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. Physical Review Fluids, 2 (9). ISSN 2469-990X

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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.

Item Type:	Article
Keywords:	Scattering; long water waves; canal; rapidly; varying; cross-section; presence; current;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering
Item ID:	17098
Identification Number:	https://doi.org/10.1103/PhysRevFluids.2.094805
Depositing User:	Dr Andrei Ermakov
Date Deposited:	06 Apr 2023 10:44
Journal or Publication Title:	Physical Review Fluids
Publisher:	American Physical Society
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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