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Gravity waves on modulated flows downstream from an obstacle : the transcritical case.

Michel, Florent and Parentani, Renaud and Robertson, Scott (2018) 'Gravity waves on modulated flows downstream from an obstacle : the transcritical case.', Physical review D., 97 (6). 065018 .

Abstract

Periodic spatial modulations arise in analogue gravity experiments aimed at detecting the analogue version of the Hawking effect in a white-hole flow. Having the same spatial periodicity as low-frequency dispersive modes, they can induce resonances which significantly modify the scattering coefficients. This has been shown numerically in a previous work [X. Busch et al., Phys. Rev. D 90, 105005 (2014)], but the precise dependence of the low-frequency effective temperature on the amplitude and length of the undulation remains elusive. In this article, using the Korteweg–de Vries equation, we explicitly compute this dependence in the small-amplitude limit and find three regimes of “short,” “intermediate” and “long” undulations showing different scaling laws. In the latter, the effective temperature is completely determined by the properties of the undulation, independently of the surface gravity of the analogue white-hole flow. These results are extended to a more realistic hydrodynamical model in an Appendix C.

Item Type:Article
Full text:(AM) Accepted Manuscript
First Live Deposit - 08 March 2018
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1103/PhysRevD.97.065018
Publisher statement:Reprinted with permission from the American Physical Society: Michel, Florent, Parentani, Renaud & Robertson, Scott (2018). Gravity waves on modulated flows downstream from an obstacle: The transcritical case. Physical Review D 97(6): 065018 © 2018 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.
Record Created:08 Mar 2018 09:28
Last Modified:19 Apr 2018 10:06

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