A Simple Model for Reflection-Driven Spectral Evolution of Turbulence in the Corona and Inner Heliosphere

Dissipation of turbulence is generally considered as a prime candidate for the heating and acceleration of solar wind from the corona throughout the heliosphere, due to radially evolving dissipation processes and/or cascading of energy to dissipation scales. In order to model the latter consistently, we must consider the evolution of cross-helicity when modeling the strength of the cascade, as the non-linear interactions causing it require counterstreaming waves. In this paper, we present a simple model of non-WKB wave reflection from large-scale gradients, and apply the resulting cross-helicity to evaluate the evolution of the turbulence spectrum up to 0.3 AU by using a phenomenological cascade model. The study is restricted to a cascade in perpendicular direction. We study the ability of this spectral flux to heat the solar wind, and its dependence on the frequency of the excited waves. We find that the cascade advances fast in the low corona, and has a strong frequency dependence. The heating rate is high close to the coronal base, but decreases very quickly. In the corona, the heating rate varies by an order of magnitude in the frequency range of 10 to 10 Hz, suggesting that the shape and range of the frequency spectrum has important implications on the solar wind modeling.