Abstract
The two-dimensional, steady flow of an inviscid fluid induced by a line sink located near a vertical wall in a region of infinite depth is computed. The effects of surface tension are investigated. The solution in the limit of small Froude number is obtained analytically, and numerically for the nonlinear problem. The asymptotic solution is found to have a property that if the horizontal location of the sink, x_mathrm{{s}} < 1, there is only one stagnation point on the surface, at the wall. However, if the horizontal location x_{mathrm{s}} > 1, a second stagnation point forms on the free surface. Numerical solution for the nonlinear problem confirms these properties. The effect of moving the sink horizontally has also been considered. The maximum Froude numbers at which steady solutions exist are computed and compared with the previous work.
Highlights
Problems in mechanics that involve free surface flow have been the subject of intensive research over a long period of time, and have a wide range of important applications [1,2,3,4]
Hocking and Forbes [12] used the method of Tuck and Vanden-Broeck [7] and confirmed that there was a solution for the free surface stagnation point flows provided the Froude number was limited to F < 1.4
We investigate the flow induced by a line sink in a fluid of infinite depth when the sink is located away from a vertical wall, including the effects of surface tension
Summary
Problems in mechanics that involve free surface flow have been the subject of intensive research over a long period of time, and have a wide range of important applications [1,2,3,4]. In cases with a free surface stagnation point, solutions were limited to values beneath a critical Froude number They discovered that if the Froude number was left as an unknown parameter and found as a part of the solution, they could obtain the solution for the other type of flow for which the surface was drawn down towards the sink in a cusp shape. Hocking and Forbes [12] used the method of Tuck and Vanden-Broeck [7] and confirmed that there was a solution for the free surface stagnation point flows provided the Froude number was limited to F < 1.4. Steady or unsteady withdrawal from a fluid of finite or infinite depth through a line sink or point sink including surface-tension effects has been the subject of considerable study. In the case of infinite depth, it is not possible to have waves in the far-field as the flow slows to zero
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