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Title: Undulations from amplified low frequency surface waves

We study the linear scattering of gravity waves in longitudinal inhomogeneous stationary flows. When the flow becomes supercritical, it is known that counterflow propagating shallow waves are blocked and converted into deep waves. Here we show that in the zero-frequency limit, the reflected waves are amplified in such a way that 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 flat surfaces are unstable against incoming perturbations of arbitrary small amplitude. The relation between this instability and black hole radiation (the Hawking effect) is established.
Authors:
 [1] ;  [2]
  1. Max Planck Institute for Gravitational Physics, Albert Einstein Institute, Am Muhlenberg 1, 14476 Golm (Germany)
  2. Laboratoire de Physique Théorique, CNRS UMR 8627, Bâtiment 210, Université Paris-Sud 11, 91405 Orsay Cedex (France)
Publication Date:
OSTI Identifier:
22257207
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AMPLIFICATION; AMPLITUDES; BLACK HOLES; GRAVITY WAVES; INSTABILITY; PERTURBATION THEORY; SCATTERING; WAVE PROPAGATION