On the entry of a wedge into water: The thin wedge and an all-purpose boundary-layer equation

Abstract

In 1932, H. Wagner formulated the problem of the entry into water of an infinite wedge moving vertically downwards with constant speed. Among much else, Wagner noted that, in the absence of gravity, viscosity and surface tension, a similarity transformation removes time from the problem. Many other authors have considered the problem since 1932. The present paper settles a question, left open in earlier work, concerning the contact angle πβ this angle is shown, together with the wedge angle (or vertex angle) 2πα, in Figure 1(b). The question is whether the supremum.