Magnetohydrodynamic (MHD) wave interactions in a linear shear flow, are investigated using the Lagrangian fluid displacement ξ and entropy perturbation ΔS, 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. Implications for the interaction of MHD waves in the shear flow between fast polar coronal hole solar wind and slow streamer belt solar wind are discussed.
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