Summer 2015 Undergrad Research Program
This summer the topic of interest is the applicability of the KdV equations to undular bore waves in Turnagain Arm. Collecting field velocity and wave height data is cost preventative so we focus on the use of pictures to gather data. To this effect we have developed three methods that can be used to show whether or not KdV is an accurate model for undular bore waves in Turnagain Arm. Unfortunately the images that were available to us were not of high enough resolution to yield conclusive results.
Here is some background information as to why we believe KdV is an appropriate model for the undular bore wave in Turnagain Arm.
The initial condition for undular bore waves in Turnagain Arm is a step-like bore wave. An example of a step-like wave is shown here:
When a step-like bore moves into Turnagain Arm, it sometimes transforms into an undular bore wave depending on factors such as the wind velocity and the location in Turnagain Arm. An example of a undular bore wave in Turnagain Arm is given here:
On the other hand, the work by Hruslov [1] shows that KdV equation turns a step-like initial profile into a train of solitons. For example after 4 minutes of propagation, the step-like initial profile with a wave height of 0.5 meters in a bay 3 meters deep becomes
This wave profile is visually similar to the bores seen in Turnagain Arm.
[1] Hruslov, E. 1976. Asymptotics of the Solution of the Cauchy Problem for the Korteweg-deVries Equation with Initial Data of Step Type. Matematics of the USSR-Sbornik. Vol 28.
Mentors and Students
Prof. Alexei Rybkin is the private investigator for 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 is a Research Assistant Professor at the Geophysical Institute and a State Science Representative on the Coordinating Committee of the National Tsunami Hazard Mitigation Program. His research is focused on development of models to assess tsunami hazard along the Alaska coast.
Matthew Harris has just recieved his Masters degree in mathematics from the University of Alaska, Fairbanks. He was an REU student during the 2012 REU, and a post-baccalaureate mentour during the 2013 REU and a Master's student mentour this year. Matthew is enrolled in the Applied Mathematics PhD program at the University of Waterloo this Fall.
Jody Gaines is studying undergraduate mathematics at UAF. He hopes to receive his Secondary Education licensure by Spring 2016.
Michael Saccone is concluding his undergraduate Physics degree at UAF and will continue on to a PhD program at UCSC. His interests include Parkour, dynamical systems, and forcing the computers to gather data for us before robots rule us all.