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November 25, 2010

Speaker: Dr. Francis Poulin, Department of Applied Mathematics, University of Waterloo

Title: The Instability of Time Dependent Shear Flows

Abstract: In the atmosphere and oceans there are a variety of jets that, due to their strong shear, become unstable to produce vortices. These rotating features can live very long, several months, and therefore contribute significantly to the transport of chemistry, biology or physical properties (such as heat and momentum) over vast distances.  

There are many classical theories that analyze the stability of these systems with some success. However, almost all of these theories are limited in that they assume that the jet is steady. The steady assumption greatly simplifies the analysis at the cost of ignoring the time-dependency that is always present in atmospheric and oceanic flows. At present, with the powerful computers we have at our disposal, it is possible to compute the stability of time-dependent systems and compare the results with the classical predictions. There are some very interesting cases when the time dependency yields an inherently more unstable state since the perturbations continually extract energy from the mean flow even after nonlinear saturation has set in.

This talk is directed to a general audience and will begin by reviewing stability theory in the simple context of a pendulum. Then, we will extend the analysis to a two-layer vertical shear flow to determine the importance of time variations in producing spatial and temporal variability in the system.