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In this paper, we develop a formalism in order to incorporate the contribution of internal gravity waves to the transport of angular momentum and chemicals over long time-scales in stars. We show that the development of a double peaked shear layer acts as a filter for waves, and how the asymmetry of this filter produces momentum extraction from the core when it is rotating faster than the surface. Using only this filtered flux, it is possible to follow the contribution of internal waves overdoi:10.1051/0004-6361:20053020 fatcat:zaou25msrvfedjosvnmnrmjd4q