The “Bathtub Vortex” has been much studied, by good hydrodynamicists and others, like me. It is a fine example of the Navier-Stokes Equations in their full glory, and can be solved (more or less) by techniques of Computational Fluid Dymanics (CFD). Turbulence, that often occurs, is dealt with, approximately, by Reynolds Averaging (RA) or Large Eddy Simulation (LES). Occasionally the theoretical solutions are supported by test. I have had humbling experiences trying to predict this flow for real aircraft vortex wakes and “validating” my results with flight tests on a B-707. Truth can be brutal! I would not venture into hand waving or word waffling on this topic. Friam folks may be entertained by Todor von Karman’s take. He relates that, in the waning days of the Austro-Hungarian Empire, the Viennese trolley cars had a passive ventilator on their roofs – a kind of funky S shaped impeller on a vertical axis that spun around in the breeze, and putatively sucked out the smoke from the professor’s cigars. The aero students asked their prof. to explain how it worked. He went into patient, painstaking detail with figures, equations and other Eulerian stratagems, finally deriving the sense in which it would rotate (but not the speed). The students then triumphantly noted, “But, Herr Professor, it goes the other way!” “Ah”, said the learned prof, “Zen I can explain zat, too!” I assume that aerodynamics is the same in Vienna as everywhere else, although we know, happily, the air itself isn’t. It is full of Arias, Bel Cante and Leit Motifs swirling, drifting in the breeze, that make Alt Wien truly the “City of any Dream”. If folks are interested in the “discovery” of the Karman Vortex Street , a classic phenomenon of unsymmetrical flow, I will be glad to post my article on this, as related by Todor himself, if someone can show me how to. On these subjects one resorts to a statement I’ve often made in expert witness work. “Theory crumbles before the Facts”. Peter Lissaman, Da Vinci Ventures Expertise is not knowing everything, but knowing what to look for. 1454 Miracerros Loop South, Santa Fe, New Mexico 87505,USA tel:(505)983-7728 ----- Original Message -----
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