Finite element analysis of second order wave resonance by multiple cylinders in a uniform current

The purpose of this paper is to study the diffraction of second order Stokes waves by four cylinders in a uniform current and mainly focus on the near-trapping phenomenon. A time domain second-order theory is employed to establish the mathematical Smodel by splitting the total potential into the disturbed velocity potential caused by current, the first- or linear and second-order potentials, which satisfy their own boundary conditions. Each potential is calculated through the finite element method (FEM). Numerical results for four bottom-mounted cylinders in a uniform current are provided to show the resonant behaviour of waves and hydrodynamic forces including linear and second order at near-trapped frequencies, and the current effect on the wave and force are also analysed and discussed. Some results for a single- and four-cylinder cases are compared with previous studies.