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

Article history: Received 12 October 2011 Received in revised form 8 December 2011 Accepted 9 December 2011 Available online 13 December 2011 Communicated by F. Porcelli 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. © 2011 Elsevier B.V. All rights reserved.