Surface gravity waves over a two-dimensional random seabed

Jørgen H. Pihl; Chiang C. Mei; Matthew J. Hancock

doi:10.1103/PhysRevE.66.016611

Surface gravity waves over a two-dimensional random seabed

Jørgen H. Pihl, Chiang C. Mei, and Matthew J. Hancock

Phys. Rev. E 66, 016611 – Published 26 July 2002

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.

Received 20 January 2002

DOI:https://doi.org/10.1103/PhysRevE.66.016611

Authors & Affiliations

Jørgen H. Pihl^*, Chiang C. Mei^†, and Matthew J. Hancock^‡

Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

^*Present address: Øverødvej 23, 1-12, DAK-2840 Holt, Denmark. Electronic address: jh@pihl.as
^†Electronic address: ccmei@mit.edu
^‡Electronic address: hancock@mit.edu

References (Subscription Required)

Click to Expand

Issue

Vol. 66, Iss. 1 — July 2002

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics