, Volume 12, Issue 3, pp 321-334
Date: 10 Dec 2008

Resolution of d’Alembert’s Paradox

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Abstract.

We propose a resolution of d’Alembert’s Paradox comparing observation of substantial drag/lift in fluids with very small viscosity such as air and water, with the mathematical prediction of zero drag/lift of stationary irrotational solutions of the incompressible inviscid Euler equations, referred to as potential flow. We present analytical and computational evidence that (i) potential flow cannot be observed because it is illposed or unstable to perturbations, (ii) computed viscosity solutions of the Euler equations with slip boundary conditions initiated as potential flow, develop into turbulent solutions which are wellposed with respect to drag/lift and which show substantial drag/lift, in accordance with observations.

Communicated by R. Rannacher
How wonderful that we have met with a paradox. Now we have some hope of making progress. (Nils Bohr)