In extremely shallow water environments, the limited water depth is comparable to the maximum bubble radius. The pulsation of an underwater explosion bubble is strongly constrained by both the free surface and the rigid seabed, exhibiting complex nonlinear coupling effects, which are of great significance for the safety assessment and protection design of nearshore engineering. To address this issue, an axisymmetric two-dimensional numerical model based on the Eulerian finite element method (EFEM) with operator splitting technique and the volume of fluid (VOF) interface-capturing approach is established. Under the assumptions of inviscid and compressible flow, a systematic numerical investigation is carried out to examine the effects of the water depth parameter λ, position parameter γ, and buoyancy parameter δ on the bubble dynamics and the evolution of free surface structures. The results show that the maximum bubble radius, pulsation period, and jet characteristics are all significantly regulated by the above three parameters. Moreover, under multi-period bubble pulsation, different parameter conditions lead to diverse evolution characteristics of free surface structures, including the water spike, wrinkles, and water skirt. The findings reveal the governing mechanisms of key dimensionless parameters on the nonlinear bubble-multi-boundary coupling dynamics in extremely shallow water explosions, providing an important numerical basis and theoretical reference for the theoretical analysis and safety design of related shallow water explosion engineering problems.
Zhao et al. (Fri,) studied this question.