Reflection-driven MHD turbulence in the solar atmosphere and solar wind
Abstract
We present 3D numerical simulations and an analytic model of reflection-driven MHD turbulence in the solar wind. Our simulations describe transverse, non-compressive MHD fluctuations within a narrow magnetic flux tube that extends from the photosphere out to a heliocentric distance r of 21 solar radii (Rs). We launch outward-propagating "z+ fluctuations" into the simulation domain by imposing a randomly evolving photospheric velocity field. As these fluctuations propagate away from the Sun, they undergo partial reflection, producing inward-propagating "z- fluctuations." Counter-propagating fluctuations subsequently interact, causing fluctuation energy to cascade to small scales and dissipate. Our analytic model incorporates alignment, allows for strongly or weakly turbulent nonlinear interactions, and divides the z+ fluctuations into two populations with different characteristic radial correlation lengths. The inertial-range power spectra in our simulations evolve toward a k-3/2 scaling at r>10 Rs, where k is the wave-vector component perpendicular to the background magnetic field. In two of our simulations, the z+ power spectra are much flatter between the coronal base and r 4 Rs. We argue that these spectral scalings are caused by: (1) high-pass filtering in the upper chromosphere; (2) the anomalous coherence of inertial-range z- fluctuations in a reference frame propagating outwards with the z+ fluctuations; and (3) the change in the sign of the radial derivative of the Alfv\'en speed at r=rm 1.7 Rs, which disrupts this anomalous coherence between r=rm and r 2rm. At r>1.3 Rs, the turbulent heating rate in our simulations is comparable to the heating rate in a previously developed solar-wind model that agreed with a number of observational constraints.