Murdoch University Research Repository

Welcome to the Murdoch University Research Repository

The Murdoch University Research Repository is an open access digital collection of research
created by Murdoch University staff, researchers and postgraduate students.

Learn more

Withdrawal from a fluid of finite depth through a line sink, including surface-tension effects

Hocking, G.C.ORCID: 0000-0002-5812-6015 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.

Link to Published Version:
*Subscription may be required


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.

Item Type: Journal Article
Murdoch Affiliation(s): School of Chemical and Mathematical Science
Publisher: Springer
Copyright: © 2000 Kluwer Academic Publishers
Item Control Page Item Control Page