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

Michel, Florent; Parentani, Renaud; Robertson, Scott

doi:10.1103/physrevd.97.065018

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

Michel, Florent; Parentani, Renaud; Robertson, Scott

Authors

Florent Michel

Renaud Parentani

Scott Robertson

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.

Citation

Michel, F., Parentani, R., & Robertson, S. (2018). Gravity waves on modulated flows downstream from an obstacle: The transcritical case. Physical Review D, 97(6), Article 065018. https://doi.org/10.1103/physrevd.97.065018

Journal Article Type	Article
Acceptance Date	Feb 21, 2018
Online Publication Date	Mar 29, 2018
Publication Date	Mar 29, 2018
Deposit Date	Feb 21, 2018
Publicly Available Date	Mar 8, 2018
Journal	Physical Review D
Print ISSN	2470-0010
Electronic ISSN	2470-0029
Publisher	American Physical Society
Peer Reviewed	Peer Reviewed
Volume	97
Issue	6
Article Number	065018
DOI	https://doi.org/10.1103/physrevd.97.065018
Related Public URLs	https://arxiv.org/abs/1801.03840

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Copyright 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.