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Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects
journal contributionposted on 2023-05-16, 12:01 authored by Hocking, GC, Lawrence ForbesLawrence Forbes
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 B 3 ) -1/2 , and the nondimensional sink depth Î» = 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 titleJournal of Engineering Mathematics
Department/SchoolSchool of Natural Sciences
PublisherKluwer Academic Publishers
Place of publicationNetherlands