Summer 2012 Undergrad Research Program

From left: Viacheslav Garayshin, Dr. Alexei Rybkin, Dr. Dmitry Nicolsky, Jeremiah Harrington, Matthew Harris, and Lander Ver Hoef

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.

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