title: Localization of harmonics generated in nonlinear shallow water waves.
abstract: The propagation of nonlinear shallow water waves over a random seabed is studied. A bathymetry which fluctuates randomly from a constant mean adds multiple scattering to resonant interactions and harmonic generation. By the method of multiple scales, nonlinear evolution equations for the harmonic amplitudes are derived. Effects of multiple scattering are shown to be represented by certain linear damping terms with complex coefficients related to the correlation function of the seabed disorder. For any finite number of harmonics, an equation governing the total wave energy is derived. By numerical solution of the amplitude equations, the effects of spatial attenuation (localization) on harmonic generation are studied.
authors.affiliation: Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
authors.forename: Géraldine L
authors.initials: GL
authors.lastname: Grataloup
authors.forename: Chiang C
authors.initials: CC
authors.lastname: Mei