  We study the formation and evolution of a turbulent spectrum of Alfv\'en
waves driven by reflection off the solar wind density gradients, starting from
the coronal base up to 17 solar radii, well beyond the Alfv\'enic critical
point. The background solar wind is assigned and 2D shell models are used to
describe nonlinear interactions. We find that the turbulent spectra are
influenced by the nature of reflected waves. Close to the base, these give rise
to a flatter and steeper spectrum for the outgoing and reflected waves
respectively. At higher heliocentric distance both spectra evolve toward an
asymptotic Kolmogorov spectrum. The turbulent dissipation is found to account
for at least half of the heating required to sustain the background imposed
solar wind and its shape is found to be determined by the reflection-determined
turbulent heating below 1.5 solar radii. Therefore reflection and
reflection-driven turbulence are shown to play a key role in the accelerationof
the fast solar wind and origin of the turbulent spectrum found at 0.3 AU in the
heliosphere.
