Jet formation at a free surface

Abstract

Most asymmetrical collapses of bubbles result in jet formation. Other free surface flows also create jets or sheets (2D jets) of liquid. The overturning jet of a breaking wave and the sheet of water projected skyward when a steep wave meets a wall are further examples. Frequently jets are the most significant flow feature where applications involving fluid impact are concerned. The velocities in jets and the pressures involved in their creation or destruction may be the largest in the flow field. The importance of jet-like flows mean that it is desirable to have a general understanding of when they do arise and some measure of their likely strength.

Jet flows have a wide range of behaviour. There is one characteristic where extreme examples can easily be recognised: low and high energy. A low energy jet occurs when there is no significant acceleration of the liquid. In highly energetic examples we find that for roughly similar flows, the more energetic jets are smaller: the more tightly “focused” the flow the more violent the jet creation. This leads to the view that the most severe flow may actually have a singularity. Although we have yet to derive a suitable singularity solution for these cases there are a number of singular solutions for free-surface flows some of which may be relevant to water-wave breaking. Perhaps proximity to a singularity may be a way to quantify jet formation.