The generalized Doppler effect for surface waves

E-ISSN： 1286-4854|116|4|44002-44002

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.116, Iss.4, 2017-01, pp. : 44002-44002

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Abstract

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.