Undulations from amplified low frequency surface waves
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.
Cite
@article{arxiv.1211.2001,
title = {Undulations from amplified low frequency surface waves},
author = {Antonin Coutant and Renaud Parentani},
journal= {arXiv preprint arXiv:1211.2001},
year = {2014}
}
Comments
19 pages, 2 figures - Pulished version. Added clarifications, and relations to fluid mechanics standard treatments