W. G. Pritchard Lab Seminar: 4:00-5:00 PM, 101 Osmond Laboratory
**Tuesday September 30, 2003**
Elliptic functions and wave interactions: some interesting problems
David Hill
Department of Civil & Environmental Engineering
Penn State University
Abstract:
Water waves can be resonantly forced either by external sources or by
interactions between waves. While it lacks the capability to predict wave
breaking, weakly-nonlinear analysis is a powerful tool in analyzing these
problems. Generally, an equation describing the evolution of the amplitude
in time and / or space can be derived for each wave present. In some cases,
these equations can be solved analytically in terms of Jacobian elliptic
functions.
Two problems will be discussed. The first is concerned with the generation
of seiches in a body of water in response to horizontal periodic forcing. A
natural application is the prediction of the performance of fluid storage
containers and small water-supply reservoirs during a seismic shaking
event. The second problem is concerned with the generation of interfacial
waves by surface waves. In this case, the analysis may help to understand
the processes controlling the depth of the oceanic mixed layer and the
resuspension of fine-grained sediments in estuaries.