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 over long ( evolutionary ) time-scales .

We then present the evolution of the internal rotation profile using this formalism for stars which are spun down via magnetic torquing .
We show that waves tend to slow down the core , creating a “ slow ” front that may then propagate from the core to the surface .
Further spin down of the surface leads to the formation of a new front .
Finally we show how this momentum transport reduces rotational mixing in a 1.2 M _ { \odot } , Z = 0.02 model , leading to a surface lithium abundance in agreement with observations in the Hyades .