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UBC Theses and Dissertations

A new variational principle in fluid mechanics Purcell, Anthony


A new variational principle in fluid mechanics is presented, based on a generalized version of the conservation of particle label constraint. The variational principle represents an extension of the work of Clebsch (1859) and C.C. Lin (1959) and for the one-component case it describes a perfect fluid with a finite density of vortices ; for the two-component fluid it yields the Khalatnikov equations for rapidly rotating superfluid ⁴He. In the latter case two particle label constraints are needed, which express the possibility of labelling both an element of normal fluid and a superfluid vortex, averaged over many vortices. In addition a negative result for a variational formulation of viscous fluids based on a generalized particle label constraint is given.

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