Comptes Rendus
Joseph Boussinesq's legacy in fluid mechanics
Comptes Rendus. Mécanique, Volume 345 (2017) no. 7, pp. 427-445.

Joseph Boussinesq was the most prolific of all French contributors to nineteenth-century fluid mechanics. His scientific production included a novel theory of solitary waves, the KdV equation for finite deformations of the water surface in an open channel, a systematic study of open channel and pipe flow based on the concept of effective viscosity, pioneering derivations of boundary layers and entrance effects, new exact solutions of the Navier–Stokes equation under geometrically simple boundary conditions, and the ‘Boussinesq approximation’ for heat convection in a moving fluid under gravity. Although his extraordinary skills were quickly recognized and rewarded, other experts in the field were often unaware even of his most important results and they ended up rediscovering some of them. Boussinesq's unusual background and the resulting peculiarities of his style explain this problematic diffusion. They also account for the richness of his legacy.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2017.05.008
Keywords: Joseph Boussinesq, Solitary waves, KdV equation, Open-channel flow, Boussinesq approximation, Physical mechanics, Adhémar Barré de Saint-Venant

Olivier Darrigol 1

1 CNRS: UMR SPHere, Université Paris-7, France
@article{CRMECA_2017__345_7_427_0,
     author = {Olivier Darrigol},
     title = {Joseph {Boussinesq's} legacy in fluid mechanics},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {427--445},
     publisher = {Elsevier},
     volume = {345},
     number = {7},
     year = {2017},
     doi = {10.1016/j.crme.2017.05.008},
     language = {en},
}
TY  - JOUR
AU  - Olivier Darrigol
TI  - Joseph Boussinesq's legacy in fluid mechanics
JO  - Comptes Rendus. Mécanique
PY  - 2017
SP  - 427
EP  - 445
VL  - 345
IS  - 7
PB  - Elsevier
DO  - 10.1016/j.crme.2017.05.008
LA  - en
ID  - CRMECA_2017__345_7_427_0
ER  - 
%0 Journal Article
%A Olivier Darrigol
%T Joseph Boussinesq's legacy in fluid mechanics
%J Comptes Rendus. Mécanique
%D 2017
%P 427-445
%V 345
%N 7
%I Elsevier
%R 10.1016/j.crme.2017.05.008
%G en
%F CRMECA_2017__345_7_427_0
Olivier Darrigol. Joseph Boussinesq's legacy in fluid mechanics. Comptes Rendus. Mécanique, Volume 345 (2017) no. 7, pp. 427-445. doi : 10.1016/j.crme.2017.05.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.05.008/

[1] É. Picard La vie et l'œuvre de Joseph Boussinesq, Académie des sciences, Discours et notices, Gauthier–Villars, Paris, 1933

[2] P.-A. Bois Joseph Boussinesq (1842–1929): A pioneer of mechanical modeling at the end of the 19th Century, C. R. Mecanique, Volume 335 (2007), pp. 479-495

[3] O. Darrigol A History of Optics from Greek Antiquity to the Nineteenth Century, Oxford University Press, Oxford, UK, 2012

[4] R. Fox The rise and fall of Laplacian physics, Hist. Stud. Phys. Sci., Volume 4 (1974), pp. 89-136

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

[6] J. Principe da Silva La réception française de la mécanique statistique, Université Paris-Diderot, 2008 (Thèse de doctorat)

[7] R. Romero La philosophie naturelle mécaniste de Joseph Boussinesq (1842–1929), Université de Lille-1, France, 1999 (Thèse de doctorat)

[8] B. Pourprix La mécanique physique au sens de Joseph Boussinesq, Almageste, Volume 6 (2015), pp. 126-155

[9] J. Thomson On the winding of rivers in alluvial plains, Proc. R. Soc. Lond., Volume 25 (1876), pp. 5-8

[10] R.A. Callander River meandering, Annu. Rev. Fluid Mech., Volume 10 (1978), pp. 129-158

[11] A. Barré de Saint-Venant Sur l'hydrodynamique des cours d'eau, C. R. Hebd. Séances Acad. Sci., Volume 74 (1872), pp. 570-577 (649–657, 693–701, 770–774)

[12] F. Savart Mémoire sur le choc d'une veine liquide lancée contre un plan circulaire, Ann. Chim. Phys., Volume 54 (1833), pp. 55-87

[13] F. Savart Suite du mémoire sur le choc d'une veine liquide lancée contre un plan circulaire, Ann. Chim. Phys., Volume 54 (1833), pp. 113-145

[14] C. Clanet Dynamics and stability of water bells, J. Fluid Mech., Volume 430 (2001), pp. 111-147

[15] D. Bernoulli Hydrodynamica, sive de viribus et motibus fluidorum commentarii, Dulsecker, Strasbourg, 1638

[16] J. Scott Russell Experimental researches into the laws of certain hydrodynamical phenomena that accompany the motion of floating bodies, and have not previously been reduced into conformity with the known laws of the resistance of fluids, Trans. R. Soc. Edinb., Volume 14 (1839), pp. 47-109

[17] D. Korteweg; G. de Vries On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag., Volume 39 (1895), pp. 422-443

[18] Lord Rayleigh On waves, Philos. Mag., Volume 1 (1876), pp. 257-279

[19] J.-B. Bélanger Essai sur la solution numérique de quelques problèmes relatifs au mouvement permanent des eaux courantes, Carilian–Goeury, Paris, 1928

[20] G. Bidone Expériences sur le remou et sur la propagation des ondes, Mem. Accad. Sci. Torino, Volume 25 (1820), pp. 21-112

[21] H. Rouse; S. Ince History of Hydraulics, Iowa Institute of Hydraulic Research, Ann Arbor, MI, USA, 1957

[22] G. Coriolis Sur l'établissement de la formule qui donne la figure des remous, et sur la correction qu'on doit y introduire pour tenir compte des différences de vitesse dans les divers points d'une même section d'un courant, Ann. Ponts Chaussées (1836), pp. 314-335

[23] A. Barré de Saint-Venant Mémoire sur des formules et des tables nouvelles pour la solution des problèmes relatifs aux eaux courantes, Ann. Mines, Volume 20 (1851), pp. 183-357

[24] A. Barré de Saint-Venant Démonstration élémentaire de la formule de propagation d'une onde ou d'une intumescence dans, un canal prismatique; remarque sur les propagations du son et de la lumière, sur les ressauts, ainsi que sur la distinction entre des rivières et des torrents, C. R. Hebd. Séances Acad. Sci., Volume 71 (1870), pp. 186-195

[25] G. Biddell Airy, Tides and waves, Encycl. Metrop., Volume 5 (1845), pp. 291-396

[26] A. Barré de Saint-Venant Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit, C. R. Hebd. Séances Acad. Sci., Volume 73 (1871), pp. 147-154 (237–240)

[27] C.L. Navier Mémoire sur les lois du mouvement des fluides [read on 18 March and 16 December 1822], Mém. Acad. Sci., Volume 6 (1823), pp. 389-440

[28] A. Barré de Saint-Venant Note à joindre au mémoire sur la dynamique des fluides, présenté le 14 avril 1834, C. R. Hebd. Séances Acad. Sci., Volume 17 (1843), pp. 1240-1243

[29] H. Darcy; H. Bazin Recherches hydrauliques. Deuxième partie : Recherches expérimentales relatives aux remous et à la propagation des ondes, Imprimerie impériale, Paris, 1865

[30] A. Flamant Mécanique appliquée: Hydraulique, Baudry, Paris, 1891

[31] A. Boulanger Hydraulique générale, 2 vols, Doin et fils, Paris, 1909

[32] A. Barré de Saint-Venant Des diverses manières de poser les équations du mouvement varié des eaux courantes, Ann. Ponts Chaussées, Volume 13 (1887), pp. 148-228

[33] G.G. Stokes On the effect of the internal friction of fluids on the motion of pendulums [read on 9 December 1850], Trans. Camb. Philos. Soc., Volume 9 (1851), pp. 8-106

[34] S.D. Poisson Mémoire sur les équations générales de l'équilibre et du mouvement des corps solides élastiques et des fluides [read on 12 October 1829], J. Éc. Polytech., Cah., Volume 20 (1831), pp. 1-174

[35] F. Schmitt About Boussinesq's turbulent viscosity hypothesis: Historical remarks and a direct evaluation of its validity, C. R. Mecanique, Volume 335 (2007), pp. 617-627

[36] Lord Rayleigh On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side, Philos. Mag., Volume 32 (1916), pp. 529-546

[37] G. Maugin Continuum Mechanics Through the Twentieth Century: A Concise Historical Perspective, Springer, Dordrecht, The Netherlands, 2013

[38] I. Todhunter; K. Pearson A History of Elasticity and of the Strength of Materials from Galileo to the Present Times, vol. 2: Saint-Venant to Lord Kelvin, Cambrige University Press, Cambridge, UK, 1893

[39] R. de Boer Theory of Porous Media: Highlights in Historical Development and Current State, Springer, Berlin, 2000

[40] M. Corradi De la statique des demi-fluides à la théorie de la poussée des terres (P. Radelet-de Grave; E. Benvenuto, eds.), Entre mécanique et architecture (Between Mechanics and Architecture), Birkhäuser, Basel, Switzeland, 1995, pp. 249-255

[41] O.G. Tietjens Hydro- und Aeromechanik nach Vorlesungen von L. Prandtl, vol. 2: Bewegung reibender Flüssigkeiten und technische Anwendungen, Springer, Berlin, 1931

[42] L. Prandtl Neuere Ergebnisse der Turbulenzforschung, Kaiser-Wilhelm-Institut für Strömungslehre, Mitteilungen, 1933, Gesammelte Abhandlungen zur Mechanik, Hydro- und Aerodynamik, 3 vols., vol. 2, Springer, Berlin, 1961, pp. 819-845 (also)

[43] E. de Jager On the Origin of the Korteweg–de Vries equation, 8 December 2011 | arXiv

[44] J.W. Miles The Korteweg–de Vries equation: A historical essay, J. Fluid Mech., Volume 106 (1981), pp. 131-147

[45] O. Reynolds On the dynamical theory of incompressible viscous fluids and the determination of the criterion, Philos. Trans. R. Soc., Volume 186 (1895), pp. 123-164

[46] A. Barnard Basset On the motion of a sphere in a viscous liquid, Philos. Trans. R. Soc., Volume 179 (1888), pp. 43-64

[47] A. Barnard Basset A Treatise on Hydrodynamics, with Numerous Examples, Deighton, Bell and Co., Cambridge, UK, 1888

[48] L. Prandtl Über Flüssigkeitsbewegung bei sehr kleiner Reibung (A. Krazer, ed.), III. Internationaler Mathematiker-Kongress in Heidelberg vom 8. bis 13. August 1904, Verhandlungen, Teubner, Leipzig, 1905, pp. 484-491

[49] D. Aubin ‘Audacity or Precision’: The paradoxes of Henri Villat's fluid mechanics in interwar France, 2011 | arXiv

[50] L. Schwartz Un mathématicien aux prises avec le siècle, Odile Jacob, Paris, 1997

[51] P. Forchheimer Wasserströmungen (H. Geiger; K. Scheel, eds.), Handb. Phys., vol. 7, Springer, Berlin, 1927

Cited by Sources:

Comments - Policy