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 1.2Msun, Z=0.02 model, leading to a surface
lithium abundance in agreement with observations in the Hyades.Comment: 14 pages, accepted for publication in A&
