TIME-DOMAIN SOLUTION FOR WAVE CURRENT INTERACTIONS WITH A 2-DIMENSIONAL BODY

The effects of a current on the radiation and diffraction of regular w aves around a two-dimensional body are examined by a time-domain metho d. The Froude number is assumed to be small so that the steady wave sy stem associated with the current is insignificant. The boundary-value problem is then separated into a steady current problem with a rigid-w all condition applied at the still water level and an unsteady wave pr oblem with modified free surface boundary conditions accounting for th e disturbed current field. The boundary conditions for the unsteady pr oblem are satisfied to first order in wave amplitude by a time-steppin g procedure, and the field solution at each time step is obtained by a n integral equation based on Green's theorem. For the case of a semi-c ircular cylinder with axis at the still water level, the wave amplitud es, the first-order oscillatory forces and the second-order steady for ces at various values of Froude number are presented, and the effects of the current on the solution are discussed. Comparisons are also mad e with previous numerical results and good agreement is indicated.