Using a novel wavenumber-advection algorithm, we show that profile curvature (shear in the profile gradient) can be implemented with spectral accuracy in gyrokinetic turbulence simulations. This approach enables a global simulation capability with the relatively low cost and high accuracy of local simulations. Using this new algorithm, we show that for a well-studied tokamak core test case, the effect of temperature-gradient curvature is below the threshold of detectability for experimentally-relevant values of curvature.