M. Isaacson et Kf. Cheung, TIME-DOMAIN SOLUTION FOR WAVE CURRENT INTERACTIONS WITH A 2-DIMENSIONAL BODY, Applied ocean research, 15(1), 1993, pp. 39-52
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.