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.

This study investigates how the traditional Chinese “philosophy of self-cultivation and awakening” (xiu-wu) can be systematically harnessed to foster Higher-Order Thinking Skills (HOTS) among undergraduates. Through historical–philosophical reconstruction and conceptual analysis, the study distills three recurring instructional principles—gradual cultivation (jian-xiu), gradual awakening (jian-wu), and sudden awakening (dun-wu), and their dialectical synthesis, and re-casts them as design parameters for thinking-centered instruction. These principles are then translated into a macro-level instructional metaphor, the Bridge-Building Model, which sequences curricular elements as bridge piers (the teaching process of “gradual cultivation”), bridge deck (student-constructed “an isolated fragments of knowing”), and final closure (holistic knowledge). The model integrates constructivist, behaviorist and intuitive dimensions: repetitive, scaffolded tasks foster behavioral automaticity; guided reflection precipitates incremental insight; and calibrated “epistemic shocks” elicit sudden reorganization of conceptual schemata. The framework clarifies the locus, timing and contingency of each phase while acknowledging the metaphysical indeterminacy of ultimate “holistic” mastery. By translating classical Chinese pedagogical insights into operational design heuristics, the paper offers higher-education instructors a culturally grounded, theoretically coherent blueprint for systematically nurturing HOTS without sacrificing the spontaneity essential to creative cognition.