Journal of Fluid Mechanics

A note on Hamilton's principle for perfect fluids

Francis P.  Bretherton a1
a1 Department of Earth and Planetary Sciences, The Johns Hopkins University

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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.

(Published Online March 29 2006)
(Received September 24 1969)
(Revised May 12 1970)