Flows emerging from a nozzle and falling under gravity

Abstract

Steady two-dimensional free-surface flows of an inviscid and incompressible fluid emerging from a nozzle and falling under gravity are calculated numerically. The nozzle is aimed at an angle β above the horizontal. It is shown that there are flows for which the fluid falls down along the underside of the nozzle and other flows which split into two sheets. The latter flows occur for each value of β when the Froude number F is greater than a critical value. Local solutions are constructed to describe the limiting behaviour of the flows as F → 0 and as F → ∞.