Numerical simulation of wide-area Kelvin's ship wake based on high-order spectral method

The surface wake generated by a vessel sailing on the water surface can persist for kilometers and may disclose navigation parameters. Conventional viscous flow models entail high computational costs for large-scale wake simulation, while potential flow methods also struggle to efficiently capture kilometer-scale wake structures. In this study, the open-source software high-order spectral (HOS)-Ocean, based on the HOS method, is extended to simulate the wide-area wave wakes by inducing a moving surface disturbance. The ship is simplified by a moving two-dimensional (2D) Gaussian pressure distribution. A preliminary analysis is conducted on the effects of pressure distribution steepness, HOS order, and the use of an equivalent inflow condition. Wake structures under varying Froude numbers Fr (based on ship length or water depth) and heading angles θ are analyzed using power spectral density derived from 2D discrete Fourier transform. A preliminary investigation into the effects of environmental waves on wakes is conducted. Results demonstrate distinctive spectral signatures and validate the proposed approach, providing an efficient and reliable framework for wide-area wake prediction in surface vessel operations.