Strutture coerenti in onde oceaniche superficiali: risultati sperimentali

We have analyzed ocean surface wave data in Currituck Sound, North Carolina on the East coast of the United States of America. The data were taken by a directional array (antenna) with nine probes in 2.6 m water depth. Traditional analyses use the linear Fourier transform to analyze data of this type: the data are projected onto sine waves that obey the linear superposition principle. In the present thesis we instead address the possibility of nonlinearities in the data and in this way we use the nonlinear Fourier transform (formally called the inverse scattering transform, IST), to carry out the data analysis: the data are projected onto nonlinear modes which obey a nonlinear superposition principle. We apply the IST to analyze the data and demonstrate the presence of two types of coherent structures in the measured time series: Both solitons and coherent breather trains are found. This conclusion comes from the simultaneous analysis of the data using the inverse scattering transform for both the Korteweg-deVries (KdV) and nonlinear Schroedinger (NLS) equations. In this approach, we project the time series simultaneously onto the modes of both equations and separate the physics into asymptotic expansions about wavenumber k=0 (for which one finds the KdV equation) and about k0 (for which one obtains the NLS equation about the carrier wavenumber k0). We are thus able to nonlinearly filter the wave train into a solitonic part and into a part that contains breather states. We then describe the full physics in terms of the spectrum in both the KdV and the NLS regimes. We obtain a clear picture of a typical nonlinear spectrum in the coastal zone that contains both solitons and rogue wave packets. The soliton spectrum is quite robust and for a time series of about 6000 points, we obtain about 100 solitons. The breather spectrum is ¿saturated¿, i.e. over 95% of the spectral components correspond to breather packets. Additional work will be performed to fully understand the nonlinear interactions between the two types of spectral components.