  We have performed the first three-dimensional non-linear simulation of the
turbulent convective envelope of a rotating 0.8 Msun RGB star using the ASH
code. Adopting a global typical rotation rate of a tenth of the solar rate, we
have analyzed the dynamical properties of the convection and the transport of
angular momentum within the inner 50% in radius of the convective envelope. The
convective patterns consist of a small number of large cell, associated with
fast flows (about 3000 m/s) and large temperature fluctuations (about 300 K) in
order to carry outward the large luminosity (L* = 400 Lsun) of the star. The
interactions between convection and rotation give rise to a large radial
differential rotation and a meridional circulation possessing one cell per
hemisphere, the flow being poleward in both hemisphere. By analysing the
redistribution of angular momentum, we find that the meridional circulation
transports the angular momentum outward in the radial direction, and poleward
in the latitudinal direction, and that the transport by Reynolds stresses acts
in the opposite direction. From this 3-D simulation, we have derived an average
radial rotation profile, that we will ultimately introduce back into 1-D
stellar evolution code.
