On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac's theory of constraints

Cristel Chandre (1, 2) , Philip Morrison (3) , Emanuele Tassi (1, 2)

1 CPT - Centre de Physique Théorique - UMR 7332
2 CPT - Ex E8 Dynamique non linéaire
3 IFS - Institute for Fusion Studies

The Hamiltonian structures of the incompressible ideal fluid, including entropy advection, and magnetohydrodynamics are investigated by making use of Dirac's theory of constrained Hamiltonian systems. A Dirac bracket for these systems is constructed by assuming a primary constraint of constant density. The resulting bracket is seen to naturally project onto solenoidal velocity fields.

Domaines: Physique des plasmas [physics.plasm-ph]; Dynamique des Fluides [physics.flu-dyn]; Dynamique Chaotique [nlin.CD]

Cristel Chandre, Philip Morrison, Emanuele Tassi. On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac's theory of constraints. Physics Letters A, 2012, 376 (5), pp.737. ⟨10.1016/j.physleta.2011.12.015⟩. ⟨hal-00631410⟩