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Unsteady flows induced by a point source or sink in a fluid of finite depth
journal contribution
posted on 2023-05-19, 06:50 authored by Stokes, TE, Hocking, GC, Lawrence ForbesLawrence ForbesThe time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a point sink or source of variable strength beneath a free surface is considered. Backed up by some analytic work, a numerical method is used, and the results are compared with previous work on steady and unsteady flows. In the case of withdrawal for an impulsively started flow, it is found that the critical flow rate increases with reservoir depth, although it changes little as the depth increases beyond double the sink submergence depth. The largest flow rate at which steady solutions can evolve in source flows follows a similar pattern although at a considerably higher value. Simulations indicate that some of the previously calculated steady state solutions at higher flow rates may be unstable, if they exist at all.
History
Publication title
European Journal of Applied MathematicsVolume
28Pagination
357-379ISSN
0956-7925Department/School
School of Natural SciencesPublisher
Cambridge Univ PressPlace of publication
40 West 20Th St, New York, USA, Ny, 10011-4211Rights statement
Copyright 2016 Cambridge University PressRepository Status
- Restricted