Tsunamis: Linear and Nonlinear Waves
Dr. Richard Haberman
Department of Mathematics
Southern Methodist University
Tuesday, February 22, 2005
2 p.m.
Location: GR 3.302
Open to the public
Coffee will be served in ECSN 3.106 at 1:30 p.m.
Description
Tsunamis have three stages: formation, mid-ocean propagation, and breaking and run-up on the beach.
We discuss mid-ocean propagation. We will mathematically formulate the fully nonlinear water wave problem. We will linearize and derive the well-known dispersion relation.
Linear waves disperse with the energy spreading out. Linear theory describes the usual waves at beaches due to storms. Waves generated from earthquakes can be long waves with wave length much greater than the 5 mile depth of the ocean.
We will derive one elementary formula for long waves which accurately predicts the over 500 mile per hour propagation of waves and arrival times of tsunamis. We will describe two theories of long wave tsunamis.
Weakly nonlinear dispersive long waves are known to satisfy the Korteweg-de Vries (KdV) nonlinear partial differential equation. The KdV equation has solitary pulse traveling wave solutions which have coherent structure, and the energy does not spread out.
However, we will show that the 2004 tsunami satisfied a linear two-dimensional wave equation. We will briefly discuss the destructive nonlinear process near the shore by which a shock forms.
For More Information
Lorre Antoine
phone (972)883-2161
fax (972)883-6622
- Updated: June 7, 2005
