Exact self-similar solutions for axisymmetric wakes

Damien Biau

doi:10.1016/j.crme.2011.01.003

Exact self-similar solutions for axisymmetric wakes

Damien Biau ¹

¹ Institut Pprime, CNRS–université de Poitiers–ENSMA, téléport 2, boulevard Marie-et-Pierre-Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France

Comptes Rendus. Mécanique, Volume 339 (2011) no. 4, pp. 245-249.

Résumé

This Note presents an analytical solution of two-dimensional axisymmetric wakes valid in the development region, before the ultimate equilibrium state. Based on the boundary layer equations in polar coordinates, assuming a small velocity defect, the problem reduces to a linear diffusive equation and can be expressed as an eigenvalue problem. Then a complete set of eigenfunctions is analytically obtained, which are damped and evolve self-similarly in space. The first mode corresponds to the Schlichtingʼs solution, in agreement with the downstream asymptotic behavior.

Reçu le : 2010-06-02
Accepté le : 2011-01-20
Publié le : 2011-03-05

DOI : 10.1016/j.crme.2011.01.003

Mots clés : Fluid mechanics, Wake flow, Self-similar solutions

Affiliations des auteurs :

Damien Biau ¹

¹ Institut Pprime, CNRS–université de Poitiers–ENSMA, téléport 2, boulevard Marie-et-Pierre-Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France

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     title = {Exact self-similar solutions for axisymmetric wakes},
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     pages = {245--249},
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     year = {2011},
     doi = {10.1016/j.crme.2011.01.003},
     language = {en},
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Damien Biau. Exact self-similar solutions for axisymmetric wakes. Comptes Rendus. Mécanique, Volume 339 (2011) no. 4, pp. 245-249. doi : 10.1016/j.crme.2011.01.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.01.003/

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