Trapped waves on interfacial hydraulic falls over bottom obstacles

Wang, Z., Chai, J., Parau, E. I. ORCID: https://orcid.org/0000-0001-5134-2068, Page, C. and Wang, M. (2022) Trapped waves on interfacial hydraulic falls over bottom obstacles. Physical Review Fluids, 7 (7). ISSN 2469-990X

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Abstract

Hydraulic falls on the interface of a two-layer density stratified fluid flow in the presence of bottom topography are considered. We extend the previous work [Philos. Trans. R. Soc. London A 360, 2137 (2002)] to two successive bottom obstructions of arbitrary shape. The forced Korteweg-de Vries and modified Korteweg-de Vries equations are derived in different asymptotic limits to understand the existence and classification of fall solutions. The full Euler equations are numerically solved by a boundary integral equation method. New solutions characterized by a train of trapped waves are found for interfacial flows past two obstacles. The wavelength of the trapped waves agrees well with the prediction of the linear dispersion relation. In addition, the effects of the relative location, aspect ratio, and convexity-concavity property of the obstacles on interface profiles are investigated.

Item Type: Article
Additional Information: Funding Information: This work was supported by the National Natural Science Foundation of China (Grants No. 11911530171 and No. 11772341), the key program of the National Natural Science Foundation of China (Grant No. 12132018), and the Royal Society International Exchanges Travel Grant (No. IEC/NSFC/181279).
Uncontrolled Keywords: computational mechanics,modelling and simulation,fluid flow and transfer processes ,/dk/atira/pure/subjectarea/asjc/2200/2206
Faculty \ School: Faculty of Science > School of Mathematics
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Depositing User: LivePure Connector
Date Deposited: 30 May 2022 13:30
Last Modified: 22 Oct 2022 07:52
URI: https://ueaeprints.uea.ac.uk/id/eprint/85255
DOI: 10.1103/PhysRevFluids.7.074801

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