On the dynamic characteristics of ship wave propagation over sloping bathymetry

Ship wave propagation over sloping bathymetry is critical for coastal safety and navigation, yet a systematic understanding of how slope gradient and ship speed jointly govern wave evolution remains scarce. This study employs the Boussinesq model to investigate the nonlinear interaction between ship waves and slopes ranging from steep (1:15) to mild (1:120) under subcritical to supercritical conditions (Fr = 0.8–1.2). Key findings reveal that (i) steeper slopes intensify wave reflection and shoaling, yielding larger peak amplitudes; (ii) milder slopes produce wider, flatter elliptical wave envelopes whose amplitudes decay more rapidly in shallower water; (iii) increasing Fr enlarges wave-crest heights and alters the Kelvin wake pattern from wide-crested to narrow-crested, yet also accelerates energy dissipation on slopes; and (iv) both horizontal (u) and vertical (v) wave speeds increase as water depth decreases; however, this amplification is stronger at lower Fr. These insights advance the prediction of ship wave behavior in variable-depth bathymetry, offering critical implications for ship design, coastal infrastructure safety, and environmental impact assessment.