Evolution of the air cavity during a depressurized wave impact. II. The dynamic field

The present paper on wave-impact events in depressurized environments completes the analysis of Part I by focusing on the dynamical features of the impacts and on the influence of the ambient pressure. Connection is made between the impact regimes typically described in the literature and the stages described in Part I [C. Lugni, M. Miozzi, M. Brocchini, and O. M. Faltinsen, “Evolution of the air cavity during a depressurized wave impact. I. The kinematic flow field,” Phys. Fluids 22, 056101 (2010)]. The stages of isotropic/anisotropic compression and expansion of the air cavity are of particular interest. The impact duration at the wall is almost independent of its height above the undisturbed surface level, but its intensity rapidly decreases in the body of the fluid (the peak pressure halves within the first two compression/expansion cycles). The time evolution of the pressure loads on the wall is analyzed by means of the Hilbert transform and an empirical mode decomposition of the signals. This enables identification of the intrinsic mode functions which best fit the original signal during its evolution and quantification of the frequency downshifting which characterize the whole process. The pressure decay, largely governed by air leakage out of the cavity, is found to be very intense during the air cavity closure and the isotropic compression/expansion cycle [stages (1) and (2)]; the decay observed during stage (3), i.e., during the anisotropic compression/expansion cycles, is weaker and independent of the vertical location down the wall. Differences between the observed decay rates and those of a three-dimensional bubble in an infinite fluid are mainly due to the bubble being two-dimensional, being close to the free surface and loosing air. The role of both ullage and vapor pressures on the impact is described, respectively, by means of the Euler and cavitation numbers. The frequency of the bubble oscillation depends on these numbers in a way that is closely similar to that displayed by the bubble area, see Part I.