Latitudinal flux variations of thermal anelastic convection in a rotating spherical shell

International audienceFollowing interferometric observations of fast rotating stars, which now give new constraints on the latitudinal heat flux distribution, we investigate the influence of rotation on this quantity in solar-type stars, which own an outer convective envelope. To that end, we carried out a systematic parameter study of three-dimensional direct numerical simulations of anelastic convection in rotating spherical shells. As a first step, we neglect the centrifugal acceleration and retain only the Coriolis force. The fluid instability is driven by a fixed entropy drop between the inner and outer boundaries where stress-free boundary conditions are applied for the velocity field. Restricting our investigations to hydrodynamical models with a thermal Prandtl number fixed to unity, we consider both thick and thin shells with different degrees of stratification. We measure the heat transfer efficiency in terms of the Nusselt number, defined as the output luminosity normalised by the conductive state luminosity. We report diverse Nusselt number profiles in latitude, ranging from brighter (usually at the onset of convection) to darker equator and uniform profiles. We find that the luminosity contrast is mainly controlled by the surface value of the local Rossby number: when the Coriolis force dominates the force balance, the heat flux is weakened in the equatorial region by the zonal wind and enhanced at the poles by convective motions inside the tangent cylinder. But in presence of a strong background stratification, the radial dependence of the conductive entropy profile favours the sharp increase of the local Rossby number in the outer layers, which ultimately leads to the uniformisation of the surface heat flux distribution