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Vorticity (Molecular Spin)

  • Percival McCormackEmail author
Chapter
Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Abstract

The curl of the fluid velocity vector 7is known as the vorticity or, physically, the angular velocity at a point in space (see [1, p. 68]). It has also been called Rotationgeschwindigkeit by Helmholtz, rotation by Kelvin, molecular rotation by Kelvin, and spin by Clifford.

Keywords

Stagnation Point Vortex Line Magnetic Helicity Vorticity Equation Vorticity Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Truesdell, C.: The Kinematics of Vorticity. Indiana University Press, Bloomington (1954)zbMATHGoogle Scholar
  2. 2.
    Thompson, W. (Lord Kelvin): On vortex motion. Math. Phys. 4, 49 (1869)Google Scholar
  3. 3.
    Batchelor, G.K.: An Introduction to Fluid Dynamics. Cambridge University Press, Cambridge (1967)zbMATHGoogle Scholar
  4. 4.
    Hadamard, J.: Sur les Tourbillons Produit par les Ondes De Choc. Note III. Lecons sur la Propagation des Ondes. In: Herman, A. (ed.). Paris, 362 (1903)Google Scholar
  5. 5.
    Vazsonyi, A.: On rotational gas flows. Quart. J. Appl. Math. 3(1), 29–37 (1945)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Holton, J.R.: An Introduction to Dynamic Meteorology. Academic, New York, NY (1979)Google Scholar
  7. 7.
    Green, S.I. (ed.): Fluid Vortices. Kluwer Academic, Boston, Massachusetts (1995) (Chapter 11)zbMATHGoogle Scholar
  8. 8.
    Oseen, C.W.: Uber Wirbelbewegung in einer Reibenden Flussigkeit. Ark. f. Mat. Astron. Fyz 7, 14 (1912)Google Scholar
  9. 9.
    Lighthill, M.J.: Boundary layer theory. Part II. In: Rosenhead, L. (ed.) Laminar Boundary Layers, p. 389. Dover, Mineola (1963)Google Scholar
  10. 10.
    Morton, B.R.: The generation and decay of vorticity. Geophys. Astrophys. Fluid Dyn. 28, 277–308 (1984)ADSzbMATHCrossRefGoogle Scholar
  11. 11.
    Heimenz, H.: On integrals of the hydrodynamical equations which express vortex motion. Dingler’s Polytech. 326, 311 (1867)Google Scholar
  12. 12.
    Burgers, J.M.: A mathematical model illustrating the theory of turbulence. Adv. Appl. Mech. 17, 1 (1948)Google Scholar
  13. 13.
    Hill, M.J.M.: On a spherical vortex. Phil. Trans. Roy. Soc. Lond. A 185, 213 (1894)ADSzbMATHCrossRefGoogle Scholar
  14. 14.
    Panton, R.I.: Incompressible Flow. Wiley, New York, NY (1984). p. 333zbMATHGoogle Scholar
  15. 15.
    Bjerknes, V.: Uberdie Bildung Circulations bewegung Skrifter (1898)Google Scholar
  16. 16.
    Lamb, H.: Hydrodynamics. Cambridge University Press, Cambridge (1932)zbMATHGoogle Scholar
  17. 17.
    Mockros, L.: Ph.D. Thesis, University of California, Los Angeles (1962)Google Scholar
  18. 18.
    Goertler, H.: Uber eine Dreidimensionale Instabilitat Laminaren Grenzschichten am Koncaven Wander. Naschr Wiss Gas,Gottingen Math Phys Klasse, 2(1) (1940)Google Scholar
  19. 19.
    Witting, H.: Theorie der Sekundaren Instabilitat der Laminaren Grenzschichten. In: Goertler, H. (ed.) Boundary Layer Research. Springer, Berlin (1958)Google Scholar
  20. 20.
    Witting, H.: Einige Neuer Ergebnisse zur Hydrodynamischen Stabilitats Theorie. Zeits.fur Flugwissenschaften 8 Jahrgang, Heft 1 (1960)Google Scholar
  21. 21.
    McCormack, P., Welcher, H.: J. Heat Transfer (1967)Google Scholar
  22. 22.
    Crocco, L.: Zeits. Angew. Math. Mech. 17, p. 1 (1937)Google Scholar
  23. 23.
    Black, W.Z., Hartley, J.G.: Thermodynamics. Harper Collins, New York, NY (1991)Google Scholar
  24. 24.
    Currie, I.G.: Fundamental Mechanics of Fluids. McGraw-Hill, New York (1974)zbMATHGoogle Scholar
  25. 25.
    Fetter, A., Donnelly, R.: On the equivalence of vortices and current filaments. Phys. Fluids 9, 619 (1966)ADSCrossRefGoogle Scholar
  26. 26.
    Spitzer Jr., L.: Influence of fluid motions in the decay of an external magnetic field. Astrophys. J. 125, 525 (1957)ADSCrossRefGoogle Scholar
  27. 27.
    Tilley, D.R., Tilley, J.: Superfluidity and Super-Conductivity, 3rd edn. Graduate Student Series in Physics, Institute of Physics Publishing, Philedelphia (1990)Google Scholar
  28. 28.
    Vinen, W.F., et al.: Quantized Vortex Dynamics and Superfluid Turbulence. Springer, Berlin (2001)zbMATHGoogle Scholar
  29. 29.
    Landau, L.D.: The theory of superfluidity of helium II. J. Phys. Moscow 5, 71 (1941)Google Scholar
  30. 30.
    Onsager, L.: Nuevo Cimento. 6(2), 249 (1949)Google Scholar
  31. 31.
    Osborne, L.: Proc. Phys. Soc. A63, 909 (1949)Google Scholar
  32. 32.
    Hall, H.E.: On the rotation of liquid helium II. Adv. Phys. 9, 89 (1960)ADSCrossRefGoogle Scholar
  33. 33.
    Hess, G.B., Fairbank, W.M.: Measurements of angular momentum in superfluid helium. Phys. Rev. Letts. 19, 216 (1967)ADSCrossRefGoogle Scholar
  34. 34.
    Packard, R.F., Sanders, T.M.: Observation of single vortex lines in rotating superfluid helium. Phys. Rev. A6, 799 (1972)ADSGoogle Scholar
  35. 35.
    Rayfield, G.W., Reif, F.: Quantized vortex rings in superfluid helium. Phys. Rev. 136, 1194 (1964)ADSCrossRefGoogle Scholar

Copyright information

© Percival McCormack 2012

Authors and Affiliations

  1. 1.Department of BioEngineeringUniversity of Illinois at ChicagoChicagoUSA

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