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We present a high-resolution, highly stratified numerical simulation ofrotating thermal convection in a spherical shell. Our aim is to study in detailthe processes that can maintain a near surface shear layer (NSSL) as inferredfrom helioseismology. Using the reduced speed of sound technique we can extendour global convection simulation to $0.99\,R_{\odot}$ and include near the topof our domain small-scale convection with short time scales that is only weaklyinfluenced by rotation. We find the formation of a NSSL preferentially in highlatitudes in the depth range $r=0.95-0.975R_\odot$. The maintenance mechanismsare summarized as follows. Convection under weak influence of rotation leads toReynolds stresses that transport angular momentum radially inward in alllatitudes. This leads to the formation of a strong poleward directed meridionalflow and a NSSL, which is balanced in the meridional plane by forces resultingfrom the $\langle v'_r v'_\theta\rangle$ correlation of turbulent velocities.The origin of the required correlations depends to some degree on latitude. Inhigh latitudes a positive correlation $\langle v'_rv'_\theta\rangle$ is inducedin the NSSL by the poleward meridional flow whose amplitude increases with theradius, while a negative correlation is generated by the Coriolis force in bulkof the convection zone. In low latitudes a positive correlation $\langlev'_rv'_\theta\rangle$ results from rotationally aligned convection cells("banana cells"). The force caused by these Reynolds stresses is in balancewith the Coriolis force in the NSSL.

High-resolution calculation of the solar global convection with the reduced speed of sound technique: II. Near surface shear layer with the rotation