Undulations from amplified low frequency surface waves
Résumé
We study the scattering of gravity waves in longitudinal stationary flows. When the flow velocity becomes supercritical, counterflow propagating waves are amplified in such a way that, in the zero-frequency limit, the free surface develops an undu- lation, i.e., a zero-frequency wave of large amplitude with nodes located at specific places. From this, we show that the unperturbed flat surface is unstable against perturbations of arbitrary small amplitude. We then show that this instability also appears when treating low frequency waves by a stochastic ensemble. The relation between the generation of undulations and black hole radiation (the Hawking effect) is discussed.