Free surface flow due to a sink

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Abstract
Two-dimensional free surface flows without waves, produced by a submerged sink in a reservoir, are computed numerically for various configurations. For a sink above the horizontal bottom of a layer of fluid, there are solutions for all values of the Froude number F greater than some particular value. However, when the fluid is sufficiently deep, there is an additional solution for one special value of F < 1. The results for a sink at the vertex of a sloping bottom, treated by Craya and by Hocking, and for a sink in fluid of infinite depth, treated by Tuck & Vanden-Broeck, are confirmed and extended. In particular it is shown that as the bottom tends to the horizontal, the solution for a sink at the vertex of a sloping bottom approaches a solution for a horizontal bottom with F = 1. However solutions are found for all values of the Froude number F [ges ] 1 for a sink on a horizontal bottom.

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