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Experiments on ripple instabilities. Part 2 Selective amplification of resonant triads

Resonant three-wave interactions among capillary–gravity water waves are studied experimentally using a test wavetrain and smaller background waves (noise) generated mechanically in a channel. The spectrum of the background waves is varied from broad-banded to one with discrete components. When the noise spectrum is broad-banded, the test wavetrain amplifies all waves in its low-frequency band of allowable triads B[ell ], as anticipated from RIT (resonant interaction theory). When the noise spectrum has a discrete component in the high-frequency band of allowable triads Bh, the test wavetrain selectively amplifies a triad with two waves from B[ell ], contrary to expectations based on RIT. (Although, in accordance with RIT, no waves in Bh are amplified.) We conjecture that the mechanism for selective amplification comprises a sequence of exceedingly weak, higher-order interactions, normally neglected in RIT. This sequence allows the small amount of energy in a discrete spectral component to cascade to two waves in B[ell ], which then amplify, as anticipated from RIT, and dominate all other waves in B[ell ]. The conjectured sequence of nonlinear interactions is tested using both frequency and wave-vector data, which are obtained by in situ probes and by remote sensing of the water surface with a highspeed imaging system. Our predictions of selective amplification, as well as its absence, are consistent with all of the experiments presented herein and in Part 1. Selective amplification occurs for signal-to-noise (amplitude) ratios as large as 200, and its effects are measurable within ten wavelengths of the wavemaker. When selective amplification occurs, it has a profound impact on the long-time evolution of a ripple wavetrain.