Curious Notions

Procrastination has led me to various topics on Wikipedia, many of which have something to do with turbulence, which will, arguably, be the driving factor for the next five years of my life as I do my PhD research in that field. All panicky and stressful thoughts on such things aside, here are a few of my discoveries:

• Included in Science Magazine’s description of the Clay Mathematics Institute’s Millennium Problems (which, for you CS-types, includes P vs. NP) is the following:
  

  Will mathematicians unleash the power of the Navier-Stokes equations? First written down in the 1840s, the equations hold the keys to understanding both smooth and turbulent flow. To harness them, though, theorists must find out exactly when they work and under what conditions they break down.

  Sadly, no one told the reporter who wrote this (or the mathematicians that he/she may have spoken to) that scientists and engineers know exactly when the Navier-Stokes equations work–it’s something that every student learns as he/she learns to derive them. The more serious issue, which CMI picked up on, is that there is no general solution to the equations. Basically, the few flows that have been solved are possible only through approximation or gross oversimplification of the issue. Yes, I too ask why I set myself up for these things.

• A couple of famous scientists have had very similar turbulence-related stories attributed to them. I’m rather amused by this one:
  

  A similar witticism has been attributed to Horace Lamb (who had published a noted text book on Hydrodynamics)—his choice being quantum mechanics (instead of relativity) and turbulence. Lamb was quoted as saying in a speech to the British Association for the Advancement of Science, “I am an old man now, and when I die and go to heaven there are two matters on which I hope for enlightenment. One is quantum electrodynamics, and the other is the turbulent motion of fluids. And about the former I am rather optimistic.” #

• Earlier this semester one of my professors spent nearly an entire lecture discussing the brilliance of Lewis F. Richardson in terms of applying a finite differences approach to the solution of partial differential equations–thereby making numerical computation of solutions possible. Oddly enough, his famous first paper in that area is not at all mentioned on Wikipedia, though a later paper (from 1922) on numerical processing of differential equations in the field of meteorology is featured. #
• Being a pacifist, Richardson also, interestingly, applied his mathematical knowledge to international conflicts, creating mathematical models to describe armament of two nations and their likelihood to go to war based on the length of their mutual border. #
• He also wrote a great little rhyme about turbulence that I had to write up on my whiteboard:
  

  Big whorls have little whorls that feed on their velocity,
  and little whorls have smaller whorls and so on to viscosity. #

  Priceless!

• In the I-need-to-remember-that-one-later category, the German word for fluid mechanics is Strömungsmechanik, and I was right about the German term for a Von Karman vortex street being Wirbelstraße. I win.

We now return you to your regularly scheduled lives.