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In this paper, we develop a formalism in order to incorporate thecontribution of internal gravity waves to the transport of angular momentum andchemicals over long time-scales in stars. We show that the development of adouble peaked shear layer acts as a filter for waves, and how the asymmetry ofthis filter produces momentum extraction from the core when it is rotatingfaster than the surface. Using only this filtered flux, it is possible tofollow the contribution of internal waves over long (evolutionary) time-scales.  We then present the evolution of the internal rotation profile using thisformalism for stars which are spun down via magnetic torquing. We show thatwaves tend to slow down the core, creating a "slow" front that may thenpropagate from the core to the surface. Further spin down of the surface leadsto the formation of a new front. Finally we show how this momentum transportreduces rotational mixing in a 1.2Msun, Z=0.02 model, leading to a surfacelithium abundance in agreement with observations in the Hyades.Comment: 14 pages, accepted for publication in A&

Hydrodynamical stellar models including rotation, internal gravity waves, and atomic diffusion