A note on Hamilton's principle for perfect fluids

A derivation is given of the Eulerian equations of motion directly from the Lagrangian formulation of Hamilton's principle. The circulation round a circuit of material particles of uniform entropy appears as a constant of the motion associated with the indistinguishability of fluid elements wit...

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Bibliographic Details
Published in:Journal of fluid mechanics 1970-10, Vol.44 (1), p.19-31
Main Author: Bretherton, Francis P.
Format: Article
Language:English
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Summary:A derivation is given of the Eulerian equations of motion directly from the Lagrangian formulation of Hamilton's principle. The circulation round a circuit of material particles of uniform entropy appears as a constant of the motion associated with the indistinguishability of fluid elements with equal density, entropy and velocity. A discussion is given of the Lin constraint, and it is pointed out that, for a barotropic fluid, the variational principle recently suggested by Seliger & Whitham does not permit velocity fields in which the vortex lines are knotted.
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112070001660