Flow around a corner in the water impact problem

Abstract

In this work, we study the local flow in the vicinity of a flat sector of arbitrary angle α in the water impact problem as motivated by recent experimental observations in the author's laboratory. The key question is as to why the ejecta formed during the impact at zero deadrise angle is considerably higher along a straight edge of the sector compared to that near a sharp corner α < π, e.g., if the impacting body is a rectangular plate. Resolving this question is made possible by the discovered here mathematical equivalence of the problem to electromagnetic diffraction phenomena. The main result of the present study is the revealed and quantified influence of the geometry of a flat plate corner on the fluid flow around it, which also contributes to the understanding of certain three-dimensional effects in the water impact problem and provides a generalization of the classical two-dimensional results on the impact at zero deadrise angle. The offered theoretical solution is also qualitatively supported with the help of particle image velocimetry measurements.