Comptes Rendus
Exact self-similar solutions for axisymmetric wakes
Comptes Rendus. Mécanique, Volume 339 (2011) no. 4, pp. 245-249.

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.

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DOI: 10.1016/j.crme.2011.01.003
Keywords: Fluid mechanics, Wake flow, Self-similar solutions

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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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/

[1] G.G. Stokes On the effect of the internal friction of fluids on the motion of pendulums, Trans. Cambridge Philos. Trans., Volume 9 (1851), pp. 8-106

[2] A.N. Whitehead Second approximations to viscous fluid motion, Q. J. Math., Volume 23 (1889), pp. 143-152

[3] C.W. Oseen Über die Stokesʼsche Formel, und über eine verwandte Aufgabe in der Hydrodynamik, Ark. Math. Astron. Fys., Volume 6 (1910), p. 29

[4] I. Proudman; J.R.A. Pearson Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder, J. Fluid Mech., Volume 2 (1957), pp. 237-262

[5] A.A. Townsend The Structure of Turbulent Shear Flows, Cambridge University Press, 1956

[6] M.P. Satijn; M.G. van Buren; H.J.H. Clercx; G.J.F. van Heijst Vortex models based on similarity solutions of the two-dimensional diffusion equation, Phys. Fluids, Volume 16 (2004), pp. 3997-4011

[7] R.C. Kloosterziel On the large-time asymptotics of the diffusion equation on infinite domains, J. Engrg. Math., Volume 24 (1990), pp. 213-236

[8] J. Barker; G. Wilks Axisymmetric wake and jet in decelerating streams, Z. Angew. Math. Phys., Volume 53 (2002), pp. 35-47

[9] H. Schlichting Boundary Layer Theory, McGraw–Hill, 1955

[10] W.K. George, The self-preservation of turbulent flows and its relation to initial conditions and coherent structures, in: Advances in Turbulence, 1989, pp. 39–73.

[11] P.M. Bevilaqua; P.S. Lykoudis Turbulence memory in self-preserving wakes, J. Fluid Mech., Volume 89 (1978), pp. 589-606

[12] P. Luchini Reynolds-number-independent instability of the boundary layer over a flat surface, J. Fluid Mech., Volume 327 (1996), pp. 101-115

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