  The helioseismic observations of the internal rotation profile of the Sun
raise questions about the two-dimensional (2D) nature of the transport of
angular momentum in stars. Here we derive a convective prescription for
axisymmetric (2D) stellar evolution models. We describe the small scale motions
by a spectrum of unstable linear modes in a Boussinesq fluid. Our saturation
prescription makes use of the angular dependence of the linear dispersion
relation to estimate the anisotropy of convective velocities. We are then able
to provide closed form expressions for the thermal and angular momentum fluxes
with only one free parameter, the mixing length.
  We illustrate our prescription for slow rotation, to first order in the
rotation rate. In this limit, the thermodynamical variables are spherically
symetric, while the angular momentum depends both on radius and latitude. We
obtain a closed set of equations for stellar evolution, with a self-consistent
description for the transport of angular momentum in convective regions. We
derive the linear coefficients which link the angular momentum flux to the
rotation rate ($\Lambda$- effect) and its gradient ($\alpha$-effect). We
compare our results to former relevant numerical work.
