Abstract
Surface water waves are a physically important phenomenon with which we all have some experience. They are also surprisingly complex and interesting from a mathematical perspective. I will discuss two recent projects in water wave modeling. The first deals with ocean waves, such as tsunamis, passing over the continental slope. It has long been known that the amplification of such waves is greater than what the traditional transmission coefficient would predict. The recent investigation of this phenomenon has led to a completely new way to apply the method of characteristics to general wave problems with continuously-varying coefficients. The second project is the modeling of a circular hydraulic jump that forms when a jet of water impacts a flat plate, as happens when running the water in a typical kitchen sink. The stability of this jump is a complex and open question.
Brief Biography
Prof. David Ketcheson is a Professor of Applied Mathematics and Computational Science at KAUST. He received his Ph.D. in 2009 from the University of Washington.