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Magnetohydrodynamic wave mixing in shear flows: Hamiltonian equations and wave action

Published online by Cambridge University Press:  01 February 2007

G. M. WEBB ,
E. Kh. KAGHASHVILI  and
G. P. ZANK
G. M. WEBB
Affiliation:
Institute of Geophysics and Planetary Physics, University of California Riverside, Riverside, CA 92521, USA ([email protected])
E. Kh. KAGHASHVILI
Affiliation:
Institute of Geophysics and Planetary Physics, University of California Riverside, Riverside, CA 92521, USA ([email protected])
G. P. ZANK
Affiliation:
Institute of Geophysics and Planetary Physics, University of California Riverside, Riverside, CA 92521, USA ([email protected])
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Abstract.

Magnetohydrodynamic wave interactions in a linear shear flow are investigated using the Lagrangian fluid displacement ξ and entropy perturbation Δ S, in which a spatial Fourier solution is obtained in the frame of the background shear flow (Kelvin's method). The equations reduce to three coupled oscillator equations, with time-dependent coefficients and with source terms proportional to the entropy perturbation. In the absence of entropy perturbations, the system admits a wave action conservation integral consisting of positive and negative energy waves. Variational and Hamiltonian forms of the equations are obtained. Examples of wave amplification phenomena and sharp resonant-type wave interactions are obtained. Implications for the interaction of magnetohydrodynamic waves in the shear flow between fast, polar coronal-hole solar wind and slow, streamer belt solar wind are discussed.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 1 , February 2007 , pp. 15 - 68
Copyright
Copyright © Cambridge University Press 2006

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