Abstract
AbstractThis paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.
Highlights
The study of the resonance mechanism in water waves is of fundamental importance, as the nonlinear interactions between different wave components may result in energy transfers in the spectrum
The spectra of the resonant wave system generated by the eight wave components listed in tables 2 and 4 are as shown in figure 5(c,f ): the amplitudes of the dominant frequency vary from A1 = 7.65 cm at the first gauge to A9 = 6.48 cm at the ninth gauge, while the amplitude spatial variance decreases to δr,9 = 0.08 as listed in table 5, which is even smaller than the inherent system error δr,9 = 0.11 for steady-state waves
Five cases of resonant waves in deep water are considered: the first four cases (S1–S4) correspond to steady-state resonant waves, while case S5 relates to an non-steady-state ones that provides a contrasting experiment
Summary
The study of the resonance mechanism in water waves is of fundamental importance, as the nonlinear interactions between different wave components may result in energy transfers in the spectrum. We focus on the symmetrical and anti-symmetrical groups of the steady-state resonant waves that are composite of short-crested ones in this paper. To find the origin of the unsteadiness in the basin, the final composite wave groups are generated in such a way that more components are considered in our experiments, step by step, starting from the simplest oblique long-crested wave. In the two subsequent 30 s intervals, the wave amplitude at every gauge site Ai changes slightly (so does the absolute error δa,5), while the spatial variations, especially δr,, keep almost constant This indicates that the spatial steadiness of oblique long-crested waves is reliable over a long time in the basin and δr,9 ≈ 0.11 may serve as the inherent system error for a steady-state wave in the basin. If the spatial variation δr, of a wavefield is approximately 0.11, we may regard it as a steady state
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