Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems

Abstract

We present a Hamiltonian derivation of a class of reduced plasma two-dimensional fluid models, an example being the Charney-Hasegawa-Mima equation. These models are obtained from the same parent Hamiltonian model, which consists of the ion momentum equation coupled to the continuity equation, by imposing dynamical constraints. It is shown that the Poisson bracket associated with these reduced models is the Dirac bracket obtained from the Poisson bracket of the parent model.

References in corpus (4)

• The Hamiltonian description of incompressible fluid ellipsoids
• Hamiltonian derivation of the Charney-Hasegawa-Mima equation
• Canonical description of incompressible fluid -- Dirac brackets approach
• Recursive properties of Dirac and Metriplectic Dirac brackets with Applications

Cited by in corpus (7)

• On the Hamiltonian formulation of incompressible ideal fluids and magnetohydrodynamics via Dirac's theory of constraints
• The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
• Hamiltonian formulation of the modified Hasegawa Mima equation
• Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description
• Casimir invariants and the Jacobi identity in Dirac's theory of constrained Hamiltonian systems
• Mode signature and stability for a Hamiltonian model of electron temperature gradient turbulence
• Beatification: Flattening the Poisson Bracket for Two-Dimensional Fluid and Plasma Theories