Helicity conservation laws

  • Zbigniew PeradzyŃSki
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)


Using the language of differential forms on a space-time, one can write the equation of an ideal fluid in a form similar to the Maxwell equations. Vorticity current plays then the role of the source term and the Euler equations can be interpreted as the generalisation, to the whole space-time, of the well-known fact that the number of vortex lines passing through any two-dimensional surface spanned on a closed contour can be expressed by a circulation associated with this contour. A similar procedure can be used for the ideal MHD. It appears that by using this formulation various helicity conservation theorems may be derived in the natural and straightforward manner.


Euler Equation Differential Form Vortex Line Exterior Derivative Vector Notation 
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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Zbigniew PeradzyŃSki
    • 1
    • 2
  1. 1.Institute of Applied Mathematics and MechanicsWarsaw UniversityWarsaw
  2. 2.Institute of Fundamental Technological ResearchWarsawPoland

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