On the Equation Satisfied by a Steady Prandtl-Munk Vortex Sheet
Lopes Filho, Milton C. ; Nussenzeig Lopes, Helena J. ; Souza, Max O.
Commun. Math. Sci., Tome 1 (2003) no. 1, p. 68-73 / Harvested from Project Euclid
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We show the the voricity distribution obtained by minimizing the induced drag on a wing, the so called Prandtl-Munk vortex sheet, is not a travelling-wave weak solution of the Euler equations, contrary to what has been claimed by a number of authors. Instead, it is a weak solution of a non-homogeneous Euler equation, where the forcing term represents a "tension" force applied to the tips. This is consistent with a heuristic arguement due to Saffman. Thus, the notion of weak solution captures the correct physical behavior in this case.
Publié le : 2003-03-14
Classification:  
@article{1118150400,
     author = {Lopes Filho, Milton C. and Nussenzeig Lopes, Helena J. and Souza, Max O.},
     title = {On the Equation Satisfied by a Steady Prandtl-Munk Vortex Sheet},
     journal = {Commun. Math. Sci.},
     volume = {1},
     number = {1},
     year = {2003},
     pages = { 68-73},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1118150400}
}

Lopes Filho, Milton C.; Nussenzeig Lopes, Helena J.; Souza, Max O. On the Equation Satisfied by a Steady Prandtl-Munk Vortex Sheet. Commun. Math. Sci., Tome 1 (2003) no. 1, pp.  68-73. http://gdmltest.u-ga.fr/item/1118150400/