Summer 2012 Undergrad Research Program
Tsunami Modeling in Trapezoidal Shaped Bays
This summer the topic of interest is the tsunami run-up problem in sloping bays with constant cross-sections. The run-up of long waves can be modeled by the 2D nonlinear shallow water wave equations. In sloping bays of constant cross-sections the Carrier-Greenspan (CG) transformation can simplify shallow water wave equations into a linear system with coulomb potential. The main feature of the new system is that the shoreline becomes a fixed point.
Using the CG transformation, an analytic solution can be found for tsunami run-up in bays of parabolic cross-section. An example of such a bay is:
Our program focused on numerically implementing the CG transform to model run-up in bays of trapezoidal cross-section. An example of such a bay is:
See here for more information.
Mentors and Students
Prof. Alexei Rybkin is the main coordinator of the REU program. He has a PhD in mathematics from Leningrad University (1985). Dr. Rybkin's area of research includes operator theory, complex analysis and mathematical physics.
Dmitry Nicolsky (left) is a tsunami numerical modeler at the UAF Geophysical Institute. His research is focused on the development and implementation of various geophysical models.
Viacheslav Garayshin is currently a masters student at UAF. His research focuses on modeling tsunami run-up. He is originally from Russia.
Jeremiah Harrington is now a senior in the Math Department. He declared a math major in the middle of his sophomore year, and that summer (2011) he learned about Alexei Rybkin’s research program. As a student in the UAF Honors Program, he's required to complete a capstone project, and although he'd prefer to focus his project on more abstract mathematics, he thought the REU on modeling Tsunamis would give him a good research experience in preparation for his own capstone project, and for graduate school.
Matthew Harris is a 21 year old senior at the University of Evansville. He has taken many independent studies, and the summer prior to this program, he worked on a mercury modeling project. His mathematical interests are mainly in analysis, but he is also interested in algebra to a lesser extent. He was born in Evansville, Indiana, and has lived 30 miles outside of Evansville for most of his life. He spent a semester in England.
Lander Ver Hoef is currently a senior in the mathematics program at UAF. While not doing math homework, he enjoys sailing, singing, and acting. He holds a 200 Ton Offshore Yachtmaster license that he received after spending a semester as crew on Argo, a schooner in the Caribbean. After he graduates, Lander intends to pursue a career in the NOAA Corps of Commissioned Officers, combining his love of science and the sea as an officer on a NOAA research or survey vessel.