Interdisciplinary Seminar in Nonlinear Science

Speaker: Professor S. Wiggins
Speaker Info: CalTech
Brief Description:
Special Note: Unfortunately, the talk by S. Wiggins has to be cancelled.

There is a remarkable similarity between the mathematical framework of dynamical systems theory and the experimental and observational framework of modern oceanography. On the one hand, quasi-Lagrangian current following floats and drifters, as well as remote sensing data, show numerous localized, coherent motions ranging from major currents like the Gulf Stream to mesoscale phenomena such as rings, and associated vortex structures, down to a variety of submesoscale vortical motions. On the other hand, the theoretical tools of dynamical systems address the role that localized structures play in governing the motion over extended regions of space.

In the past five years there have been significant advances in dynamical systems theory to the point where the framework can now be utilized in the context of "real" problems. However, this approach leads to a new idea of a ``dynamical systems'' in this context. Rather than being defined by a set of equations, our dynamical systems are defined by ``data sets'', which can only be known for a finite amount of time. This brings up some fundamentally new mathematical problems that must be addressed in order to apply notions such as hyperbolic trajectories, stable and unstable manifolds, and lobe dynamics.

In this talk we will briefly describe the dynamical systems framework for Lagrangian transport, but the focus will be on transport in a coastal system (i.e., Monterey Bay) using a velocity field obtained experimentally from high frequency radar measurements. We will show how dynamical systems theory applies, and the new mathematical issues that must be addressed, as well as the new insight and results on transport that are subsequently attained.

Date: Tuesday, May 16, 2000
Time: 2:00pm
Where: Tech M416
Contact Person: Prof. Riecke
Contact email: h-riecke@nwu.edu
Contact Phone: 847-491-8316
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