Probing the thermal character of analogue Hawking radiation for shallow water waves?

TL;DR

This study numerically investigates how shallow water wave scattering by flows mimics Hawking radiation, revealing deviations from thermality in subcritical flows and proposing new interpretations and experimental tests.

Contribution

It provides a detailed numerical analysis of scattering coefficients in shallow water flows, highlighting deviations from Hawking's thermal spectrum in subcritical regimes and offering new experimental insights.

Findings

Hawking-like thermal spectrum appears in transcritical flows

Subcritical flows show suppressed and non-thermal spectra

Numerical results align with Vancouver experiment observations

Abstract

We study and numerically compute the scattering coefficients of shallow water waves blocked by a stationary counterflow. When the flow is transcritical, the coefficients closely follow Hawking's prediction according to which black holes should emit a thermal spectrum. We study how the spectrum deviates from thermality when reducing the maximal flow velocity, with a particular attention to subcritical flows since these have been recently used to test Hawking's prediction. For such flows, we show that the emission spectrum is strongly suppressed, and that its Planckian character is completely lost. For low frequencies, we also show that the scattering coefficients are dominated by elastic hydrodynamical channels. Our numerical results reproduce rather well the observations made by S. Weinfurtner {\it et al.} in the Vancouver experiment. Nevertheless, we propose a new interpretation of what has been observed, as well as new experimental tests.