1932

Abstract

▪ Abstract

After early work by Newton, the eighteenth and early nineteenth century French mathematicians Laplace, Lagrange, Poisson, and Cauchy made real theoretical advances in the linear theory of water waves; in Germany, Gerstner considered nonlinear waves, and the brothers Weber performed fine experiments. Later in Britain during 1837–1847, Russell, Green, Kelland, Airy, and Earnshaw all made substantial contributions, setting the scene for subsequent work by Stokes and others.

Loading

Article metrics loading...

/content/journals/10.1146/annurev.fluid.36.050802.122118
2004-01-21
2024-10-12
Loading full text...

Full text loading...

/deliver/fulltext/fl/36/1/annurev.fluid.36.050802.122118.html?itemId=/content/journals/10.1146/annurev.fluid.36.050802.122118&mimeType=html&fmt=ahah

Literature Cited

  1. Airy GB. 1841. art. Tides and waves. Encyclopaedia Metropolitana(1817–1845), Mixed Sciences, Vol. 3 ed. HJ Rose, et al Also Trigonometry, On the Figure of the Earth, Tides and Waves. 396pp. + Plates. n.d., n.p. [Google Scholar]
  2. Airy GB. 1845. On the laws of the tides on the coasts of Ireland, as inferred from an extensive series of observations made in connexion with the Ordnance Survey of Ireland [1844]. Philos. Trans. R. Soc. London pp. 1–124 [Google Scholar]
  3. Airy GB. 1896. Autobiography of Sir George Biddell Airy K.C.B…. ed. W Airy Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  4. Bernoulli D. 1738. Hydrodynamica, Sive de Viribus et Motibus Fluidorum Commentarii Argentorati (Strasbourg): Joh. Reinholdi Dulseckeri [Google Scholar]
  5. Bossut C. (l'Abbé). 1786. Traité Théorique et Expérimental d'Hydrodynamique 2 Vols. Paris: l'Imprimerie Royale [Google Scholar]
  6. Boussinesq JV. 1871. Théorie de l'intumescence liquide appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire. C. R. Acad. Sci. Paris 72:755–59 [Google Scholar]
  7. Bowditch N. ed 1829–1839 (1966). Celestial Mechanics by the Marquis de La Place 4Vols. Boston. New York: Chelsea [Google Scholar]
  8. Brémontier NT. 1809. Recherches sur le Mouvement des Ondes Paris: Firmin Didot [Google Scholar]
  9. Brewster D. ed 1808–1830. The Edinburgh Encyclopaedia 18Vols. Edinburgh: Blackwood [Google Scholar]
  10. Brougham F. [Lord]. et al. 1829. Library of Useful Knowledge; Natural Philosophy I London: Baldwin & Cradock [Google Scholar]
  11. Bullough RK. 1988. The Wave “par excellence,” the solitary, progressive great wave of equilibrium of the fluid—an early history of the solitary wave. In Solitons ed. M Lakshmanan Springer Ser. Nonlinear Dyn pp. 150–281 New York: Springer [Google Scholar]
  12. Bullough RK, Caudrey PJ. 1995. Solitons and the Korteweg-de Vries Equation: Integrable systems in 1834–1995. Acta Appl. Math. 39:193–228 [Google Scholar]
  13. Campbell N, Smellie RMS. 1983. The Royal Society of Edinburgh (1783–1983), the First Two Hundred Years Edinburgh: R. Soc. Edinburgh [Google Scholar]
  14. Cannell DM. 2001. George Green: Mathematician and Physicist 1793–1841 Philadelphia: SIAM, 2nd ed.. [Google Scholar]
  15. Cauchy A-L. 1827. Mémoire sur la théorie de la propagation des ondes à la surface d'un fluide pesant d'une profondeur indéfinie. Mém. Présentés Divers Savans Acad. R. Sci. Inst. France (Prix Acad. R. Sci., concours de 1815 et de 1816) I:3–312 [Google Scholar]
  16. Challis J. 1830. On the general equations of the motion of fluids, both incompressible and compressible, and on the pressure of fluids in motion. Trans. Camb. Philos. Soc. 3:383–416 [Google Scholar]
  17. Challis J. 1833. Report on the present state of the analytical theory of hydrostatics and hydrodynamics. Rep. Br. Assoc. Adv. Sci. pp. 131–51 [Google Scholar]
  18. Challis J. 1836. Supplementary report on the mathematical theory of fluids. Rep. Br. Assoc. Adv. Sci. pp. 225–52 [Google Scholar]
  19. Challis J. 1842. Discussion of a new equation in hydrodynamics. Philos. Mag. 20:287–88 [Google Scholar]
  20. Coudraye FC de Loynes de la. 1796. Théories des Vents et des Ondes Copenhagen: Christensen Kön. Ges. Wiss. Kopenhagen pp. 105–50 [Google Scholar]
  21. Craik ADD. 1998. Geometry, analysis and the baptism of slaves: John West in Scotland and Jamaica. Hist. Math. 25:29–74 [Google Scholar]
  22. Craik ADD. 1999. Calculus and analysis in early 19th century Britain: the work of William Wallace. Hist. Math. 26:239–67 [Google Scholar]
  23. Craik ADD. 2000a. Geometry versus analysis in early 19th century Scotland: William Wallace, John Leslie and Thomas Carlyle. Hist. Math. 27:133–63 [Google Scholar]
  24. Craik ADD. 2000b. James Ivory, mathematician: “the most unlucky person that ever existed.”. Notes Rec. R. Soc. 54:223–47 [Google Scholar]
  25. Dalmedico AD. 1988. La propagation des ondes en eau profonde et ses développements mathématiques (Poisson, Cauchy 1815–1825). In The History of Modern Mathematics ed. DE Rowe, J McCleary II129–68 London: Academic [Google Scholar]
  26. Earnshaw S. 1847. The mathematical theory of the two great solitary waves of the first order. Trans. Camb. Philos. Soc. 8:326–41 [Google Scholar]
  27. Earnshaw S. 1860. On the mathematical theory of sound. Philos. Trans. R. Soc. London 150:133–48 [Google Scholar]
  28. Emmerson GS. 1977. John Scott Russell: a Great Victorian Engineer and Naval Architect London: Murray [Google Scholar]
  29. Euler L. 1757a. Principes géneraux du mouvement des fluides. Mém. Acad. Sci. Berlin 11(1755)271–315 1954. Leonhardi Euleri Opera OmniaSer. 2XII ed. CA Truesdell Lausanne: Orell Füssli [Google Scholar]
  30. Euler L. 1757b. Continuation des recherches sur la théorie du mouvement des fluides. Mém. Acad. Sci. Berlin 11(1755):316–61 Also Op. Omn. [Google Scholar]
  31. Euler L. 1761. Principia motus fluidorum. Novi Commentarii Acad. Sci. Petropolitanae 6(1756/7):271–311 Also Op. Omn. [Google Scholar]
  32. Ferguson J. 1760 (1770, 1805, 1823, 1825). Lectures on Select Subjects in Mechanics, Hydrostatics, Pneumatics and Optics London: Strahan [Google Scholar]
  33. Ferrers NM,. ed 1871. Mathematical Papers of the Late George Green London: Macmillan [Google Scholar]
  34. Flaugergues M. 1793. Hollandsche Maatschappye der Weetenschappen te Haarlem xxix Deel p. 131 Also J. Savans Oct. 1789 [Google Scholar]
  35. Fourier J. 1822. Théorie Analytique de la Chaleur Paris: Firmin Didot [Google Scholar]
  36. Gerstner FJ von. 1802. Theorie der Wellen. Abhand. Kön. Böhmischen Gesel. Wiss., Prague. Also in Weber & Weber (1825)
  37. Grattan-Guinness I. 1985. Mathematics and mathematical physics from Cambridge, 1815–40: A survey of the achievements and of the French influences. See Harman 1985 pp. 84–111 [Google Scholar]
  38. Grattan-Guinness I. 1990. Convolutions in French Mathematics, 1800–1840 3 Vols. Basel: Birkhäuser [Google Scholar]
  39. s'Gravesande W-J. 1721. Mathematical Elements of Natural Philosophy Confirmed by Experiments, or an Introduction to Sir Isaac Newton's Philosophy. Engl. transl. JT Desaguliers London: Senex & Taylor, 2nd ed.. [Google Scholar]
  40. Green G. 1838. On the motion of waves in a variable canal of small depth and width. Trans. Camb. Philos. Soc. 6:457–62 See Ferrers 1871 pp. 223–30 [Google Scholar]
  41. Green G. 1839. Note on the motion of waves in canals. Trans. Camb. Philos. Soc. 7:87–96 See Ferrers 1871 pp. 271–80 [Google Scholar]
  42. Guicciardini N. 1989. The Development of Newtonian Calculus in Britain 1700–1800 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  43. Harman PM,. ed 1985. Wranglers and Physicists; Studies on Cambridge Physics in the Nineteenth Century Manchester, UK: Manchester Univ. Press [Google Scholar]
  44. Harte HH (Transl.). 1822 (1827). A Treatise of Celestial Mechanics by P.S. Laplace [Book 1], translated from the French and elucidated with explanatory notes Vol. 1, 2 Dublin/London: Millikan [Google Scholar]
  45. Howarth OJR. 1931. The British Association for the Advancement of Science: A Retrospect 1831–1931 London: Br. Assoc. [Google Scholar]
  46. Kelland P. 1840a. On the theory of waves. Rep. Br. Assoc. Adv. Sci. Part. ii: pp. 50–52 [Google Scholar]
  47. Kelland P. 1840b. On the theory of waves, Part 1. Trans. R. Soc. Edinburgh 14:497–545 [Google Scholar]
  48. Kelland P. 1844. On the theory of waves, Part 2. Trans. R. Soc. Edinburgh 15:101–44 [Google Scholar]
  49. Korteweg DJ, de Vries G. 1895. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos. Mag. 39:(5)422–43 [Google Scholar]
  50. Lagrange J-L. 1781. Mémoire sur la théorie du mouvement des fluides. Nouv. Mém. Acad. Berlin p. 196Also in 1867–1892. Oeuvres de Lagrange 4695–748 Paris: Gauthier-Villars [Google Scholar]
  51. Lagrange J-L. 1786. Sur la manière de rectifier deux entroits des Principes de Newton relatifs à la propagation du son et au mouvement des ondes. Nouv. Mém. Acad. Berlin1889. Also 1867–1892. Oeuvres de Lagrange 5591–609 Paris: Gauthier-Villars [Google Scholar]
  52. Lagrange J-L. 1788. Méchanique Analitique Paris: la Veuve Desaint Also in 1867–1892. Oeuvres de Lagrange 12 (Sect. on waves, pp. 318–22) [Google Scholar]
  53. Lamb H. 1895. Hydrodynamics Cambridge, UK: Cambridge Univ. Press, 4th ed. 1916, 6th ed. 1932. [Google Scholar]
  54. Lardner D. 1831. Treatise on Hydrodynamics and Pneumatics (Cabinet Cyclopaedia Vol. 1) London: Longman [Google Scholar]
  55. Laplace P-S Marquis de. 1776. Suite des récherches sur plusieurs points du système du monde (XXV–XXVII).. Mém. Présentés Divers Savans Acad. R. Sci. Inst. France pp. 525–52 (Sur les Ondes, pp. 542–52) [Google Scholar]
  56. Laplace P-S Marquis de. 1799. Traité de Mécanique Céleste Vols. 1, 2 Paris: Duprat [Google Scholar]
  57. Larmor Sir J. ed 1907. Memoir and Scientific Correspondence of the Late Sir George Gabriel Stokes Cambridge, UK: Cambridge Univ. Press [Selected correspondence only, excluding that with William Thomson, Lord Kelvin] [Google Scholar]
  58. Leslie J. 1823. Elements of Natural Philosophy Vol. 1 Edinburgh: Tait [Google Scholar]
  59. Maitz de Goimpy, (Count) L E G du. 1776. Traité sur la Construction des Vaisseaux etc. Paris: [Google Scholar]
  60. Miles JW. 1981. The Korteweg–de Vries equation: a historical essay. J. Fluid Mech. 106131–47 [Google Scholar]
  61. Miller WH. 1831 (1850). The Elements of Hydrostatics and Hydrodynamics Cambridge, UK: Deighton [Google Scholar]
  62. Moseley H. 1830. A Treatise on Hydrostatics and Hydrodynamics for the Use of Students in the University Cambridge, UK: J Smith [Google Scholar]
  63. Newton I. 1687 (1729). Philosophiae Naturalis Principia Mathematica London: Jussu Societatis Regiae ac Typis J. Streater. Engl. transl. N Motte [Google Scholar]
  64. Peacock G. ed 1855. Miscellaneous Works of the late Thomas Young 3Vols. London: Murray [Google Scholar]
  65. Playfair J. 1814. Outlines of Natural Philosophy: Being Heads of Lectures Delivered in the University of Edinburgh 2Vols. Edinburgh: Neill [Google Scholar]
  66. Poisson SD. 1818. Mémoire sur la théorie des ondes. Mém. Acad. R. Sci. Inst. France1816 2nd Ser. 1:70–186 [Google Scholar]
  67. Poisson SD. 1833. Traité de Mécanique Paris: Bachelier, 2nd ed.. [Google Scholar]
  68. Pratt JH. 1836. The Mathematical Principles of Mechanical Philosophy; And Their Application to the Theory of Universal Gravitation Cambridge, UK: Deighton [Google Scholar]
  69. Rankine WJM. 1863. On the exact form of waves near the surface of deep water. Philos. Trans. R. Soc. London pp. 127–38Also 1881. Miscellaneous Scientific Papers by W.J. McQuorn Rankine ed. WJ Millar pp. 481–94 London: Griffin [Google Scholar]
  70. Rayleigh B. (J.W. Strutt). 1876. On waves. Philos. Mag. (5)1257–79Also 1899. Scientific Papers of John William Strutt, Baron Rayleigh 1251–71 Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  71. Riemann GFB. 1858. Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite. Gött. Abh. 8:43 (1848–1849) [Google Scholar]
  72. Russell JS. 1842. Supplementary report of a Committee on Waves. Rep. Br. Assoc. Adv. Sci.Part ii, pp. 19–21 [Google Scholar]
  73. Russell JS. 1844. Report on waves. Rep. Br. Assoc. Adv. Sci. pp. 311–90 [Google Scholar]
  74. Russell JS, Robison Sir John. 1837. Report on waves. Rep. Br. Assoc. Adv. Sci. pp. 417–96 [Google Scholar]
  75. Russell JS, Robison Sir John. 1840. Report on waves. Rep. Br. Assoc. Adv. Sci. pp. 441–43 [Google Scholar]
  76. Stokes GG. 1846. Report on recent researches in hydrodynamics. Rep. Br. Assoc. Adv. Sci. pp. 1–20 See Stokes 1880 Vol. 1: [Google Scholar]
  77. Stokes GG. 1847. On the theory of oscillatory waves. Trans. Camb. Philos. Soc. 8:441–55 See Stokes 1880 Vol. 1: Appendices and Suppl. [Google Scholar]
  78. Stokes GG. 1880–1905. Mathematical and Physical Papers 5Vols. Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  79. Thomson AC. 1835. art. Hydrodynamics. Encyclopaedia Britannica [Google Scholar]
  80. Toplis J (Trans.). 1814. A Treatise upon Analytical Mechanics; Being the First Book of the Mécanique Céleste of M. le Comte Laplace with notes. Nottingham: Barnett [Google Scholar]
  81. Vince S. 1798 (1829). The Principles of Hydrostatics Cambridge, UK: J Smith [Google Scholar]
  82. Walton W. 1847. A Collection of Problems in Illustration of the Principles of Theoretical Hydrostatics and Hydrodynamics Cambridge, UK: Deighton [Google Scholar]
  83. Weber EH, Weber WE. 1825. Wellenlehre auf Experimente gegründet Leipzig: Gerhardt Fleischer [Google Scholar]
  84. Webster T. 1836. The Theory of the Equilibrium and Motion of Fluids Cambridge, UK: J Smith [Google Scholar]
  85. Wilson DB. 1985. The educational matrix: physics education at early-Victorian Cambridge, Edinburgh and Glasgow Universities. See Harman 1985 pp. 12–48 [Google Scholar]
  86. Wilson DB. ed 1990. The Correspondence between Sir George Gabriel Stokes and Sir William Thomson Baron Kelvin of Largs 2Vols. Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  87. Young T. 1807. A Course of Lectures on Natural Philosophy and the Mechanical Arts 2Vols. London: J Johnson 1845., 6th edn. ed. P Kelland London: Taylor & Walton [Google Scholar]
  88. Young T. 1821. Elementary Illustrations of the Celestial Mechanics of LaplaceBook 1. London: Murray Also Peacock 1855, pp. 141–58 [Google Scholar]
/content/journals/10.1146/annurev.fluid.36.050802.122118
Loading
/content/journals/10.1146/annurev.fluid.36.050802.122118
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error