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

Abstract

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.

References in corpus (4)

• The Hamiltonian description of incompressible fluid ellipsoids
• Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems
• Canonical description of incompressible fluid -- Dirac brackets approach
• Recursive properties of Dirac and Metriplectic Dirac brackets with Applications

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