Gyrokinetic global particle-in-cell simulations for a small torus with a large aspect ratio (ϵ−1>∼7) indicate a k−α⊥ spectrum for electrostatic turbulence. When electrons are treated kinetically, the simulation results fit α that grows from about 1 at the plasma core to about 3 at the plasma edge for the flux surface component of the wave vector perpendicular to the magnetic field, while for adiabatic electrons α=4 is found for all radii, in agreement with the Hasegawa-Mima model. The relation between spectra and transport is investigated through the formation of an internal transport barrier. The role of flow shear in suppressing turbulence is illustrated by spectral diagnostics. A strong dependence between the presence of small wavenumbers and transport is explicitly observed. The simulated spectra are compared to recent experimental results.