The differential rotation of the Sun, as deduced from helioseismology, exhibits a prominent radial shear layer near the top of the convection zone wherein negative radial gradients of angular velocity are evident in the low- and midlatitude regions spanning the outer 5% of the solar radius. Supergranulation and related scales of turbulent convection are likely to play a significant role in the maintenance of such radial gradients and may influence dynamics on a global scale in ways that are not yet understood. To investigate such dynamics, we have constructed a series of three-dimensional numerical simulations of turbulent compressible convection within spherical shells, dealing with shallow domains to make such modeling computationally tractable. In all but one case, the lower boundary is forced to rotate differentially in order to approximate the influence that the differential rotation established within the bulk of the convection zone might have upon a near-surface shearing layer. These simulations are the first models of solar convection in a spherical geometry that can explicitly resolve both the largest dynamical scales of the system (of order the solar radius) as well as smaller scale convective overturning motions comparable in size to solar supergranulation (20-40 Mm). We find that convection within these simulations spans a large range of horizontal scales, especially near the top of each domain, where convection on supergranular scales is apparent. The smaller cells are advected laterally by the larger scales of convection within the simulations, which take the form of a connected network of narrow downflow lanes that horizontally divide the domain into regions measuring approximately 100-200 Mm across. We also find that the radial angular velocity gradient in these models is typically negative, especially in the low- and midlatitude regions. Analyses of the angular momentum transport indicate that such gradients are maintained by Reynolds stresses associated with the convection, transporting angular momentum inward to balance the outward transport achieved by viscous diffusion and large-scale flows in the meridional plane, a mechanism first proposed by Foukal & Jokipii and tested by Gilman & Foukal. We suggest that similar mechanisms associated with smaller scale convection in the Sun may contribute to the maintenance of the observed radial shear layer located immediately below the solar photosphere.