Oblique liquid curtains with a large Froude number

This paper examines two-dimensional liquid curtains ejected at an angle to the horizontal and affected by gravity and surface tension. The flow in the curtain is, generally, sheared. The Froude number based on the injection velocity and the outlet's width is assumed large; as a result, the streamwise scale of the curtain exceeds its thickness. A set of asymptotic equations for such (slender) curtains is derived and its steady solutions are examined. It is shown that, if the surface tension exceeds a certain threshold, the curtain - quite paradoxically - bends upwards, i.e. against gravity. Once the flow reaches the height where its initial supply of kinetic energy can take it, the curtain presumably breaks up and splashes down.