tisdag 14 juli 2009

A Paradoxical Paradox Resolution

On Dec 10 2008 my article coauthored with Johan Hoffman Resolution of d'Alembert's Paradox was published in JMFM Journal of Mathematical Fluid Mechanics. In the article we resolve a fundamental paradox of mathematical fluid mechanics unresolved for 256 years, acknowledged by the leading journal of mathematical fluid mechanics to be correct. 

Mathematics predicts zero drag of a body moving through a fluid with vanishing/small viscosity like air or water with a symmetric flow pattern as indicated in the above figure, while observation shows most substantial drag from an unsymmetric flow pattern with a turbulent wake. Something is wrong with the mathematics and the enigma for 256 years has been, what is wrong?

You probably say, great! This must be of interest to the community of fluid mechanics! A community, which in the words of the Chemistry Nobel Laureate Sir Cyril Hinshelwood, has been troubled for 256 years by an unfortunate split into a field of hydraulics, observing phenomena which cannot be explained, like substantial drag, and mathematical fluid mechanics, explaining phenomena which cannot be observed, like zero drag. In other words, a complete collapse of fluid mechanics as rational science.

The number of readers of the journal article is unknown, but the knol-version of the article has 4000 pageviews and thus the resolution of d'Alembert's paradox must now be known to many.

But the reaction from the fluid dynamics community, except the couple of referees of the article in JMFM,  is zero. No response whatsoever! As if the article had neither been written nor been published. In particular, there is no fluid dynamicist who claims that the resolution is not correct.

But what is paradoxical is that there is no fluid dynamicist who acknowledges the existence of the article. As if the article had neither been written nor been published. 
Is this the way science is supposed to function? If a community of scientists collectively denies the existence of a certain fact, does it mean that the fact does not exist? What do you think? 

Is it reasonable to ask leading fluid dynamicists about their views on d'Alembert's paradox and expect to get an answer? Do you want to try? To help advance science? You could start with the Editors of Journal of Fluid Mechanics competitor to JMFM:
To get some perspective, read the Wikipedia article on d'Alembert's Paradox illustrating the confusion of the fluid mechanics community identified by Hinshelwood and the complete denial of the existence of the resolution published in JMFM. After going through the evidence, maybe you will feel an urge to correct the Wikipedia article, to help advance science?

Note that the resolution of d'Alembert's paradox opens to uncovering the secrets of Why it is Possible to Fly and Why it is Possible to Sail to which I will return in a later blog. Until then, you may if you like, ask yourself and your favorite pilot or flight company what keeps an airplane in the air? Do we know more than the birds, which apparently can fly without mathematics?

Note that the authority NASA presents three incorrect theories for flight:
  • no theory claimed to be correct!
Is NASA's logic that three incorrect theories sum up to one correct? Is this something to have in mind next time you lean back for take-off?

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