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Resolution of d'Alembert's Paradox
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.ORCID iD: 0000-0003-4256-0463
KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
2010 (English)In: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, E-ISSN 1422-6952, Vol. 12, no 3, 321-334 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2010. Vol. 12, no 3, 321-334 p.
Keyword [en]
D'Alembert's Paradox, Euler equations, inviscid flow, General Galerkin method, illposed, wellposed, separation, blowup
National Category
Mathematics Condensed Matter Physics
URN: urn:nbn:se:kth:diva-26853DOI: 10.1007/s00021-008-0290-1ISI: 000281041600001ScopusID: 2-s2.0-77955921402OAI: diva2:373761
QC 20101201Available from: 2010-12-01 Created: 2010-11-29 Last updated: 2012-01-07Bibliographically approved

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