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Third-order resonant wave interactions under the influence of background current fields

Published online by Cambridge University Press:  29 October 2015

Takuji Waseda
Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8563, Japan
T. Kinoshita
Institute of Industrial Science, University of Tokyo, Tokyo 153-8505, Japan
L. Cavaleri
Institute of Marine Sciences, Castello 2737/F, 30122 Venice, Italy
A. Toffoli
Centre for Ocean Engineering, Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
E-mail address:


A series of experiments were conducted in a wave basin (50 m long, 10 m wide and 5 m deep) generating two waves propagating at an angle by a directional wavemaker. When the two waves were selected from a resonant triplet, an initially non-existing wave grew as the waves propagated down the tank. The linear growth rate of the resonating wave agreed well with third-order resonance theory based on Zakharov’s reduced gravity equation. Additional experiments with opposing and coflowing mean current with large temporal and spatial variations were conducted. As the flow rate increased, the linear growth was suppressed. As reproduced numerically with Zakharov’s equation, the resonant interaction saturated at time scales inversely proportional to the magnitude of the forced random resonance detuning. It is conjectured that the resonance is detuned by the variation and not by the mean of the current field due to wavelength-dependent Doppler shift and to the refraction of wave rays. Further analysis of the spectral evolution revealed that while discrete peaks appear at high frequencies as a result of dynamical cascading, a continuously saturated spectrum develops in the background as the current speed increases. Additional experiments were conducted studying the evolution of the random directional wave on a dynamical time scale under the influence of current. Due to random resonance detuning by the current, the spectral tail tended to be suppressed.

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