Wavelet analysis of short wave modulation by a long wave
Résumé
An investigation of the modulation of short wind waves by a long wave is carried out using the wavelet transform technique. Observations were made in the large IRPHE-Luminy wind-wave tank where composite wave fields were obtained by a combination of mechanically-generated long waves and wind-generated short waves of various scales. An analysis of the time records of the water surface heights measured by a high-resolution capacitance wave gauge is first performed. To estimate the modulation transfer function, the long wave signal and the short wave energy component modulated by the long wave are extracted from the wave signal by means of a continuous wavelet decomposition. The potentiality of this method to analyze two-scale wave fields as well as complex wind wave fields with small long wave-short wave scale separation and waves of nonlinear shape is then examined in detail and compared with the classical methods based on the phase average or the windowed Fourier transform. Finally, the phase and the amplitude of the modulation transfer function are determined for the different wind speed, wave steepness and frequency range conditions, and the results obtained are analyzed within the framework of the recent coupled air-water flow theories.