Localization of harmonics generated in nonlinear shallow water waves
Related Experiment Video
Updated: Aug 30, 2026

Measurement of Scattering Nonlinearities from a Single Plasmonic Nanoparticle
Published on: January 3, 2016
Géraldine L Grataloup1, Chiang C Mei
1Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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.
Related Concept Videos
Modes of Standing Waves - I
Standing Waves
Wave Parameters
Damped Oscillations
Although friction and other non-conservative...
Partial Differential Equations
Modes of Standing Waves: II
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.

