2D dynamics of the radiation zone of low mass stars

The internal rotation of low mass stars all along their evolution is of primary interest when studying their rotational dynamics, internal mixing and magnetic fields generation. In this context, helio- and asteroseismology probe angular velocity gradients deep within solar type stars. Still the rotation of the close center of such stars on the main sequence is hardly detectable and the dynamical interactions of the radiative core with the surface convective envelope is not well understood. Among them, the influence of the differential rotation profile sustained by convection and applied as a boundary condition to the radiation zone may be very important leading to the formation of tachoclines. In the solar convective region, the equator is rotating faster than the pole while numerical simulations predict either a solar or an anti-solar rotation in other low mass stars envelopes depending on their convective Rossby number. In this work, we therefore build for the first time 2D steady hydrodynamical models of low mass stars radiation zone providing a full 2D description of their dynamics and studying the influence of a general shear boundary condition accounting for a solar or an anti-solar differential rotation in the convective envelope. We compute coherently differential rotation and the associated meridional circulation using the Boussinesq approximation.