The Sideband Instability and the Onset of Wave Breaking
Packets of surface gravity waves of constant frequency and similar raised cosine envelopes were generated with a variety of amplitudes by means of a hydraulic paddle. The behaviour of each packet was observed with two capacitance probes, one near the paddle and the other some distance along the tank. In the time domain each packet was observed to evolve into a single envelope soliton and a “tail” as it travelled down the tank. In the frequency domain the the initial spectral peak was observed to split into two peaks at frequencies on either side of the initial frequency in accordance with the well known “sideband” instability. In addition, for packets in excess of a particular threshold, wave breaking also occurred. The sideband instability was observed at amplitudes both above and below the threshold of breaking. At amplitudes below the threshold, energy was partitioned almost equally between the upper and lower sidebands but with the onset of breaking a smaller fraction of the initial energy was transferred to the upper sideband. The spectral behaviour of these evolving wave packets shows a number of features in common with that of wind waves observed in the open sea.
KeywordsSoliton Beach Banner
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