Wave Loading on a Group of Cylinders in Fairly Perfect Fluid

The dissipation term is introduced into the free surface boundary conditions, and a newly developed ideal fluid potential flow model is used to numerically simulate a group of vertical cylinders. The wavenumber associated with the new boundary condition at the free surface defined by the dispersion relation becomes complex and wave decay factor is represented by the imaginary part of the wavenumber. To describe the velocity potential, the analytical method based on the expansion of eigen functions is used in the.uid domain. The Bessel functions of the complex variables are then involved in the series expression of the velocity potential. The unknown coefficients are determined by satisfying the boundary condition on cylinder surface in the Galerkin form. The eigen function expansion gives an accurate expression of velocity potentials. The effect of dissipation at the free surface can then be analyzed in a reliable and practical way. By comparison with existing model measurements, it is shown that the solution with dissipation is much more realistic, in particular, the first-order wave loading and second-order drift forces which are more sensitive to the dissipation for a wave frequency in the vicinity of trapping resonance frequency.