Nonlinear dispersive water waves and tsunamis

Tsunami waves generated by the deformation of the ocean floor due to strong, underwater earthquakes are characterised as long waves of small amplitude. As such, the generation of these waves can be described accurately by nonlinear dispersive partial differential equations. 

In this talk we review the derivation and the theoretical properties of some systems of nonlinear and dispersive partial differential equations related to long waves of small amplitude. These systems are called Boussinesq systems and describe the propagation of weakly nonlinear and weakly dispersive water waves over general bottom topography.

We also present the numerical solution of such systems with special emphasis on a finite element method that has optimal convergence rate for Lagrange elements. Finally, we present applications to the tsunami generation problem using a novel active generation technique.

About the speaker

Dimitrios Mitsotakis is a Mathematician, graduated from the University of Crete with the highest honours (first in class) in the year 2000. He received a master’s degree in Applied and Numerical Analysis in the year 2003 and a PhD in Mathematics in 2007 from the University of Athens. He was introduced to high performance computing visiting the Edinburgh Parallel Computing Center at The University of Edinburgh in the year 2000.

Dimitrios worked at the Université Paris-Sud (2008-2010) as a Marie Curie researcher, at the University of Minnesota (2010-2012) as an associate postdoc and at the University of California, Merced (2012-2014) as a visiting Assistant Professor. Dimitrios is currently a Senior Lecturer at the School of Mathematics and Statistics of Victoria University of Wellington.