Bernard Deconinck's Research

Picture of Hurricane Gracee
Picture of Hurricane Grace
Role
Surface waves in water of arbitrary depth
Project Collaborators
Bernard Deconinck (UW)
John Carter (SU)
Diana Henderson (PSU)
Katie Oliveras (SU)
Harvey Segur (CU)
Vishal Vasan (PSU)
Project Description
This is a research project involving many. My objective is the fundamental understanding of different aspects of water waves. A lot of different things have been accomplished.
  • We have computed one-dimensional periodic traveling wave solutions of the water-wave problem, and we have examined their stability. This has been done both with and without surface tension. We have considered one-dimensional perturbations and two-dimensional ones.
  • We have found exact nonlinear relations between the surface elevation of a periodic traveling wave and the pressure at the bottom, resulting in a big improvement on Archimedes' Law and linear theory. Agreement with numerics and experiment is excellent.
  • We have provided a numerical solution to the inverse problem of reconstructing the water bathymetry from surface measurements. The theory works for both one-dimensional and two-dimensional surfaces.
We are using methods from analysis, computational mathematics, asymptotics and algebraic geometry, together with state-of-the-art physical experiments.

Waves play an important role in the open ocean and in coastal regions. The instabilities of wave patterns is not well understood, nor are the effects of coherence and large amplitude wave weather, air-sea transport processes, and large-scale structures. Thus, an understanding of these patterns is of importance to shipping and coastal engineering.

Department of Applied Mathematics, University of Washington, Lewis Hall #202, Box 353925, Seattle, WA 98195-3925 USA
Email 'info' (at amath.washington.edu) Phone 206-543-5493 Fax 206-685-1440