Techniques for the investigation of wave turbulence in water wave data

Abstract

Computer based tools were developed to search water wave data for a collective mode predicted by wave turbulence theory. A low frequency wave, the "swell", can drive the collective mode by compressing and expanding the field of high frequency waves, the "chop". Through non-linear interactions, the chop responds with its own collective stiffness and inertia. This inertia should cause modulations of the chop amplitude to lag in phase behind the forcing from the swell. Two methods are presented for investigating the phase relationships between the chop amplitude and the swell. Method one employs the Fast Fourier Transform to examine directly the power levels at various frequencies. Method two employs digital signal processing to separate the swell and chop frequencies and the Hubert Transform to compute the instantaneous phase of the swell and instantaneous amplitude of the chop. Various plotting techniques permit the examination of the relationships between the amplitude of the chop and the phase of the swell. The second method provided evidence of the collective mode when applied to data collected in a wave tank experiment described herein.