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

Abstract

Periodic spatial variations of some parameter 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.

34 pages, 11 figures, version 2 close to that published in Physical Review D

References in corpus (7)

• Fiber-optical analogue of the event horizon
• Measurement of stimulated Hawking emission in an analogue system
• Black/White hole radiation from dispersive theories
• Acoustic white holes in flowing atomic Bose-Einstein condensates
• Probing the thermal character of analogue Hawking radiation for shallow water waves?
• Low frequency analogue Hawking radiation: The Korteweg-de Vries model
• Suppression of infrared instability in trans-sonic flows by condensation of zero-frequency short wave length phonons

Cited by in corpus (2)

• Scattering of co-current surface waves on an analogue black hole
• Classical Hydrodynamics for Analogue Spacetimes: Open Channel Flows and Thin Films