Volume 116, Number 4, November 2016
|Number of page(s)||7|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||03 January 2017|
The generalized Doppler effect for surface waves
Laboratoire de Physique Statistique, Ecole Normale Supérieure, CNRS, Université P. et M. Curie, Université Paris Diderot - Paris, France
Received: 29 September 2016
Accepted: 16 December 2016
We investigate energy exchanges through scales occurring when a surface wave reflects on a harmonically oscillating wall. We first experimentally evidence the creation of Doppler-shifted waves and measure their height as a function of the oscillation amplitude. Then, we theoretically compute the amplitudes of these new waves in the gravity regime. Both results show that even without bulk non-linearities, oscillating paddles in a fluid container lead to a complex wave energy spectrum competing with the one predicted by wave turbulence. To exemplify this point, we characterize a simple one-dimensional model consisting of a linear wave equation in an oscillating cavity with distinct injection and dissipation mechanisms. It displays features usually associated with non-linearities, as self-similarity in a spectral domain (the so-called inertial range), appearance of energy at larger and/or lower scales than the forcing one and creation of shock waves.
PACS: 42.25.Gy – Edge and boundary effects; reflection and refraction / 47.35.Bb – Gravity waves / 43.20.+g – General linear acoustics
© EPLA, 2016
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