatic [8,10] and bichromatic [9,11] waves. The solution was achieved by solving the associated Sturm-Liouville problem.…”

A time-domain second-order FEM model for the wave diffraction-radiation problem. Validation with a semisubmersible platform

“…used for semisubmersible platforms), these have to be linearized so that RAOs can be obtained. Therefore, 26 QTFs obtained in the frequency-domain do not contain information about the nonlinear behavior of the 27 mooring. A direct diffraction-radiation TD solver, like the one to be presented in this work, accounts for 28 this sort of nonlinearities in a natural way.…”

“…This test case deals with the diffraction of a bottom mounted vertical cylinder under 11 monochromatic waves with water depth ℎ = 4 m, radius of the cylinder = 1 m (see [26]). 12…”