Fluid element relabeling symmetry
نویسندگان
چکیده
Lagrangian symmetries are found for hydrodynamics and magnetohydrodynamics, which result in conservation of potential vorticity and of cross helicity, respectively. These symmetries, which persist in the reduction from Lagrangian to Eulerian variables, directly give rise to Casimir invariants of the Hamiltonian formalism. The mechanism of spontaneous symmetry breaking in a fluid is also presented.
منابع مشابه
Relabeling Symmetries in Hydrodynamics and Magnetohydrodynamics
Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics, relabeling results in Ertel's theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eu...
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تاریخ انتشار 2008