Unsteady pressure fields which precede the launch of free–surface liquid jets

An inviscid, incompressible fluid in irrotational flow, with a prescribed free surface, responds to a specified initial velocity. The initial free surfaces treated are a horizontal plane indented by either a semicircular trench or a hemispherical crater. A paraboloidal cavity is also treated. Surface tension is neglected, but the effect of a uniform gravitational field is included, where relevant. The initial pressure field is calculated for several simple initial velocity fields, all of which direct fluid into the interior of the indentation. It is shown that a maximum in the instantaneous pressure field occurs in the fluid, just below the lowest point, B, on the free–surface indentation. This maximum in pressure is associated with a large local pressure gradient, and hence a large initial acceleration of the surface particles, especially at B, where the acceleration is directed vertically upward. By comparison with results for a flat free surface, it is shown by how much the indentation in the free surface adds to the violence with which the fluid initially moves.