Comptes Rendus
no. 7
D'Alembert's paradox, 1900–1914: Levi-Civita and his Italian and French followers
Rossana Tazzioli1
1 Université de Lille-1, Sciences et technologies, UFR de mathématiques, Laboratoire Paul-Painlevé, Cité scientifique, 59655 Villeneuve d'Ascq cedex, France
Comptes Rendus. Mécanique, Volume 345 (2017) no. 7, pp. 488-497.

Before the First World War, Tullio Levi-Civita (1873–1941) was already a well-known mathematician in Italy and abroad, in particular in France. Professor at the University of Padua since 1898, he had published important contributions to tensor calculus, theory of relativity, differential geometry, hydrodynamics, and the three-body problem. In 1918, when he moved to the University of Rome, he created an international school of mathematics. In this paper, we focus on d'Alembert's paradox to which Levi-Civita and some of his Italian and French followers contributed remarkable solutions. This case-study is used to illustrate Levi-Civita's approach to hydrodynamics and its influence in Italy and France, especially in the period 1910–1914.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2017.05.006
Mots clés : Tullio Levi-Civita, Henri Villat, d'Alembert's paradox, Hydrodynamics
Rossana Tazzioli 1

1 Université de Lille-1, Sciences et technologies, UFR de mathématiques, Laboratoire Paul-Painlevé, Cité scientifique, 59655 Villeneuve d'Ascq cedex, France 
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Rossana Tazzioli. D'Alembert's paradox, 1900–1914: Levi-Civita and his Italian and French followers. Comptes Rendus. Mécanique, Volume 345 (2017) no. 7, pp. 488-497. doi : 10.1016/j.crme.2017.05.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.05.006/

[1] O. Darrigol Worlds of Flow. A History of Hydrodynamics from the Bernoullis to Prandtl, Oxford University Press, Oxford, UK, 2005

[2] G. Grimberg; W. Paulsc; U. Frisch Genesis of d'Alembert's paradox and analytical elaboration of the drag problem, Physica D, Volume 237 (2008), pp. 1878-1886

[3] H. Villat Quelques récents progrès des théories hydrodynamiques, Bull. Sci. Math. (2), Volume 42 (1918), pp. 43-92

[4] O. Darrigol Empirical challenges and concept formation in the history of hydrodynamics, Centaurus, Volume 50 (2008), pp. 214-232

[5] J.D. Anderson A History of Aerodynamics, Cambridge University Press, Cambridge, UK, 1997

[6] T. Levi-Civita, Rend. R. Accad. Naz. Lincei (5) (Opere Matematiche, Accademia Nazionale dei Lincei, 6 vols), Volume 10, Zanichelli, Bologna, Italy, 1901, pp. 3-9

[7] I. Nazzani Trattato di idraulica pratica, Hoepli, Milano, Italy, 1883

[8] U. Cisotti Sul paradosso di D'Alembert, Atti R. Ist. Veneto Sci. Lett. Arti, Volume 63 (1904), pp. 423-426

[9] U. Cisotti Sul paradosso di D'Alembert, Atti R. Ist. Veneto Sci. Lett. Arti, Volume 65 (1906), pp. 1291-1296

[10] U. Cisotti Sul moto di un solido in un canale, Rend. Circ. Mat. Palermo, Volume 28 (1909), pp. 307-351

[11] J. Hadamard Leçons sur la propagation des ondes et les équations de l'hydrodynamique, Librairie Scientifique A. Hermann, Paris, 1903

[12] P. Nastasi; R. Tazzioli Problem of method in Levi-Civita's contributions to hydrodynamics, Rev. Histoire Math., Volume 12 (2006), pp. 81-118

[13] in Opere matematiche, vol. 2, pp. 519–562.

[14] L. Prandtl Ueber Flüssigkeitsbexegung bei sehr kleiner Reibung, Heidelberg, Teubner, Leipzig (1904), pp. 484-491

[15] É. Marey Le mouvement des liquides, étudié dans la chronophotographie, C. R. hebd. séances Acad. Sci. Paris, Volume 117 (1893), pp. 913-924

[16] F. Ahlborn Über den Mechanismus des hydrodynamischen Widerstandes, Friedrichsen, Hamburg, 1902

[17] P. Nastasi, R. Tazzioli, Aspetti di meccanica e di meccanica applicata nella corrispondenza di Tullio Levi-Civita (1873–1941), Quaderni Pristem, No. 14, Palermo, Italy, 2003.

[18] A.E.H. Love; P. Appell; H. Beghin; H. Villat Développements concernant l'hydrodynamique (J. Molk; P. Appell, eds.), Encyclopédie des Sciences Mathématiques, vol. IV-5, Gauthier-Villars, Paris & Teubner, Leipzig, 1914, pp. 102-208

[19] N.L. Ghosh The theory of resistance in potential flows, Proc. Natl. Inst. Sci. India, Volume 20 (1953), pp. 74-103

[20] U. Cisotti Idromeccanica piana, 2 vols, Libreria Editrice Politecnica, Milano, Italy, 1921 (vol. I)

[21] H. Villat Sur la résistance des fluides, Ann. Sci. Éc. Norm. Supér. (3), Volume 28 (1911), pp. 203-311

[22] T. Boggio Sul moto stazionario di una sfera in un liquido viscoso, Rend. Circ. Mat. Palermo (2), Volume 50 (1910), pp. 65-81

[23] G. Picciati Integrazione dell'equazione funzionale che regge la caduta di una sfera in un liquido viscoso, Rend. R. Accad. Naz. Lincei (5), Volume 16 (1907), pp. 45-50

[24] R. Tazzioli The eyes of French mathematicians on Tullio Levi-Civita – the case of hydrodynamics (1900–1930) (F. Brechenmacher; G. Jouve; L. Mazliak; R. Tazzioli, eds.), Images of Italian Mathematics in France. The Latin Sisters, from Risorgimento to Fascism, Springer, 2016

[25] M. Brillouin Les surfaces de glissement d'Helmholtz et la résistance des fluides, Ann. Chim. Phys. (8), Volume 23 (1911), pp. 145-230

[26] P. Duhem Sur le paradoxe hydrodynamique de M. Brillouin, C. R. hebd. séances Acad. Sci. Paris, Volume 159 (1914), pp. 790-792

[27] D. Aubin “Audacity or Precision”: the paradoxes of Henri Villat's fluid mechanics in interwar France, Rauischholzhausen, Germany, 15–18 October (2006) ([preprint; on hal-upmc])

[28] R. Thiry Sur les solutions multiples des problèmes d'hydrodynamiques relatifs aux mouvements glissants, Gauthier-Villars, Paris, 1921 (Thèse)

[29] H. Villat Sur la détermination des problèmes d'hydrodynamique relatifs à la résistance des fluides, Ann. Sci. Éc. Norm. Supér. (3), Volume 31 (1914), pp. 455-493

[30] T. Archibald; R. Tazzioli Integral equations between theory and practice: the cases of Italy and France to 1920, Arch. Hist. Exact Sci., Volume 68 (2014), pp. 547-597

[31] H. Gispert; J. Leloup Des patrons des mathématiques en France dans l'entre-deux-guerres, Rev. Hist. Sci., Volume 62 (2009), pp. 39-117

[32] H. Villat Aperçus théoriques sur la résistance des fluides, Gauthier-Villars, Paris, 1920

[33] P. Duhem Sur le paradoxe hydrodynamique de d'Alembert, C. R. hebd. séances Acad. Sci. Paris, Volume 159 (1914), pp. 592-595

[34] U. Cisotti Sul moto permanente di un solido in un fluido indefinito, Atti R. Ist. Veneto Sci. Lett. Arti, Volume 69 (1910), pp. 427-445

[35] E. Picard À propos du paradoxe hydrodynamique de d'Alembert, C. R. hebd. séances Acad. Sci. Paris, Volume 159 (1914), p. 638

[36] P. Duhem Remarque sur le paradoxe hydrodynamique de d'Alembert, C. R. hebd. séances Acad. Sci. Paris, Volume 159 (1914), pp. 638-640

[37] H. Villat Sur le paradoxe de d'Alembert et la théorie des mouvements discontinus, C. R. hebd. séances Acad. Sci. Paris, Volume 159 (1914), pp. 800-802

[38] H. Lamb Hydrodynamics, Cambridge University Press, Cambridge, UK, 1932

[39] G. Birkhoff Hydrodynamics, a Study in Logic, Facts, and Similitude, Princeton University Press, Princeton, NJ, USA, 1950

[40] J. Hoffman; C. Johnson Resolution of d'Alembert's paradox, J. Math. Fluid Mech., Volume 12 (2010) no. 3, pp. 321-333

[41] J. Hoffman; C. Johnson Computational Turbulent Incompressible Flow, vol. 4, Springer, 2007

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