Water wave propagation in unbounded domains. Part I: Nonreflecting boundaries

This paper concerns non-reflecting boundary conditions for linearized 2D incompressible, irrotational, inviscid free surface flows in deep water. The linearization at flat water of the water wave equation is factored as a product of one-way equations. The one-way factors involve a nonlocal half derivative in space. They serve to construct essentially non-reflective and absorbing layers. The one way nature of the equation prevents errors at the boundary from propagating back and polluting the solution in the interior of the domain. Two versions of the one-way equations are discussed, with and without additional wave damping. Numerical results are presented.