Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics

Philip J. Morrison; John M. Greene

doi:10.1103/PhysRevLett.45.790

Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics

Philip J. Morrison and John M. Greene

Phys. Rev. Lett. 45, 790 – Published 8 September 1980; Erratum Phys. Rev. Lett. 48, 569 (1982)

Abstract

A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, $ρ$ , $\vec{v}$ , $\vec{B}$ , and $s$ , which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables.