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(abridged) Context. Turbulent fluxes of angular momentum and heat due torotationally affected convection play a key role in determining differentialrotation of stars. Here we perform a systematic comparison between Cartesianand spherical geometries as a function of the rotation rate. Aims. We extendthe earlier studies by using spherical wedges to obtain turbulent angularmomentum and heat transport as functions of the rotation rate from stratifiedconvection. We compare results from spherical and Cartesian models in the sameparameter regime. In particular, we want to clarify whether the sharpequatorial profile of the horizontal Reynolds stress found in earlier Cartesianmodels is reproduced in spherical models. Methods. We employ direct numericalsimulations of turbulent convection. In order to reach as high spatialresolution as possible in the spherical runs, we model only parts of thelatitude and longitude. The rotational influence, measured by the Coriolisnumber, is varied from zero to roughly seven, which is the regime that islikely to be realised in the solar convection zone. Cartesian simulations areperformed in overlapping parameter regimes. Results. For slow rotation we findthat the radial and latitudinal turbulent angular momentum fluxes are directedinward and equatorward, respectively. In the rapid rotation regime the radialflux changes sign in contradiction with theory. The latitudinal flux remainsmostly equatorward and develops a maximum close to the equator. In Cartesiansimulations this peak can be explained by the strong `banana cells'. Thelatitudinal heat flux is mostly equatorward for slow rotation but changes signfor rapid rotation. The rotation profiles vary from anti-solar (slow equator)for slow and intermediate rotation to solar-like (fast equator) for rapidrotation. The solar-like profiles are dominated by the Taylor--Proudmanbalance.

Reynolds stress and heat flux in spherical shell convection