Time-domain solution for wave—current interactions with a two-dimensional body

Abstract

The effects of a current on the radiation and diffraction of regular waves around a two-dimensional body are examined by a time-domain method. The Froude number is assumed to be small so that the steady wave system associated with the current is insignificant. The boundary-value problem is then separated into a steady current problem with a rigid-wall condition applied at the still water level and an unsteady wave problem with modified free surface boundary conditions accounting for the disturbed current field. The boundary conditions for the unsteady problem are satisfied to first order in wave amplitude by a time-stepping procedure, and the field solution at each time step is obtained by an integral equation based on Green's theorem. For the case of a semi-circular cylinder with axis at the still water level, the wave amplitudes, the first-order oscillatory forces and the second-order steady forces at various values of Froude number are presented, and the effects of the current on the solution are discussed. Comparisons are also made with previous numerical results and good agreement is indicated.