Nonlinear wave forces on vertical cylinder arrays

Abstract

A complete second-order solution is presented for the hydrodynamic forces due to the action of monochromatic waves on an array of bottom-mounted, surface-piercing, vertical cylinders of arbitrary cross-section in water of uniform, finite depth. Exploiting the constant structural cross-sections, the vertical dependency of the linearized potentials is expressed in terms of eigenfunction expansions. The first-order problem is then solved utilizing a two-dimensional Green's function approach. Through the application of Green's second identity, the second-order forces due to the second-order potential are expressed in terms of free-surface and structural integrals involving first-order quantities and associated linearized radiation potentials obtained by oscillating each of the structures in turn at the second-order wave frequency. An efficient numerical technique is presented to treat the oscillatory free-surface integral appearing in the second-order force formulation. The integration of this term in the far-field is carried out analytically utilizing the asymptotic behavior of the potential components, thus eliminating the need to define a truncation boundary specifying the extent of a finite, free-surface, computational domain. Numerical results are presented for arrays of cylinders of circular and elliptical cross-sections which illustrate the relative importance of second-order effects for a range of wave frequencies and incident wave directions.