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The name Fluid Dynamics Seminar derives from my days as a graduate student at UNC Chapel Hill (the Tar Heels). We had a weekly ritual of meeting at a local watering hole, He’s Not Here, to study the rapid consumption of incompressible fluids. During this informal gathering graduate students and faculty would discuss various topics in Mathematics. The math department had a very favorable ratio of graduate students to faculty, about 1:1, so the math faculty was very friendly and we got a lot of personal attention, unlike Ph.D. factories like the University of California at Berkeley.
Here is an interesting video of an experiment which I first saw in 1979 at a meeting in New York City of the New York Academy of Sciences. At the time I was a fledgling graduate student and my thesis adviser, Sheldon Newhouse, a Ph.D. student of Fields Medal winning Steve Smale of UC Berkeley, who created the modern theory of chaotic dynamical systems, was a speaker at the meeting. The buzz at the time was "strange attractors" and their importance in explaining the "transition to turbulence" in physical systems. All of this is related to “chaos” and "fractals" and thus began the journey to my doctoral dissertation. What became fascinating to me was how these experimental and theoretical physicists were using the mathematics which I was studying to explain interesting phenomena in the real world.
To simplify things, phenomena which occur in the real world are determined by multidimensional equations. In order for phenomena to be stable and thus observable and not transitory there must be an attracting region in the space of equations where the solutions to the equations determining the phenomenon occur. When this attracting region in the space of equations is a "fractal" one says that there is a "strange attractor" responsible for the phenomenon. This was predicted by Ruelle and Takens among others, and verified experimentally by Gollub and Swinney in the following experiment. Here a fluid is suspended between two rotating cylinders. The speed of the cylinders is gradually increased and the behavior of the fluid is observed. While the behavior is a little difficult to see in this video, what happens is that first stacks of rotating donuts are observed. As the speeds are increased, the stacks of donuts exhibit more and more oscillating behavior until they finally break up into pure chaos. It is the behavior between the stacks of donuts and the pure chaos which are most interesting and where the "strange attractors" come into play. Enjoy the 40 second video!
More Fluid Dynamics: Another Strange Attractor
Another famous example of a stable phenomenon which exhibits chaotic behavior is the "red spot" of Jupiter. Once again, mathematically we explain this by saying that in the space of equations governing the swirling fluid gases which Jupiter's red spot is made of, there is a "fractal" attracting region which makes it both a stable phenomenon and a chaotic phenomenon, that is there is a "strange attractor" responsible for this behavior. Enjoy the two and a half minute video!
For those interested in the “state of the art” of chaos theory in the min-1980’s when I got my Ph.D., let me offer my strong recommendation for the excellent book "Chaos" by James Gleick as an introduction to the field of chaotic dynamical systems. How about a stocking stuffer for yourself?
From Amazon.com
Few writers distinguish themselves by their ability to write about complicated, even obscure topics clearly and engagingly. James Gleick, a former science writer for the New York Times, resides in this exclusive category. In Chaos, he takes on the job of depicting the first years of the study of chaos--the seemingly random patterns that characterize many natural phenomena.
This is not a purely technical book. Instead, it focuses as much on the scientists studying chaos as on the chaos itself. In the pages of Gleick's book, the reader meets dozens of extraordinary and eccentric people. For instance, Mitchell Feigenbaum, who constructed and regulated his life by a 26-hour clock and watched his waking hours come in and out of phase with those of his coworkers at Los Alamos National Laboratory.
As for chaos itself, Gleick does an outstanding job of explaining the thought processes and investigative techniques that researchers bring to bear on chaos problems. Rather than attempt to explain Julia sets, Lorenz attractors, and the Mandelbrot Set with gigantically complicated equations, Chaos relies on sketches, photographs, and Gleick's wonderful descriptive prose.
