Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects
Hocking, G.C. and Forbes, L.K. (2000) Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects. Journal of Engineering Mathematics, 38 (1). pp. 91-100.
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The steady withdrawal of an inviscid fluid of finite depth into a line sink is considered for the case in which surface tension is acting on the free surface. The problem is solved numerically by use of a boundary-integral-equation method. It is shown that the flow depends on the Froude number, F B=m(gH 3 B)–1/2, and the nondimensional sink depth =H S/H B, where m is the sink strength, g the acceleration of gravity, H B is the total depth upstream, H S is the height of the sink, and on the surface tension, T. Solutions are obtained in which the free surface has a stagnation point above the sink, and it is found that these exist for almost all Froude numbers less than unity. A train of steady waves is found on the free surface for very small values of the surface tension, while for larger values of surface tension the waves disappear, leaving a waveless free surface. It the sink is a long way off the bottom, the solutions break down at a Froude number which appears to be bounded by a region containing solutions with a cusp in the surface. For certain values of the parameters, two solutions can be obtained.
|Publication Type:||Journal Article|
|Murdoch Affiliation:||School of Chemical and Mathematical Science|
|Copyright:||© 2000 Kluwer Academic Publishers|
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