Turbulent cascade of incompressible unidirectional Alfvén waves in the interplanetary medium

The large-scale inhomogeneity of the solar wind is taken into account to estimate the turbulent flux due to nonlinear interactions among purely outward-traveling waves. The nonlinear interactions are mediated by secondary, incoming waves generated by the linear coupling of the dominant species to the large-scale gradients. A quasistationary self-similar turbulent cascade is possible, with a spectrum scaling as ${\mathrm{k}}^{\mathrm{-}1}$, close to what is found in the low-frequency range of solar-wind fluctuations near to the sun.