Surface gravity waves over a two-dimensional random seabed
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Updated: Sep 29, 2026

Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing
Published on: February 13, 2018
Jørgen H Pihl1, Chiang C Mei, Matthew J Hancock
1Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA. jh@pihl.as
Abstract:
We extend homogenization theory to study the two-dimensional evolution of weakly nonlinear waves in a sea where the bathymetry is random over a large area. A deterministic nonlinear Schrödinger equation is derived for the envelope of a nearly sinusoidal progressive wave train. Randomness is shown to yield a linear term with a complex coefficient depending on a certain statistical average of the bathymetry. Numerical solutions are discussed for the diffraction of a Stokes wave in head-sea incidence towards a bathymetry of given plan form. Effects of the height and plan form of the randomness, as well as wave nonlinearity are examined analytically and numerically.
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