Scattering of gravity waves in subcritical flows over an obstacle

Abstract

We numerically study the scattering coefficients of linear water waves on stationary flows above a localized obstacle. We compare the scattering on trans- and subcritical flows, and then focus on the latter which have been used in recent analog gravity experiments. The main difference concerns the magnitude of the mode amplification: whereas transcritical flows display a large amplification (which is generally in good agreement with the Hawking prediction), this effect is heavily suppressed in subcritical flows. This is due to the transmission across the obstacle for frequencies less than some critical value. As a result, subcritical flows display high- and low-frequency behaviors separated by a narrow band around the critical frequency. In the low-frequency regime, transmission of long wavelengths is accompanied by non-adiabatic scattering into short wavelengths, whose spectrum is approximately linear in frequency. By contrast, in the high-frequency regime, no simple description seems to exist. In particular, for obstacles similar to those recently used, we observe that the upstream slope still affects the scattering on the downstream side because of some residual transmission.

21 pages, 17 figures

References in corpus (7)

• Measurement of stimulated Hawking emission in an analogue system
• Observation of negative-frequency waves in a water tank: A classical analogue to the Hawking effect?
• Black/White hole radiation from dispersive theories
• The theory of Hawking radiation in laboratory analogues
• Quantum entanglement in analogue Hawking radiation, when is the final state non-separable ?
• Probing the thermal character of analogue Hawking radiation for shallow water waves?
• Suppression of infrared instability in trans-sonic flows by condensation of zero-frequency short wave length phonons

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• Gravity waves on modulated flows downstream from an obstacle: The transcritical case
• Four-wave mixing and enhanced analogue Hawking effect in a nonlinear optical waveguide
• Pairs of surface wave packets with zero-sum energy in the Hawking radiation analog
• Perturbative Approach to Analog Hawking Radiation in dielectric media in subcritical regime