Hamilton's principle and the vorticity laws for a relativistic perfect fluid |
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| Authors: | Rick Salmon |
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| Institution: | Scripps Institution of Oceanography , A-205, La Jolla, CA, 92093, USA |
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| Abstract: | Abstract The equations for a relativistic perfect fluid result from the requirement that the total mass-energy be stationary with respect to variations δxα(a, b, c, s) in the space-time location of the fluid particle identified by Lagrangian labels (a, b, c) at the point s on its world-line. By considering variations of the Lagrangian labels that leave the specific volume and entropy unchanged, we obtain a general covariant statement of vorticity conservation. The conservation laws for circulation, potential vorticity, and helicity are simple corollaries. This Noether-theorem derivation shows that the vorticity laws have no analogues in particle mechanics, where the corresponding particle labels cannot be continuously vaned. |
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| Keywords: | Vorticity Noether theorem relativistic perfect fluid |
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