Hyperbolic profile of free-surface jets

If a body of inviscid fluid is disturbed, it will typically eject a jet of fluid. If the effects of gravity and surface tension are negligible, these jets travel in straight lines, with the tips approaching a constant velocity. Earlier works have concentrated upon jets which result from the occurrence of shocks or singularities in the fluid flow. In this paper, by contrast, we describe the simplest case, in two dimensions: an infinitely deep body of inviscid fluid, with no surface tension or gravitational forces acting, responds to a generic impulsive disturbance. We find that, contrary to some earlier suggestions, the jet has a hyperbolic profile (away from its tip and its base).