In order to do numerical calculations for nonlinear wave problems, the infinite fluid region has to be truncated at a finite distance. A far field condition has to be assigned on the truncating boundary but for nonlinear cases there is no reasonably valid condition available yet. By using the Bernoulli pressure or its integral along vertical direction from water bottom to the free surface as the Lagrangian density for fluid, we have derived a local energy conservation equation. This local energy equation is integrated over the region surrounded by the free surface, water bottom, structure surface and a circular cylindrical truncating surface, and then transformed to a energy balance equation. It is reasonable to assume that the energy in the region with the fixed truncating surface will be balanced in some time interval because otherwise the energy in the region will increase without limit and the solution will finally become unstable. Under this assumption, the energy balance equation is transformed to a nonlinear condition on the truncating surface. For nonlinear waves this is the condition which can be used as the far field condition at the truncating surface to make the numerical calculations for nonlinear wave problems feasible. For linear waves it is well-known that the scattered wave energy is always flowing out away from the body and not flowing in toward the body. This energy flux direction condition is equivalent to the Sommerfeld radiation condition. We have verified the obtained far field condition for linear wave cases. But for linear waves the energy flux direction at infinity has still to be assigned in order to make the numerical solution unique.
For linear wave-structure interaction problems, the Sommerfeld or Orlanski radiation condition is needed at infinity in order to make the wave solution unique.
