Observation of Phillips' spectrum in Faraday waves

Gustavo Castillo, Claudio Falcón

Published 2016-08-31Version 1

We report the observation of the Phillips' spectrum of gravity surface waves driven by a horizontally moving wave maker interacting with Faraday waves. We measure the temporal fluctuations of the surface wave amplitude at a given location and we show that, for a wide range of forcing parameters, they display a power-law spectrum that greatly differs from the one predicted by the WT theory but coincides with Phillips' spectrum for gravity waves. We compute the probability density function of the local surface height increments, which show that they change strongly across time scales. The structure functions of these increments are shown to display power-laws as a function of the time lag, with exponents that are not linear with the order of the structure function, thus showing that the wave field is intermittent. We argue that the origin of this scale-invariant intermittent spectrum is the Faraday wave pattern breakup due to its advection by the propagating gravity waves, which can be related directly to the Phillips' spectrum phenomenology.