Shock wave reflection near the seabed: Theory and high-resolution simulation

Shock wave reflection from the seabed governs the loading on underwater structures, yet existing theories derived for gases are inapplicable due to water's high density and low compressibility. To address this gap, we establish an integrated framework that combines analytical theory, high-resolution simulation, and experiments to unravel the physics of near-seabed shock reflections. Theoretically, we derive explicit formulas for the reflection coefficients and, for the first time, the critical angle for Mach reflection in water. These predictions are validated against both high-fidelity simulations using a Runge–Kutta discontinuous Galerkin (RKDG) multiphase model and small-scale experiments, showing excellent agreement (errors < 8%). The simulations reveal the detailed dynamics of the regular-to-Mach transition and the non-uniform pressure distribution along the Mach stem. Crucially, by extending the analysis to deformable seabeds, we demonstrate that seabed stiffness is the primary factor controlling both the reflection mode and overpressure amplification—Mach reflection and high pressures occur only on stiff boundaries, while soft sediments suppress it entirely. These results provide a physically grounded, validated framework for predicting shock loads on the seabed, with direct implications for the design of resilient marine infrastructure.