  Context. Stars experience rapid contraction or expansion at different phases
of their evolution. Modelling the angular momentum and chemical elements
transport occurring during these phases remains an unsolved problem.
  Aims. We study a stellar radiative zone undergoing radial contraction and
investigate the induced differential rotation and meridional circulation.
  Methods. We consider a rotating spherical layer crossed by an imposed radial
velocity field that mimics the contraction and solve numerically the
axisymmetric hydrodynamical equations in both the Boussinesq and anelastic
approximations. An extensive parametric study is conducted to cover regimes of
contraction, rotation, stable stratification and density stratification that
are relevant for stars.
  Results. The differential rotation and the meridional circulation result from
a competition between the contraction-driven inward transport of angular
momentum and an outward transport dominated by either viscosity or an
Eddington-Sweet type circulation, depending on the value of the $P_r \left( N_0
/ \Omega_0 \right)^2 $ parameter, where $P_r$ is the Prandtl number, $N_0$ the
Brunt-V\"ais\"ail\"a frequency and $\Omega_0$ the rotation rate. Taking the
density stratification into account is important to study more realistic radial
contraction fields but also because the resulting flow is less affected by
unwanted effects of the boundary conditions. In these different regimes and for
a weak differential rotation, we derive scaling laws that relate the amplitude
of the differential rotation to the contraction timescale.

Solar and Stellar Astrophysics