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Conservation of Angular Momentum–Vorticity

  • Kolumban HutterEmail author
  • Yongqi Wang
  • Irina P. Chubarenko
Chapter
Part of the Advances in Geophysical and Environmental Mechanics and Mathematics book series (AGEM)

Abstract

We have expressed the fundamental physical ideas – that mass, momentum and energy must be conserved – in the form of mathematical equations (balance laws) and demonstrated that the balance of moment of momentum in its local expression for a continuum requests that the (Cauchy) stress tensor is symmetric, but beyond this does not produce any further local equation. So, it appears that the conservation law of moment of momentum is superfluous. This is not so; correct is that by requesting the Cauchy stress to be symmetric and exploiting pointwise the balances of mass, momentum and energy then automatically also guarantee the balance law of angular momentum to be identically satisfied. However, since physically, linear momentum is associated with the translational motion and angular momentum with the rotatory motion, the rotational behavior can often better be identified if the law of balance of angular momentum is explicitly employed.

Keywords

Angular Momentum Potential Vorticity Relative Vorticity Vortex Filament 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.
    Bearman, G. (ed.): Ocean Circulation. The Open University. Butterworth-Heinemann. Oxford, Boston, MA, 238 p. (1998)Google Scholar
  2. 2.
    Dietrich G., Kalle, K., Krauss, W. and Siedler, G.: General Oceanography. 2nd Edition Translated by Susanne and Hans Ulrich Roll. Wiley (Wiley-Interscience) New York, NY (1980)Google Scholar
  3. 3.
    Ertel, H.: Ein neuer hydrodynamischer Erhaltungssatz. Die Naturwissenschaften 30. Jg. Heft 36, 543–544 (1942)CrossRefGoogle Scholar
  4. 4.
    Ertel, H.: Ein neuer hydrodynamischer Wirbelsatz. Meteorologische Zeitschrift 59. Jg. Heft 9, 277–281 (1942)Google Scholar
  5. 5.
    Ertel, H.: Über hydrodynamische Wirbelsätze. Physik. Z. (Leipzig) 59. Jg. Heft, 526–529 (1942)Google Scholar
  6. 6.
    Ertel, H.: Über das Verhältnis des neuen hydrodynamischen Wirbelsatzes zum Zirkulationssatz von V. Bjerknes. Meteorologische Zeitschrift 59 Jg. Heft 12, 161-168, (1942)Google Scholar
  7. 7.
    Hide, R.: The magnetic analogue of Ertel’s potential vorticity theorem. Ann. Geophysicae 1(1), 59–60 (1983)Google Scholar
  8. 8.
    Katz, J.: Relativistic potential vorticity. Proc. R. Soc. London A 391, 415–418 (1984)CrossRefGoogle Scholar
  9. 9.
    Pedlosky, J.: Geophysical Fluid Dynamics. Springer, Berlin (1982)Google Scholar
  10. 10.
    Schröder, W. and Treder, H.-J.: Theoretical concepts and observational implications in meteorology and geophysics (Selected papers from the IAGA symposium to commemorate the 50th anniversary of Ertel’s potential vorticity). Interdivisional commission on history of the International Association of Geomagnetism and Aeronomy. ISSN: 179-5658.Google Scholar
  11. 11.
    Treder, H.-J.: Zur allgemeinen relativistischen und kovarianten Integralformen der Ertelschen Wirbeltheoreme. Gerlands Beitr. Geophys. 79, 1 (1970)Google Scholar
  12. 12.
    Truesdell, C.A.: On Ertel’s vorticity theorem. Zeitschrift für Angew. Math. & Phys. (ZAMP) 2, 109–114 (1951)CrossRefGoogle Scholar
  13. 13.
    Truesdell, C.A. and Toupin, R.C.: The Classical Field Theories of Mechanics: In Handbuch der Physik (ed. S. Flügge) Bd. III/1. Prinzipien der klassischen Mechanik und Feldtheorie, Springer, Berlin (1960)Google Scholar
  14. 14.
    Zatsepin, A.G., Gritsenko, V.A., Kremenetsky, V.V., Poyarkov, S.G. and Stroganov, O.Yu.: Laboratory and numerical investigation of process of propagation of density currents along bottom slope. Oceanology 45(1), 5–15 (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Kolumban Hutter
    • 1
    Email author
  • Yongqi Wang
    • 2
  • Irina P. Chubarenko
    • 3
  1. 1.ETH Zürich, c/o Versuchsanstalt für Wasserbau Hydrologie und GlaziologieZürichSwitzerland
  2. 2.Department of Mechanical EngineeringDarmstadt University of TechnologyDarmstadtGermany
  3. 3.Russian Academy of Sciences, P.P. Shirshov Institute of OceanologyKaliningradRussia

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