THE FREQUENCY MODULATION OF SHORT WAVES BY NON-UNIFORM VELOCITY FIELDS

In this study we particularly concentrate on the problem of short wave energy modufated by long waves which is considered as a non-uniform velocity. In theory ithas been concluded that the wavelengths /amplitudes of short wa ves become shorter/largerin the crest of the long waves and the wavelengths/ amplitudes of the short waves becomelonger/smaller in the trough of the long waves. Wave energy is proportional to the squareof wave amplitude. That means the energy of the short waves becomes larger in the crestof long waves and smaller in the trough of the long waves. In this study, the experimentalfrequency medulation is applicable to be compared with the theoretical approach. The elevation-time series of monochromatic and two-component waves from a wave gauge aremeasured and used to calculate the modulation frequency of short waves riding onmonochromatic long waves. The experimental modulated frequency shows similar trendsto the numerical results, which are based on Stokes’expansions for the numerical solutionof monochromatic long waves, and the theory of phase conservation while short waves riding on a monochromatic long wave. It is found that the experimental modulated frequencyof short waves is bound in a narrow strip along the long wave phase and is periodic withrespect to the long wave period. Besides, the results demonstrate the maximum/minimummodulated frequency of the short train occurs near of at the crest/trough of the long waveand, with increasing the steepness of the long waves, the modulated short wave frequencyon the long wave crest increases.