  Context: The observations of rapidly rotating stars are increasingly detailed
and precise thanks to interferometry and asteroseismology; two-dimensional
models taking into account the hydrodynamics of these stars are very much
needed.
  Aims: A model for studying the dynamics of baroclinic stellar envelope is
presented.
  Methods: This models treats the stellar fluid at the Boussinesq approximation
and assumes that it is contained in a rigid spherical domain. The temperature
field along with the rotation of the system generate the baroclinic flow.
  Results: We manage to give an analytical solution to the asymptotic problem
at small Ekman and Prandtl numbers. We show that, provided the Brunt-Vaisala
frequency profile is smooth enough, differential rotation of a stably
stratified envelope takes the form a fast rotating pole and a slow equator
while it is the opposite in a convective envelope. We also show that at low
Prandtl numbers and without $\mu$-barriers, the jump in viscosity at the
core-envelope boundary generates a shear layer staying along the tangential
cylinder of the core. Its role in mixing processes is discussed.
  Conclusions: Such a model provides an interesting tool for investigating the
fluid dynamics of rotating stars in particular for the study of the various
instabilities affecting baroclinic flows or, even more, of a dynamo effect.
