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Abstract

The time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a point sink or source of variable strength beneath a free surface is considered.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

Item Type:	Article
Authors/Creators:	Stokes, TE and Hocking, GC and Forbes, LK
Keywords:	free-surface potential flows, ideal fluids
Journal or Publication Title:	European Journal of Applied Mathematics
Publisher:	Cambridge Univ Press
ISSN:	0956-7925
DOI / ID Number:	10.1017/S0956792516000310
Copyright Information:	Copyright 2016 Cambridge University Press
Related URLs:	Google Scholar: Forbes, LK UTAS Profile: Forbes, LK
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