The influence of surface tension upon trapped waves and hydraulic falls

Page, C., Grandison, S. and Parau, Emilian ORCID: https://orcid.org/0000-0001-5134-2068 (2014) The influence of surface tension upon trapped waves and hydraulic falls. European Journal of Mechanics - B/Fluids, 43. pp. 191-201. ISSN 0997-7546

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Abstract

We consider steady two-dimensional free-surface flows past submerged obstructions on the bottom of a channel. The flow is assumed to be irrotational, and the fluid inviscid and incompressible. Both the effects of gravity and surface tension are considered. Critical flow solutions with subcritical flow upstream and supercritical flow downstream are sought using fully nonlinear boundary integral equation techniques based on the Cauchy integral formula. When a second submerged obstruction is included further upstream in the flow configuration in the absence of surface tension, solutions which have a train of waves trapped between the two obstacles before the critical flow have already been found (Dias and Vanden-Broeck 2004). We extend this work by including the effects of surface tension. Trapped wave solutions are found upstream for small values of the Bond number, for some values of the Froude number. Other types of trapped waves are found for stronger tension when the second obstruction is placed downstream of the hydraulic fall generated by the first obstacle.

Item Type:	Article
Uncontrolled Keywords:	gravity-capillary waves,hydraulic falls,free surfaces,water waves
Faculty \ School:	Faculty of Science Faculty of Science > School of Computing Sciences Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics
Depositing User:	Pure Connector
Date Deposited:	05 Nov 2013 17:00
Last Modified:	24 Oct 2022 04:58
URI:	https://ueaeprints.uea.ac.uk/id/eprint/44244
DOI:	10.1016/j.euromechflu.2013.09.002

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