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On the Limiting Behavior of Regularizations of the Euler Equations with Vortex Sheet Initial Data

Monika Nitsche Associate Professor Department of Mathematics University of New Mexico, Albuquerque ABSTRACT:
The vortex sheet is a mathematical model for a shear layer in which the layer is approximated by a surface. Vortex sheet evolution has been shown to approximate the motion of shear layers well, both in the case of free layers and of separated flows at sharp edges. Generally, the evolving sheets develop singularities in finite time. To approximate the fluid past this time, the motion is regularized and the sheet defined as the limit of zero regularization. However, besides weak existence results in special cases, very little is known about this limit. In particular, it is not known whether the limit is unique or whether it depends on the regularization. I will discuss several regularizing mechanisms, including physical ones such as fluid viscosity, and purely numerical ones such as the vortex blob and the Euler-alpha methods. I will show results for a model problem and discuss some of the unanswered questions of interest. --------------------------------------------------------------------------------Professor Nitsche received her PhD degree in 1992 from University of Michigan Ann Arbor under the guidance of Prof. Robert Krasny. She held various postdoctoral position (UC Boulder, IMA, OSU, Tufts) until she joined the faculty of the department of Mathematics at the University of New Mexico, Albuquerque in 1999. Her research interests lie in the numerical study of vortex flows and the development of numerical methods for such flows. She has also done some work on internal waves in density stratified flows.

Location: Seaver Science Library, Rm 150

Audiences: Everyone Is Invited

Contact: April Mundy