Scattering of gravity waves in subcritical flows over an obstacle

TL;DR

This study numerically analyzes how linear water waves scatter over an obstacle in subcritical flows, revealing suppressed mode amplification and frequency-dependent behaviors relevant for analog gravity experiments.

Contribution

It provides a detailed numerical comparison of wave scattering in subcritical versus transcritical flows, highlighting the suppression of amplification in subcritical flows and the impact of obstacle geometry.

Findings

High-frequency transmission is limited in subcritical flows.

Low-frequency scattering involves non-adiabatic short wavelength generation.

Upstream slope influences downstream scattering due to residual transmission.

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.