Spatiotemporal evolution of hydrodynamic pressure during ship–wave encounters using Boussinesq modeling

In shallow water, accurately identifying hull target is significantly challenged by wave-induced interference. To address this, a Boussinesq modeling approach is proposed that couples wave generation and moving pressure effects within a single combined source term formulation. This approach forms an efficient theoretical model for simulating the spatiotemporal evolution of hydrodynamic pressure during ship–wave encounters. Considering different depth Froude numbers, a validated finite-difference method is employed for systematic simulations across subcritical, near-critical, and supercritical speed ranges, with emphasis on how wave interactions modify pressure signatures under various conditions. Key findings are as follows: At subcritical speeds, the pressure fluctuation curve near the hull exhibits a stable “V”-shaped pattern, which is basically unaffected by waves; at near-critical speeds, there are drastic positive pressure peak fluctuations and transient “W”-shaped negative pressure zones near the hull, primarily driven by strong unsteady and nonlinear effects in wave environments; at supercritical speeds, wave-induced interference significantly alters the pressure curves near the hull, with the negative pressure peak shifting toward the stern, which is notably different from the subcritical case. The comparative analysis between head waves and oblique waves demonstrates that wave direction affects the symmetry of pressure distribution, which diminishes with increasing transverse distance. The Boussinesq modeling method has proven efficient and flexible in shallow water with regular waves, and its scalable framework shows strong potential for adaptation to shallow water with random waves, providing a theoretical and technical basis for predicting and identifying hull target in the ocean.