A causal transient water wave diffraction formulation

The frequency-domain description of the potential function corresponding to a sinusoidal progressing wave can form the basis for describing an arbitra ry incident wave field in linearized free-surface hydrodynamics. Fourier te chniques make it possible to relate the incident sea state to the resulting hydrodynamic forces on a floating body. This paper develops a rational des cription in the frequency domain for the corresponding dynamical system whi ch can then be realized in the time domain as a system of constant-coeffici ent differential equations driven by incident wave height at a datum and wh ose output is the Froude-Krylov force. This is made possible by showing tha t the time-domain version of the potential for a sinusoidal progressing wav e satisfies a fourth-order time-varying ordinary differential equation (ODE ) analogous to that satisfied by the three-dimensional time-domain source f unction. Laplace transformation of this ODE followed by bilinear transforma tion supplies the analytical basis for generating the rational approximatio n. Various causality issues associated with the diffraction forces are neat ly handled by the approach presented here. (C) 2000 Elsevier Science Ltd. A ll rights reserved.