Hassan Aref

Several problems related to the dynamics of vortex patterns as observed in wake flows are addressed. These include: The universal Strouhal-Reynolds number relation. The Hamiltonian dynamics of point vortices in a periodic strip, both the classical two-vortices-in-a-strip problem, which gives the structure and self-induced velocity of the traditional vortex street, and the three-vortices- in-a-strip problem, which is argued to be relevant to the wake behind an oscillating body. The bifurcation diagram for wake structure found experimentally by Williamson and Roshko is addressed theoretically.

The concept was developed some twenty years ago as an outgrowth of work on advection by interacting point vortices. The term ’chaotic advection’ was first introduced in the title of an abstract for the 35th annual meeting of the APS Division of Fluid Dynamics (DFD) in 1982. The main reference, a Journal of Fluid Mechanics paper published in 1984, may be the true ’birthdate’ of the term. Earlier work from the 1960s by Arnol’d and Henon on advection by steady 3D flows already contained closely related ideas and results but was not widely appreciated. The present paper, based on the 2000 Otto Laporte Memorial Lecture delivered at the 53rd APS/DFD annual meeting, traces these and other precursors and the development of chaotic advection over the past two decades. Some exciting recent developments, such as application to fluid mixing in MEMS, and to materials processing, and the introduction of topological methods of analysis, are highlighted. On balance, chaotic advection is now established as a subtopic of fluid mechanics with wide ramifications and continued promise for theory, experiment and applications.