Interview with Editors of Journal of Fluid Mechanics

Interview with S. H. Davis and M. G. Worster Editors of Journal of Fluid Mechanics including also Associate Editors.

CJ: d'Alembert's paradox represents a basic problem of fluid mechanics: Zero drag of theoretical potential flow but substantial drag in real slightly viscous flow. As Editors of the most influential journal of fluid mechanics, I ask you about the current status of the paradox. Is it resolved and if so how and by whom?

SHD: This has not been a "paradox" for perhaps 100 years. See for example the fluid mechanics book by George Batchelor.

CJ: Thanks for response. The discussion is most essential and important for the science of fluid mechanics. As Editor of the main fluid dynamics journal you have an important position in the discussion. However, I don't see that Batchelor, founder of Journal of Fluid Mechanics, in his book An Introduction fo Fluid Mechanics presents a resolution of the paradox, nor claims that there is no paradox: On pages 332, 338 and 342 in his book he states:

• The result that an inviscid fluid offers no resistance to steady translational motion of a rigid body when the flow is irrotational is sometimes referred to as d'Alembert's paradox, since rigid bodies do experience a resistance to motion through a real fluid. The result is in serious disagreement with observation in the case of bluff bodies, which is hardly surprising, since the flow at the rear of a bluff body is far from having the assumed irrotational form...
• Analysis of the flow due to a bluff body moving steadily through fluid is effectively prohibited by the large scale unsteadiness of the flow behind the body...Knowledge of this type of flow is mostly empirical...the part of the boundary of this irrotational region formed by the separating streamlines is of complex, fluctuating and unknown shape and as a consequence the irrotational flow cannot be determined...
• Prandtl suggested in 1914 that the explanation lies in the behaviour of the boundary layer...

Is this your evidence that d'Alembert's paradox "has not been a "paradox" for 100 years"? If not, what is it? It is not even clear that Batchelor was a great admirer of Prandtl and believed in his boundary layer resolution. Right? Too bad that Batchelor is not among us so that he can tell us. 

SHD: d'Alembert's paradox was resolved by the inclusion of viscosity in the fluid.

CJ: Oh, really? How? Please be explicit: d'Alembert's paradox is a central problem in fluid mechanics! It is interesting that Batchelor on page 338 states as his opinion that

• Although the flow behind a bluff body is unsteady in practice, there is no reason to doubt that a steady (unstable) solution of the equations of motion does exist.

Unstable! This is precisely what is shown in the knol D'Alembert's Paradox based on the article Resolution of d'Alembert's Paradox in Journal of Mathematical Fluid Mechanics JMFM. Batchelor was on the right track = instability of potential flow, which is completely different from Prandtl's suggestion indicating mysterious effects from vanishing skin friction in a very thin boundary layer! What do you say as a successor of Batchelor? Prandtl or Batchelor??

SHD: ???

CJ: Summing up the interviews so far we have: The entire editorial board of the leading journal of fluid mechanics combined with the fluid mechanics expertize at KTH, altogether 22 experts of fluid mechanics, has produced two statements concerning the present status of d'Alembert's paradox, one of the most basic problems of fluid mechanics: 

• There is no paradox.
• If there is a paradox, it can somehow be resolved by viscosity.  

Conclusion? Is fluid mechanics not a science?  Is fluid mechanics still split into hydraulics observing phenomena which cannot be explained, and theoretical fluid mechanics explaining phenomena which cannot be observed? What will be the effect on future funding, when the truth gets revealed?  When readers of Journal of Fluid Mechanics read also Journal of Mathematical Fluid Mechanics? How is it possible that so many experts have so little to say? What prevents them?

Note that the official JFM standpoint presented in the Wikipedia article about d'Alembert's paradox, which ranks 1st on Google, does not mention my knol D'Alembert's Paradox, which ranks 2nd on Google. Anyone who finds this incorrect can correct the Wiki article.