Undulations from amplified low frequency surface waves

TL;DR

This paper investigates how gravity waves interacting with supercritical flows lead to amplified undulations at zero frequency, revealing an instability related to negative energy waves and discussing connections to black hole radiation.

Contribution

It demonstrates that amplified low-frequency surface waves cause undulations and surface instability in supercritical flows, linking wave amplification to black hole analogues.

Findings

Reflected waves are amplified near supercritical flow transitions.

Zero-frequency undulations develop with large amplitude.

The instability involves negative energy waves and relates to Hawking radiation.

Abstract

We study the scattering of gravity waves in longitudinal inhomogeneous stationary flows. When the flow becomes supercritical, counterflow propagating shallow waves are blocked and converted into deep waves. We show that the reflected waves are amplified in such a way that, in the zero-frequency limit, the free surface develops an undulation, i.e., a zero-frequency wave of large amplitude with nodes located at specific places. This amplification involves negative energy waves, and implies that the unperturbed flat surface is unstable against incoming perturbations of arbitrary small amplitude. The relation between this instability and black hole radiation (the Hawking effect) is discussed.