While the classical problem of a flat plate impact on a water surface at zero dead-rise angle has been studied for a long time both theoretically and experimentally, it still presents a number of challenges and unsolved questions. Hitherto, the details of the flow field – especially at early times and close to the plate edge, where the classical inviscid theory predicts a singularity in the velocity field and thus in the free surface deflection, so-called ejecta – have not been studied experimentally, which led to mutually contradicting suppositions in the literature. On one hand, it motivated Yakimov’s self-similar scaling near the plate edge. On the other hand, a removal of the singularity was previously suggested with the help of the Kutta–Joukowsky condition at the plate edge, i.e. enforcing the free surface to depart tangentially to the plate. In the present experimental study we were able to overcome challenges with optical access and investigate, for moderate Reynolds ($0.5<Re<25\,000$) and Weber ($1<We<800$) numbers, both the flow fields and the free surface dynamics at the early stage of the water impact, when the penetration depth is small compared to the plate size, thus allowing us to compare to the classical water impact theory valid in the short time limit. This, in particular, enabled us to uncover the effects of viscosity and surface tension on the velocity field and ejecta evolution usually neglected in theoretical studies. While we were able to confirm the far-field inviscid and the near-edge Stokes theoretical scalings of the free surface profiles, Yakimov’s scaling of the velocity field proved to be inapplicable and the Kutta–Joukowsky condition not satisfied universally in the studied range of Reynolds and Weber numbers. Since the local near-edge phenomena cannot be considered independently of the complete water impact event, the experiments were also set up to study the entirety of the water impact phenomena under realistic conditions – presence of air phase and finite depth of penetration. This allowed us to obtain insights also into other key aspects of the water impact phenomena such as air entrapment and pocketing at the later stage when the impactor bottoms out. In our experiments the volume of trapped air proved not to decrease necessarily with the impact speed, an effect that has not been reported before. The observed fast initial retraction of the trapped air film along the plate bottom turned out to be a consequence of a negative pressure impulse generated upon the abrupt deceleration of the plate. This abrupt deceleration is also the cause of the subsequent air pocketing. Quantitative measurements are complemented with basic scaling models explaining the nature of both retraction of the trapped air and air pocket formation.
Novel Techniques to Speed Up the Computation of the Automorphism Group of a Graph
