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.