Water Wave Impulse Response Function on Moving Point with Constant Speed in Head Wave

Accurate wave prediction is essential for moving ships at forward speed under head wave conditions. To achieve precise short-term wave predictions, the direct convolution integral of the measured wave elevation with an impulse response function can be employed, which has recently been proven as an efficient tool for static conditions. Comparatively, much research has not been conducted on moving conditions yet; however, it is essential to predict encounter water waves for ships at forward speed. This paper presents the analytical solution of the impulse response function on the moving point at a constant speed in head waves based on the finite-depth dispersion relation. The impulse response function is divided into three time domains, named small, middle, and large time domains. For each domain, the impulse response functions are derived, respectively. Additionally, the optimal limit of the proposed solution has been investigated in terms of speeds and distances. It has been observed that the proposed solution is valid within the optimal region, and the influence of non-causality is small. The analytical solution is compared with a numerical solution derived using the inverse discrete Fourier transform (IDFT). Towing tank experiments were conducted for different distances and speeds to validate the proposed solution by predicting regular and irregular water waves. For all cases, the comparison between experimental and predicted wave elevations shows good agreement, ensuring the prediction accuracy of the proposed analytical solution.