Analytical solution of impulse response function of finite-depth water waves

Short-term deterministic water wave prediction is of great importance to the operations of ships and offshore structures. The use of the convolution integral of input wave profiles and an impulse response function is one of the candidates to predict water waves on the basis of the linear time-invariant system. However, this approach is not often used today because of the non-causality and the absence of the analytical solution of the impulse response function of finite-depth water; only the deep water impulse response function is available. In the paper, we present the analytical solution of the impulse response function using the dispersion relation of finite-depth water waves. In addition, the prediction abilities in space and time are investigated. It is shown that non-causal influence decreases exponentially and the predictable time increases linearly as the distance between measuring and prediction points. We conducted a tank experiment to predict irregular waves based on the JONSWAP spectrum. The prediction accuracy by the impulse response function of finite-depth water is higher than that by the deep water impulse response function. Besides, we find that the errors of the use of the analytical solution and that of the numerical solution obtained by the inverse discrete Fourier transform are comparable.