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

Published online by Cambridge University Press:  13 March 2009

Jonas Larsson
Jonas Larsson
Affiliation:
Department of Plasma Physics, Umeå University, S-90187 Umeå, Swedent† and Lawrence Berkeley Laboratory, University of California, California 94720, U.S.A.
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Abstract

The new Hamiltonian formulation of the perfect fluid equations presented in part 1 of this series of papers is generalized to a class of IVIHD 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.

Type
Research Article
Information
Journal of Plasma Physics , Volume 55 , Issue 2 , April 1996 , pp. 261 - 278
Copyright
Copyright © Cambridge University Press 1996

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