Helicity conservation laws
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.
KeywordsEuler Equation Differential Form Vortex Line Exterior Derivative Vector Notation
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- Peradzyński, Z. 1988 Properly posed boundary condition and the existence theorem insuperfluid He4. In Trends in Applications of Mathematics to Mechanics, Proc. 7th Symposium (ed. J.F. Besseling & W. Eckhaus), pp. 224–237. Springer Verlag.Google Scholar