In this talk I will present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfven critical point. These are the first such simulations that take into account the solar-wind outflow velocity and the radial inhomogeneity of the background solar wind without approximating the nonlinear terms in the governing equations. Our simulation domain is a narrow magnetic flux tube with a square cross section centered on a radial magnetic field line. RMHD turbulence is driven by outward-propagating Alfven waves (z^+ fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfven waves (z^- fluctuations). Nonlinear interactions between z^+ and z^- then cause fluctuation energy to cascade from large scales to small scales and dissipate. The simulations address the radial dependence of turbulence spectral slopes, energy cascade rates as well as other important turbulence characteristics in the context of existing phenomenological models.