Alfvenic Turbulence and the Acceleration of the Fast Solar Wind

Alfvenic turbulence is usually invoked and used in many solar wind models (Isenberg & Hollweg 1982, Tu et al. 1984, Hu et al. 2000, Li 2003, Isenberg 2004) as a process responsible for the transfer of energy released at large scales in the photosphere towards small scales in the corona, where it is dissipated. Usually an initial spectrum is prescribed since its closest constraint is given by Helios measurements at 0.3 AU. With this work we intend to study the efficiency of the reflection as a driver for the nonlinear interactions of Alfven waves, the eventual development of a turbulent spectrum and its evolution in the highly stratified solar atmosphere inside coronal holes. We start imposing an upcoming flux of Alfven waves in a limited range of perpendicular wave numbers, at the base of the corona. Open boundary conditions allow the reflected waves to leave the domain form below and to be advected by the solar wind outside the top boundary. The nonlinear interaction in planes perpendicular to that of propagation (assumed to be radial) are treated with a 2D shell model, so that large Reynolds numbers are reached. Continuous interactions of counter propagating waves form a turbulent spectrum in the low corona, before the sonic point, in very short timescales (compared to the propagation timescales). Both the location and the value of the maximum of the dissipation (per unit mass) scale with the rms amplitude of the velocity fluctuations at the coronal base (delta u), while they are less sensitive to the frequency of the input flux of Alfven waves, provided it is small enough to power the turbulent cascade by means of reflection. For values of delta u in agreement with observational constraints, the turbulent dissipation achieves levels capable of sustaining a fast solar wind, with the maximum dissipation located at 2 solar radii, just below the sonic point. Despite the back reaction of the solar wind is not taken into account, this model shows that, under reasonable assumptions, a turbulent spectrum forms in the corona and it is able to sustain the heating and acceleration of the fast solar wind. Finally, the scaling laws obtained with this simplified 2D turbulence can be further constrained in order to include this mechanism of reflection driven turbulence in more complex solar wind models.