A new Hamiltonian formulation for fluids and plasmas. Pt. 2: MHD models

The new Hamiltonian formulation of the perfect fluid equations presented in part 1 of this series of papers is generalized to a class of MHD models, including for example ideal MHD and the Chew-Goldberger-Low equations. The mathematical structure is to a great extent unchanged by this generalization, and most results about the small-amplitude expansion of the perfect fluid equations remain obviously valid. For example, we now have a rigorous proof of the Manley-Rowe relations in resonant three-wave interaction, valid for this class of MHD models and for quite general inhomogeneous but stationary background states, including equilibrium flows. (author)