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Applied Math Colloquium

Friday, April 19, 2013, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Hollow Vortices

Stefan Llewellyn Smith

Department of Mechanical and Aerospace Engineering, UCSD

Abstract

Hollow vortices are vortices whose interior is at rest. They possess vortex sheets on their boundaries and can be viewed as a desingularization of point vortices. After giving a brief history of point vortices, we obtain exact solutions for hollow vortices in linear and nonlinear strain and examine the properties of streets of hollow vortices. The former can be viewed as a canonical example of a hollow vortex in an arbitrary flow, and its stability properties depend. In the latter case, we reexamine the hollow vortex street of Baker, Saffman and Sheffield and examine its stability to arbitrary disturbances, and then investigate the double hollow vortex street. Implications and extensions of this work are discussed.