Lord Kelvin on fluid mechanics

T   &   T′ = Treatise on Natural Philosophy, Part 1. 2 vols. (Thomson and Tait 1867 etc.). MPP = Mathematical & Physical Papers 6 vols. (Kelvin 1882-1911). Letters = The Correspondence between Sir George Gabriel Stokes and Sir William Thomson Baron Kelvin of Largs. 2 vols. (Wilson 1990). PLA = Popular Lectures and Addresses 3 vols. (Kelvin 1889; 1894; 1891). Airy, George B. 1826. Mathematical Tracts, edited by J. Smith, Cambridge Airy, George B. 1841. Tides and Waves. Encyclopaedia Metropolitana (1817–1845), in Mixed Sciences, edited by HJ Rose, Vol. 3, Also in Trigonometry, On the Figure of the Earth, Tides and Waves [Airy’s articles from the Encyclopaedia], n.d., n.p. Aref, Hassan. 2007. Point vortex dynamics : a classical mathematics playground. J. Math. Phys. 48 : 1-23 Arnol’d, Vladimir I. 1965. Variational principle for three-dimensional steady-state flows of an ideal fluid. Prikl. Mat. Mekh. 29 : 846-851. English trs. J. Appl. Math. Mech. 29 : 1002-1008 Arnol’d, Vladimir I. 1966. Sur un principe variationnel pour les écoulements stationnaires des liquides parfaits et ses applications aux problèmes de stabilité non lineaires. J. Méchanique 5 : 29-43 Batchelor, George K. 1953. The Theory of Homogeneous Turbulence. Cambridge Univ. Press, Cambridge Benjamin, T. Brooke. 1957. Wave formation in laminar flow down an inclined plane. J. Fluid Mech. 2 : 554-574. Corrigendum (1958) 3 : 657 Benjamin, T. Brooke. 1959. Shearing flow over a wavy boundary. J. Fluid Mech. 6 : 161-205 Burchfield, Joe D. 1975. Lord Kelvin and the Age of the Earth. Science History Publications, New York; also Univ. of Chicago Press, 1990 Cartwright, David E. 1999. Tides : A Scientific History. Cambridge Univ. Press, Cambridge Cauchy, Augustin-L. 1827. Mémoire sur la théorie de la propagation des ondes à la surface d’un fluide pesant d’une profondeur indéfinie. Mém. Acad. R. Sci. Inst. France (Prix de 1815 et 1816) 1 : 3-312 Craik, Alex D.D. 1985. Wave Interactions and Fluid Flows. Cambridge Univ. Press, Cambridge Craik, Alex D.D. 2004. The origins of water wave theory. Annu. Rev. Fluid Mech. 36 : 1-28 Craik, Alex D.D. 2005. George Gabriel Stokes on water wave theory. Annu. Rev. Fluid Mech. 37 : 23-42 Craik, Alex D.D. 2007. Mr Hopkins’ Men : Cambridge reform and British mathematics in the nineteenth century. Springer, New York, etc. Craik, Alex D.D. 2008. Educating William : Belfast, Glasgow, and Cambridge. Chap. 2, pp. 23–43, Flood, McCartney and Whitaker, 2008 Craik, Alex D.D. 2010. Thomas Young on fluid mechanics. J. Engng. Math. 67 : 95-113 Crilly, Tony. 2004. The Cambridge Mathematical Journal and its descendants : the linchpin of a research community in the early and mid-Victorian Age. Historia Mathematica 31 : 455-497 Darrigol, Olivier. 2000. Electrodynamics from Ampère to Einstein. Oxford Univ. Press, Oxford Darrigol, Olivier. 2003. The spirited horse, the engineer, and the mathematician : water waves in nineteenth-century hydrodynamics. Arch. Hist. Exact Sci. 58 : 21-95 Darrigol, Olivier. 2005. Worlds of Flow : a history of hydrodynamics from the Bernoullis to Prandtl. Oxford Univ. Press, Oxford Darwin, George H. 1907-1916. Scientific Papers 5 vols. Cambridge Univ. Press, Cambridge Dikii, L.A. 1965. On the nonlinear theory of hydrodynamic stability. Prikl. Mat. Mekh. 29 : 852-855. English trs. J. Appl. Math. Mech. 29 : 1009-1012 Drazin, Philip G. and Reid, William H. 1981. Hydrodynamic Stability. Cambridge Univ. Press, Cambridge Dritschel, David G. 1988. The repeated filamentation of two-dimensional vorticity interfaces. J. Fluid Mech. 194 : 511-547 Eckert, Michael. 2006. The Dawn of Fluid Mechanics. A Discipline between Science and Technology. Wiley-VCH, Weinheim Eckert, Michael. 2010. The troublesome birth of hydrodynamic stability theory : Sommerfeld and the turbulence problem. Eur. Phys. J. H 35 : 29-51 England, P., Molnar, P. and Richter, F. 2007. John Perry’s neglected critique of Kelvin’s age for the Earth : a missed opportunity in geodynamics. Geol. Soc. Am. Today 17 : 4-9 Epple, Moritz. 1999. Geometric aspects in the development of knot theory, in History of Topology, edited by I.M. James, pp. 301–357. North Holland, Amsterdam Flood, Raymond. 2008a. Thomson and Tait : The Treatise on Natural Philosophy. Chap. 11, pp. 175-191, Flood, McCartney and Whitaker, 2008 Flood, Raymond, McCartney, Mark and Whitaker, Andrew (Eds.). 2008b. Kelvin : Life, Labours and Legacy. Oxford Univ. Press, Oxford Fourier, Joseph. 1822. Théorie analytique de la chaleur. Firmin Didot, Paris Gibbs-Smith, Charles H. 1960. The aeroplane : an historical survey of its origins and development. Science Museum, HMSO, London. Grattan-Guinness, Ivor. 2008. On the Early Work of William Thomson : Mathematical Physics and Methodology in the 1840s. Chap. 3, pp. 44–55, Flood, McCartney and Whitaker, 2008 Gray, Andrew. 1908. Lord Kelvin : an account of his scientific life and work. Dent, London and Dutton, New York Green, George. 1828. Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism. privately printed, Nottingham Helmholtz, Hermann. 1858. Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. J. Reine Angewandte Mathematik 55 : 25-55 Helmholtz, Hermann. 1867. On the integrals of the hydrodynamic equations, which express vortex motion. Philos. Mag. 33 : 485-512 [Translation by P.G. Tait of (Helmholtz 1858)] Hicks, William M. 1885. Researches on the theory of vortex rings. Part II. Phil. Trans. R. Soc. London 176 : 725-780 Jeffreys, Harold. 1925. On the formation of water wave by wind. Proc. Roy. Soc. Lond. A 107 : 189-206 Jeffreys, Harold. 1926. On the formation of water waves by wind (Second paper). Proc. Roy. Soc. Lond. A 110 : 241-247 Kelland, Philip. 1837. Theory of Heat. Deighton. Cambridge Kelvin, Baron (W. Thomson). 1882-1911. [MPP] Mathematical & Physical Papers 6 vols. (4-6 ed. J. Larmor). Cambridge Univ. Press, Cambridge Kelvin, Baron (W. Thomson). 1872. Reprint of Papers on Electrostatics and Magnetism, 2nd edn. 1884. Macmillan, London Kelvin, Baron (W. Thomson). 1889; 1894; 1891. [PLA] Popular Lectures and Addresses. 3 vols. Macmillan, London Kelvin, Baron (W. Thomson). 1904. Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. Clay, London Kerswell, Richard R. 2002. Elliptical instability. Annu. Rev. Fluid Mech. 34 : 83-113 Kida, Shigeo & Takaoka, M. 1994. Vortex reconnection. Annu. Rev. Fluid Mech. 26 : 169-189 Knott, Cargill G. 1911. Life and Scientific Work of Peter Guthrie Tait. Cambridge Univ. Press, Cambridge Kragh, Helge. 2002. The vortex atom : a Victorian theory of everything. Centaurus 44 : 32-114 Lagrange, Joseph-Louis 1788. 1st edn. Méchanique analitique Desaint, Paris. 3rd edn. Mécanique analytique. 1853-55, 2 vols. ed. M.J. Bertrand. Mallet-Bachelier, Paris. Also in Oeuvres de Lagrange, ed. J.-A. Serret, 11-12 (1888-89). Gauthier-Villars, Paris Lamb, Horace. 1879. A Treatise on the Mathematical Theory of the Motion of Fluids. Cambridge Univ. Press, Cambridge Lamb, Horace. 1895; 1916; 1932. Hydrodynamics (4th edn. 1916; 6th edn. 1932). Cambridge Univ. Press, Cambridge Laplace, Pierre-Simon 1799-1825. Traité de mécanique céleste, 5 vols. Duprat, Paris Lighthill, M. James. 1978. Waves in Fluids. Cambridge Univ. Press, Cambridge Lin, Chia-Ch’iao. 1955. The Theory of Hydrodynamic Stability. Cambridge Univ. Press, Cambridge Lindley, David. 2004. Degrees Kelvin : The Genius and Tragedy of William Thomson. Aurum, London Lützen, Jesper. 1984. Joseph Liouville’s work on the figures of equilibrium of a rotating mass of fluid. Arch. Hist. Exact Sci. 30 : 113-166 Maslowe, Sherwin A. 1986. Critical layers in shear flows. Annu. Rev. Fluid Mech. 18 : 405-432 Maxwell, James Clerk. 1856. On Faraday’s lines of force. Trans. Cambridge Philos. Soc. 10 : 27-83. Also in The Scientific Papers of James Clerk Maxwell 1 : 155-229 Maxwell, James Clerk. 1867. On the Dynamical Theory of Gases. Phil. Trans. Roy. Soc. Lond. 157 : 49-88. Also in The Scientific Papers of James Clerk Maxwell 2 : 26 Maxwell, James Clerk. 1873. A Treatise on Electricity and Magnetism. 2 vols. Clarendon, Oxford Miles, John W. 1957. On the generation of surface waves by shear flows. J. Fluid Mech. 3 : 185-204. Corrigenda (1959) 6 : 582 Miles, John W. 1959a. On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6 : 568-582 Miles, John W. 1959b. On the generation of surface waves by shear flows. Part 3 : Kelvin-Helmholtz instability. J. Fluid Mech. 6 : 583-598 Moffatt, H. Keith. 2002. G.K. Batchelor and the homogenization of turbulence. Annu. Rev. Fluid Mech. 34 : 19-35 Moffatt, H. Keith. 2008. Vortex dynamics : the legacy of Helmholtz and Kelvin. IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence, edited by A.V. Borisov et al., Springer, pp. 1–10 Poisson, Siméon D. 1818. Mémoire sur la théorie des ondes. Mém. Acad. R. Sci. Inst. Fr. 2nd Ser. 1 : 70-186 Rayleigh, Baron (J.W. Strutt). 1877-1978 etc. The Theory of Sound. 2 vols. Macmillan, London. Also Dover 1945 Rayleigh, Baron (J.W. Strutt). 1880. On the stability, or instability, of certain fluid motions. Proc. London Math. Soc. Ser. 1, 11 : 57-70 (Also Scientific Papers 1 : 474-487) Rayleigh, Baron (J.W. Strutt).1883. The form of standing waves on the surface of running water. Proc. London Math. Soc. Ser. 1, 15 : 69-78 (Also Scientific Papers 2 : 258-267) Rayleigh, Baron (J.W. Strutt). 1892. On the question of the stability of the flow of fluids. Philos. Mag. 34 : 59-70 (Also Scientific Papers 3 : 575-584) Reynolds, Osborne. 1883. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil. Trans. Roy. Soc. London 174 : 935-982 Reynolds, Osborne. 1895. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. Roy. Soc. Lond. A 186, 123-164. Also in Reynolds’ Papers on Mechanical and Physical Subjects 3 vols. (1900-1903), 2 : 535-577. Cambridge Univ. Press, Cambridge Russell, John Scott. 1839. Experimental researches into the laws of certain hydrodynamic 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. Edinburgh 14 : 47-109 Russell, John Scott. 1844. Report on Waves. Rep. Br. Assoc. Adv. Sci., 311-390 Sharlin, Harold I. 1979. Lord Kelvin : The Dynamic Victorian. Penn. State Univ. Press, University Park & London Siegel, Daniel M. 1981. Thomson, Maxwell, and the universal ether in Victorian physics. Chap. 8, pp. 239-268, in Conceptions of Ether : Studies in the history of ether theories 1740-1900, edited by Cantor, G.N. and Hodge, M.J.S. Cambridge Univ. Press, Cambridge Smith, Crosbie and Wise, M. Norton. 1989. Energy and Empire : A Biographical Study of Lord Kelvin. Cambridge Univ. Press, Cambridge Stuart, J. Trevor. 1971. Nonlinear stability theory. Annu. Rev. Fluid Mech. 3 : 347-370 Taylor, Geoffrey I. 1923. Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223 : 289-343 Thompson, Silvanus P. 1910. The Life of William Thomson Baron Kelvin of Largs, 2 vols. Macmillan, London Thomson, Joseph J. 1883. A Treatise on the Motion of Vortex Rings. Macmillan, London Thomson W (Baron Kelvin), Tait PG. []. 1867. Treatise on Natural Philosophy, Part 1. 2nd enlarged edn. 2 vols. 1886, 1890 : reprinted 1912. Cambridge Univ. Press, Cambridge Thomson, William (Baron Kelvin) and Tait, Peter G. 1873. Elements of Natural Philosophy. Cambridge Univ. Press, Cambridge Thomson, William : see also “Kelvin, Baron” Whittaker, Edmund T. 1951. A History of the Theories of Aether and Electricity. Vol.1 : The classical theories. 2nd enlarged edn. Nelson, London Wilson, David B. 1985. The educational matrix : physics education at early Victorian Cambridge, Edinburgh and Glasgow Universities. Harman, 1985, pp. 12-48 Wilson, David B. 1987. Kelvin & Stokes, a Comparative Study in Victorian Physics. Adam Hilger, Bristol Wilson David B. (ed.) 1990. [Letters] The Correspondence between Sir George Gabriel Stokes and Sir William Thomson Baron Kelvin of Largs. 2 vols. Cambridge Univ. Press, Cambridge Wise, M. Norton. 1979. William Thomson’s mathematical route to energy conservation : a case study of the role of mathematics in concept formation. Hist. Stud. Phys. Sci. 10 : 49-83 Young, Arthur P. 1945. Lord Kelvin, Physicist, Mathematician, Engineer. Longmans, Green, London