  The purpose of this paper is to improve the modelization of the rotational
mixing which occurs in stellar radiation zones, through the combined action of
the thermally driven meridional circulation and of the turbulence generated by
the shear of differential rotation. The turbulence is assumed to be
anisotropic, due to the stratification, with stronger transport in the
horizontal directions than in the vertical. The main difference with the former
treatments by Zahn (1992) and Maeder & Zahn (1998) is that we expand here the
departures from spherical symmetry to higher order, and include explicitly the
differential rotation in latitude, to first order. This allows us to treat
simultaneously the bulk of a radiation zone and its tachocline(s). Moreover, we
take fully into account the non-stationarity of the problem, which will enable
us to tackle the rapid phases of evolution. The system of partial differential
equations, which govern the transport of angular momentum, heat and chemical
elements, is written in a form which makes it ready to implement in a stellar
evolution code. Here the effect of a magnetic field is deliberately ignored; it
will be included in forthcoming papers.
