The hydrodynamic pressure field and wake field generated by an advancing underwater vehicle are used as key factors for its detection and identification. In this paper, a numerical method is established based on the Reynolds-averaged Navier–Stokes equation. Following grid convergence verification for seven kinds of grids, the differences between the hydrodynamic pressure field and wake field are investigated using the gridding method and turbulence model. Subsequently, on a validation basis, the characteristics and correlation of the hydrodynamic pressure field and wake field for an underwater vehicle at different water depths are studied, showing that the SST turbulence model is applicable to underwater vehicle hydrodynamic pressure fields with low grid requirements. A high grid density and the LES turbulence model are needed to accurately capture information about the wake field’s flow field. As the underwater vehicle approaches the bottom, the hydrodynamic pressure field characteristics change significantly, and the wake field characteristics do not significantly change. In the region behind the hull, the influence of the wake field on the hydrodynamic pressure field is complex, but it has a short acting distance. The correlation in the area behind the hull is crucial for identifying, detecting, and tracking targets.

A ship advancing in restricted waters may cause a change in the surrounding velocity field, which in turn results in the hydrodynamic pressure field according to the variations in the ship speed. Accurate prediction of ship hydrodynamic pressure fields in restricted waters is therefore essential and important in the military and engineering fields. Based on the potential flow theory and the thin-ship assumption, dividing complex restricted waters with varying depths into the inner and outer domains with constant depths, a mathematical modeling method is developed and carried out for analyzing and solving the partial differential equations consisting of the governing equation with a dispersion effect, initial and boundary conditions, then the analytical solution of hydrodynamic pressure field caused by a ship advancing in complex restricted waters is obtained. The continuity of the analytical solution is confirmed and the correctness of the analytical solution is validated by simplifying to a simple water and comparing with available data. Moreover, the mathematical modeling method can be extended to study the hydrodynamic problems of ships in more complex waters.

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.

1. Ice flood disasters, as typical seasonal hazards, pose severe challenges to the safe operation of river channels due to the induced ice-jam floods (Wang and Wang 2024; Zhou et al. 2025). Taking ...