Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current

Churilov, Semyon and Ermakov, Andrei and Rousseaux, Germain and Stepanyants, Yury (2017) Scattering of long water waves in a canal with rapidly varying cross-section in the presence of a current. Physcial Review Fluids, 2 (9). 094805.

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Abstract

The analytical study of long-wave scattering in a canal with a rapidly varying cross-section is presented. It is assumed that waves propagate on a stationary current with a given flow rate. Due to the fixed flow rate, the current speed is different in the different sections of the canal, upstream and downstream. The scattering coefficients (the transmission and reflection coefficients) are calculated for all possible orientations of incident wave with respect to the background current (downstream and upstream propagation) and for all possible regimes of current (subcritical, transcritical, and supercritical). It is shown that in some cases negative energy waves can appear in the process of waves scattering. The conditions are found when the over-reflection and over transmission phenomena occur. In particular, it is shown that a spontaneous wave generation can arise in a transcritical accelerating flow, when the background current enhances due to the canal narrowing. This resembles a spontaneous wave generation on the horizon of an evaporating black hole due to the Hawking effect.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Published version deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 07 Nov 2017 03:03
Last Modified: 27 Apr 2018 04:41
Uncontrolled Keywords: water waves; canal with varying cross-section; non-uniform current; wave scattering; transformation coefficients
Fields of Research : 02 Physical Sciences > 0203 Classical Physics > 020303 Fluid Physics
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: 10.1103/PhysRevFluids.2.094805
URI: http://eprints.usq.edu.au/id/eprint/33159

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