Comptes Rendus
no. 3
The transition to turbulence in parallel flows: A personal view
Yves Pomeau1
1 University of Arizona, Tucson, USA
Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 210-218.

This is a discussion of the present understanding of transition to turbulence in parallel flows, based upon the idea that it arises from a subcritical instability. The result is a coupled set of equations, one amplitude equation in the direction of translational invariance of the geometry coupled with the standard Reynolds equation for the average transfer of momentum. It helps to understand a basic feature of the transition in parallel flows, namely that turbulence manifests itself in localised domains growing at a constant speed depending on the Reynolds number.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2014.10.002
Mots clés : Fluid dynamics, Turbulence, Bifurcations
Yves Pomeau 1

1 University of Arizona, Tucson, USA 
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Yves Pomeau. The transition to turbulence in parallel flows: A personal view. Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 210-218. doi : 10.1016/j.crme.2014.10.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.10.002/

[1] O. Reynolds An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels, Philos. Trans. R. Soc. Lond., Volume 174 (1883), p. 935

[2] D. Coles Prospects for useful research on coherent structure in turbulent shear flow, Proc. Indian Acad. Sci., Eng. Sci., Volume 4 (1981), p. 111

[3] P. Coullet Bifurcation at the dawn of modern science, C. R. Mecanique, Volume 340 (2012), p. 777 (We can only urge interested readers to read this beautiful piece on Science of classical times)

[4] Y. Pomeau; M. Le Berre, Nonlinearity and nonequilibrium together in nature: wind waves in the open Ocean, Eur. Phys. J. D, Volume 62 (2011), p. 73

[5] W. Heisenberg Über Stabilität und Turbulenz von Flüssigkeitsströmen, Ann. Phys., Volume 74 (1924), p. 577

[6] S.V. Iordanskii; A.G. Kulikovskii The absolute stability of some parallel flows at high Reynolds number, Sov. Phys. JETP, Volume 22 (1966), p. 915

[7] H.W. Emmons The laminar-turbulent transition in a boundary layer. Part I, J. Aeronaut. Sci., Volume 18 (1951), p. 490

[8] Y. Pomeau Front motion, metastability and subcritical bifurcations in hydrodynamics, Physica D, Volume 23 (1986), p. 3

[9] L.D. Landau On the problem of turbulence, Dokl. Akad. Nauk SSSR, Volume 44 (1944), p. 339

[10] P. Manneville; P. Manneville On the transition to turbulence of wall bounded flows in general and plane Couette flow in particular, Fluid Dyn. Res., Volume 43 (2014), p. 065501 | DOI

[11] P. Bergé; Y. Pomeau; C. Vidal Transition vers la turbulence dans les écoulements paralléles, L'Espace chaotique, Hermann, Paris, 1998, pp. 61-96 Chapter 4 (in French)

[12] T. Leweke; M. Provansal The flow behind rings: bluff body wakes without end effects, J. Fluid Mech., Volume 288 (1995), p. 265

[13] Y. Kuramoto Chemical Oscillations, Waves, and Turbulence, Springer-Verlag, New York, 1984

[14] H. Poincaré Sur les courbes définies par une équation différentielle, J. Math. Pures Appl., Ser. 2, Volume 7 (1881), p. 375 (Those four papers, based on Poincaré PhD thesis are a monument of the history of Mathematics)

[15] D. Ruelle; F. Takens On the nature of turbulence, Commun. Math. Phys., Volume 20 (1971), p. 167

[16] B.A. Malomed; V. Hakim; P. Jakobsen; Y. Pomeau; T. Price; M.E. Brachet; Y. Pomeau Numerical characterization of localized solutions in plane Poiseuille flow, Phys. Fluids A, Volume 29 (1987), p. 155 (See also Fronts vs solitary waves in nonequilibrium systems Europhys. Lett., 11, 1990, pp. 19)

[17] J.C. Maxwell; J.D. van der Waals Verhandel. Konink. Akad. Weten. Amsterdam (Sect. 1), vol. 2 (1952), p. 541 (in Dutch). A commented English translation is J.S. Rowlinson J. Stat. Phys., 20, 1979, pp. 197

[18] L.D. Landau; E.M. Lifshitz Fluid Mechanics, Pergamon Press, Oxford, 1987

[19] L.A. Segel; A.C. Newell; J.A. Whitehead J. Fluid Mech., 38 (1969), p. 203

[20] I.J. Wygnanski; F.H. Champagne; I.J. Wygnanski; M. Sokolov; D. Friedman On transition in a pipe. Part 2. The equilibrium puff, J. Fluid Mech., Volume 59 (1973), p. 281

[21] H. Chaté; P. Manneville Transition to turbulence via spatiotemporal intermittency, Phys. Rev. Lett., Volume 58 (1987), p. 112

[22] S.P. Obukhov The problem of directed percolation, Physica A, Volume 101 (1980), p. 145

[23] D. Barkley Simplifying the complexity of pipe flow, Phys. Rev. E, Volume 84 (2011), p. 016309 (and references therein)

[24] Y. Pomeau Time reversal symmetry of fluctuations, J. Phys., Volume 43 (1982), p. 859

[25] J.J. Hegseth; C.D. Andereck; F. Hayot; Y. Pomeau; F. Hayot; Y. Pomeau Turbulent domain stabilisation in annular flows, Phys. Rev. E, Volume 62 (1989), p. 257 (2019)

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