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

Decomposition and Prediction of Initial Uniform Bi-Directional Water Waves Using an Array of Wave-Rider Buoys

“…Note that the impulse response function of water waves is never causal because of the dispersion of water waves [25]. However, such non-causality decreases as the distance x AP [26], and the causality can be assumed in practice. The form of the impulse response function of water waves and resultant prediction accuracy are described in the following subsections.…”

“…The analytical solution of the impulse response function subject to deep water dispersion k = ω|ω| throughout frequency is wellknown [9,10,24,27]. However, this impulse response function overestimates a non-causality because of the dispersion relation [26]. To obtain more accurate prediction results, the impulse response function using the dispersion relation of finitedepth water ω|ω| = k tanh k is examined [26,28].…”

“…Nevertheless, this impulse response function is strongly non-causal, and a prediction error may not be acceptable. Recently, an analytical solution of the impulse response function for finite-depth water waves is also derived [26]. Although this impulse response function is still non-causal, such non-causal influence can be exponentially reduced with distance [26].…”

“…Recently, an analytical solution of the impulse response function for finite-depth water waves is also derived [26]. Although this impulse response function is still non-causal, such non-causal influence can be exponentially reduced with distance [26]. Moreover, it is indicated that this method can be used to predict future waves with an arbitrary non-causal error when the distance is sufficiently long.…”

“…These decomposed progressive and regressive waves predict waves of the middle buoy. For the prediction, the analytical solution of the impulse response function under the finite-depth dispersion relation [26] is applied. In addition, a new analytical solution using a window function (cosine-type) is combined to eliminate a truncation error.…”