Relabeling Symmetries in Hydrodynamics and Magnetohydrodynamics
نویسنده
چکیده
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 Eulerian variables are used to construct the Casimir invariants of the Hamiltonian formalism. In memory of Vladimir Petviashvili, who consistently had a sense of what is important.
منابع مشابه
Fluid element relabeling symmetry
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.
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