Resolution of d'Alembert's Paradox
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
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.
D'Alembert's Paradox, Euler equations, inviscid flow, General Galerkin method, illposed, wellposed, separation, blowup
Mathematics Condensed Matter Physics
IdentifiersURN: urn:nbn:se:kth:diva-26853DOI: 10.1007/s00021-008-0290-1ISI: 000281041600001ScopusID: 2-s2.0-77955921402OAI: oai:DiVA.org:kth-26853DiVA: diva2:373761
QC 201012012010-12-012010-11-292012-01-07Bibliographically approved