Conservation of Angular Momentum–Vorticity

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


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.


Angular Momentum Potential Vorticity Relative Vorticity Vortex Filament Vorticity Vector 
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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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