Flow from a vertical slot into a layer of finite depth

Abstract

The flow of water upward from a vertical slot into a fluid of finite depth is considered. The shape of the free surface is computed for a range of parameter values. It is shown that solutions in which the free surface separates smoothly from the vertical wall can be obtained for a range of Froude numbers and slot sizes but that the absolute lower bound on these flows is F = 1, provided the slot width is less than approximately one half the depth of the layer. If the slot size is larger than this, the lower bound on F increases. Solutions for infinite Froude number are shown toexist up to a maximum slot width equal to the depth of the flowing layer, and for finite Froude number a limiting value on the slot width is found that depends upon the Froude number.