Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2

Churilov, Semyon M. and Stepanyants, Yury A. ORCID: https://orcid.org/0000-0003-4546-0310 (2022) Reflectionless wave propagation on shallow water with variable bathymetry and current. Part 2. Journal of Fluid Mechanics, 939:A15. pp. 1-12. ISSN 0022-1120


Abstract

We show that in the linear approximation there are three classes of reflectionless wave propagation on a surface of shallow water in the channel with spatially varying depth, width and current speed. Two of these classes have been described in our previous paper (Churilov & Stepanyants, J. Fluid Mech., vol. 931, 2022, A15), and the third one was discovered recently and is described here. The general analysis of the problem shows that, within the approach used in both of our papers, these three classes apparently exhaust all possible cases of exact solutions of the problem considered.We show that the reflectionless flow can be global for certain conditions, i.e. it can exist on the entire x-axis. There are also reflectionless flows which exist only on limited intervals of the x-axis.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Files associated with this item cannot be displayed due to copyright restrictions.
Faculty/School / Institute/Centre: Current – Faculty of Health, Engineering and Sciences - School of Mathematics, Physics and Computing (1 Jan 2022 -)
Faculty/School / Institute/Centre: Current – Faculty of Health, Engineering and Sciences - School of Mathematics, Physics and Computing (1 Jan 2022 -)
Date Deposited: 19 Apr 2022 03:31
Last Modified: 19 Apr 2022 03:31
Uncontrolled Keywords: ocean processes; shallow water flows; surface gravity waves
Fields of Research (2020): 37 EARTH SCIENCES > 3708 Oceanography > 370803 Physical oceanography
49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490109 Theoretical and applied mechanics
51 PHYSICAL SCIENCES > 5103 Classical physics > 510399 Classical physics not elsewhere classified
Socio-Economic Objectives (2020): 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280120 Expanding knowledge in the physical sciences
28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280107 Expanding knowledge in the earth sciences
Identification Number or DOI: https://doi.org/10.1017/jfm.2022.208
URI: http://eprints.usq.edu.au/id/eprint/47643

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