Hollow vortices are vortices whose interior is at rest. They posses vortex sheets on their boundaries and can be viewed as a desingularization of point vortices. After giving a 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.
Stefan G. Llewellyn Smith received his Ph.D. in applied mathematics from the University of Cambridge in 1996. He was a research fellow of Queens' College, Cambridge, from 1996 to 1999, working in the Department of Applied Mathematics and Theoretical Physics. He spent a year from 1996 to 1997 on a Lindemann Trust Fellowship at the Scripps Institution of Oceanography in La Jolla. He joined the Department of Mechanical and Aerospace Engineering at UCSD in 1999 as Assistant Professor of Environmental Engineering. His research interests include fluid dynamics, especially its application to environmental and engineering problem, acoustics and asymptotic methods.