Nonlinear Wave Forces on Vertical Cylinders of Arbitrary Cross Section

Abstract

A complete second‐order solution is presented for the hydrodynamic forces on a bottom‐mounted, surface‐piercing vertical cylinder of arbitrary cross section in water of uniform, finite depth. Exploiting the constant structural cross section, the vertical dependency of the linearized potentials is expressed in terms of eigenfunction expansions. The first‐order problem is solved using a two‐dimensional Green's function approach. Through 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 the structure at the second‐order wave frequency. An efficient numerical technique treats the oscillatory free‐surface integral appearing in the second‐order force formulation. Integration of this term in the far‐field utilizes the asymptotic behavior of the potential components, eliminating need to define a truncation boundary specifying the extent of a finite, free‐surface computational domain. Numerical results are presented for a cylinder of elliptical cross section that illustrate the relative importance of secondorder effects for a range of wave frequencies and incident wave directions.