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

Abstract

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.

Rapid spectral evolution of steep surface wave groups with directional spreading

“…Rapizo et al (2016) found that the development of the spectral tail is disturbed for waves propagating on a coflowing current, due to detuning of the quartet resonance interactions. Similarly, Waseda et al (2015) found that the spectral tail can be suppressed by detuning due to currents. Ice sheets also tend to suppress high-wavenumber components, attenuating the amplitude of high-wavenumber components more severely than low-wavenumber components (see Toffoli et al 2015;Meylan et al 2018), possibly suppressing the tail of the spectrum.…”

Experiments on higher-order and degenerate Akhmediev breather-type rogue water waves

“…Laboratory experiments on AB solutions have been performed in large water wave facility, installed at The University of Tokyo, that is 50 m long and 10 m wide while the water depth is 5 m (see Mozumi et al 2015;Waseda et al 2015 for a photography and a schematic description). The 11 wave gauges g i ∈ [g 1 , .…”

Effect of Wave Group Interactions on the Distribution of Wave Height

“…NLS has since then been widely used in studies of modulation of water waves. In the case of two wave groups, the evolution of the envelope can be described by two coupled nonlinear Schrödinger equations (CNLS) [9][10][11][12][13]. CNLS has been used in stability problems in wave group evolution and it has been proved that under certain conditions the interaction of two wave groups can generate waves with very large wave height [10].…”