Dynamos in Physics Today

One of the standard jokes in astrophysical modeling is that if there is ever a discrepancy between your model and observations you simply attribute it to some combination magnetic fields and turbulence.  Let's say your model of star formation fails miserably to reproduce the observed initial mass function in our galaxy.  What do you do?  Blame turbulence and magnetic fields, present some overly simplistic explanation of why turbulence and magnetic fields would give you the right answer if you could just capture them properly, and then promise to include them in some ill-defined future simulation.

These two phenomena have a fundamental link  - dynamo action.  In the words of a very well-written article by two of the top researchers in the field of laboratory dynamos, Cary Forest and Daniel Lathrop, "[a]ll astrophysical plasmas are, as far as we know, magnetized and turbulent" and thus ripe for dynamo action.  The problem is that we are orders of magnitude removed in both simulations and experiments from some of the physical regimes where dynamo action takes place, even within our own solar system (see the graph on the right).

Check out the article over at Physics Today for a great explanation of why dynamos are so ubiquitous, why they are so hard to predict, and what is being done with theory, modeling, and laboratory experiments to unravel the mystery.

Physics Spotlights Turbulent Convection

If you're not familiar with the American Physical Society's online review Physics, you should take a look right now. What is Physics? From the APS:

"Physicists are drowning in a flood of research papers in their own fields and coping with an even larger deluge in other areas of physics. The Physical Review journals alone published over 18,000 papers last year. How can an active researcher stay informed about the most important developments in physics?

Physics highlights exceptional papers from the Physical Review journals. To accomplish this, Physics features expert commentaries written by active researchers who are asked to explain the results to physicists in other subfields. These commissioned articles are edited for clarity and readability across fields and are accompanied by explanatory illustrations."

In other words, Physics is the cliff notes version of the best new research being done across all of physics. It's like a 5 minute version of a colloquium, without the speaker playing with his or her microphone.

And why do I bring this up now? Because the latest issue features a review of current issues in turbulent convection, a topic near and dear to my heart. And they used a great picture of convective cells on the solar surface (at right). Hooray for Physics!

Transitory Turbulence

Turbulence is often called the last unsolved problem of classical mechanics. It is a ubiquitous phenomenon that anyone who has ever flown on a airplane knows about, but there have been exactly two major breakthroughs in turbulence theory in the past 70 years. Both of these breakthroughs came in the early 1940's and both were made by a Russian mathematician and physicist named Andrey Kolmogorov. However, there has been a lot of work on the problem, especially since the development of the theory of dynamical chaos in the 1990's. One of the big questions, in the language of dynamical chaos, is whether turbulent states are attractors or repellers. Put another way, if you get a system into a turbulent state, will it remain turbulent indefinitely or will it eventually decay into a laminar state? There are, of course, three possible answers to this question: yes, no, or maybe.

We can throw out the yes answer by common counter examples. If you pour water into a glass the flow is normally turbulent, however it quickly becomes laminar if you stop pouring. The real debate then, is whether turbulent systems always decay into laminar systems or if there are some special cases where turbulence is a chaotic attractor.

Before we go further, I need to introduce you to a parameter known as the Reynolds number. Fluid dynamics is full of dimensionless parameters and in turbulence the Reynolds number (abbreviated Re) is the most important one. Essentially, the bigger the Reynolds number the more turbulent the system is. More specifically, the Reynolds number is the ratio of inertial forces to viscous forces. In laminar flows, small chaotic motions are damped by viscous forces (low Re), while in turbulent flows viscosity is insufficient to damp out the small chaotic motions (high Re).

The maybe answer comes from the argument that above some Reynolds number, turbulence is self-sustaining. However, a new paper in Physical Review Letters by Bjorn Hof, Alberto de Lozar, Dirk Jan Kuik, and Jerry Westerweel (and nicely summarized by the APS at http://physics.aps.org/) claims that the correct answer is that there is no such thing as a turbulent attractor. They conduct a number of experiments that show that the decay time from turbulence to laminar flow goes as a super-exponential function of the Reynolds number ( tau = k*exp[exp[Re]] ). This trend fits very nicely over 6 orders of magnitude in decay times from ~5 seconds to ~150 days as seen in the figure to the right. This gives strong evidence that turbulence always decays into laminar flow, it just takes a while in some cases. In fact, for a system with a Reynolds number of 2200, the decay time is longer than the age of the universe.

By comparison, in the solar convection zone the Reynolds number is something like 10^10. That's a decay time of 10^[10^(10^9)] seconds. As they say in Brazil, don't wait standing.

While the debate may not be concluded quite yet, it appears that turbulence is really a temporary phenomena - if by temporary one means it commonly lasts orders of magnitude longer than the age of the universe. More meaningfully, it means that from a theoretical standpoint, turbulence is a chaotic repeller rather than a chaotic attractor. Perhaps most importantly, this means that we are still making progress on the last major puzzle of classical mechanics.