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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 Forbes
The time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a point sink or source of variable strength beneath a free surface is considered.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 Mathematics

Volume

28

Pagination

357-379

ISSN

0956-7925

Department/School

School of Natural Sciences

Publisher

Cambridge Univ Press

Place of publication

40 West 20Th St, New York, USA, Ny, 10011-4211

Rights statement

Copyright 2016 Cambridge University Press

Repository Status

  • Restricted

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Expanding knowledge in the mathematical sciences

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