A framework is established for describing the transfer of magnetosheath energy along open field lines to the ionosphere in terms of MHD (magnetohydrodynamic) waves. The evolution of field lines crossing an initial velocity shear is shown to extract momentum and energy from the faster flow (magnetosheath) and deposit it in the slower flow. If the slower plasma is taken to be at rest and have density &rgr;0 and Alfv¿n speed VA, while the faster plasma has flow speed V0 and Alfv¿n speed VA', then the rate of energy density exchange is &rgr;0V20V3A/(VA+VA')2, while that of momentum density is &rgr;0V0V2A/(VA+VA'). The effect of an ionosphere is included by introducing a height-integrated Pedersen conductivity (&Sgr;p), and we find that field lines slip with a velocity V0/(1+&mgr;0&Sgr;pVA) just above the ionosphere. By considering the accelerated flows associated with newly opened field lines, it may be possible to understand transient features seen in data such as initial azimuthal surges. ¿ American Geophysical Union 1996