Dond’escono quei vortici?

Just time for a quickie today. I seem to be writing that virtualy every day at this time, in fact. Anyway, yesterday I gave the last of a series of lectures on Fluid Dynamics during which I talked a little bit about the Navier-Stokes equation, and introduced the concept of turbulence, topic that Richard Feynman described as “the most important unsolved problem in classical physics”. Given that the origin of turbulence is so poorly understood, I had to cover it all fairly qualitatively but did at least explain that its onset is associated with high values of the Reynold’s Number, an interesting dimensionless number that characterizes the properties of viscous fluid flow in such a way as to bring out the dynamical similarity inherent in the equations. The difficulty is that there is no exact theory that allows one to calculate the critical value of the Reynold’s number and in any particular situation; that has to be determined by experiments, such as this one which shows turbulent vortices (or “eddies”) forming downstream of a cylindrical obstacle placed in flowing fluid. The (laminar) flow upstream, and in regions far from the cylinder, has no vorticity.

What happens is obviously extremely complicated because it involves a huge range of physical scales – the vorticity is generated by very small-scale interactions between the fluid elements and the boundary of the object past which they flow. It’s a very frustrating thing for a physicist, actually, because one’s gut feeling is that it should be possible to figure it out. After all, it’s “just” classical physics. It’s also of great practical importance in a huge range of fields. Nevertheless, despite all the progress in “exotic” field such as particle physics and cosmology, it remains an open question in many respects.

That’s why it’s important to teach undergraduates about it. Physics isn’t just about solved problems. It’s a living subject, and it’s important for students to know those fields where we don’t really know that much about what is going on…

PS. The title is a quotation from the libretto of Mozart’s opera, Don Giovanni, uttered by the eponymous Count as he is dragged down to hell. It translates as “Whence come these vortices?” Pretentious, moi?

4 Responses to “Dond’escono quei vortici?”

  1. Anton Garrett Says:

    Here it is in context, from Joseph Losey’s visually magnificent film of the opera:

    • telescoper Says:

      I hasten to add that I did not intend to suggest that anyone deciding to work on turbulence would necessarily be damned to eternal torment, although that is clearly a possibility.

      • Anton Garrett Says:

        The Navier-Stokes equations are nonlinear and have chaotic solutions…

        The original subtitles shown in the cinema were a bit too literal, including Don Giovanni saying of the vortices or demons that “they agitate my viscera”.

      • telescoper Says:

        Sounds like the norovirus…

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