Vertical jets from standing waves; The bazooka effect

Abstract

It is shown that a sufficient condition for the occurrence of a high vertical acceleration in a two-dimensional standing wave is for the initial profile of to have a narrow trough that is approximately circular. In such cases we find vertical accelerations of the free surface exceeding 109. Much higher accelerations are obtained when the initial wave trough is somewhat flattened so that jets emerging from the two corners of the trough meet on the axis of symmetry. In such a case we find accelerations exceeding 100g. Lastly we consider a different, but complementary, class of initial conditions when the free surface is initially flat but is given an upwards velocity dependent sinusoidally on the horizontal coordinate. When the kinetic energy injected into the fluid exceeds the maximum possible fora time-periodic standing wave it is found that a new type of breaking can occur in which air is trapped by the collapse of the wave trough. Throughout this paper surface tension is ignored and the fluid flow is treated as inviscid and irrotational. © 2001 Kluwer Academic Publishers.