Direct Numerical Simulations of Reflection-Driven, Reduced MHD Turbulence from the Sun to the Alfvén Critical Point

We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfvén 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. We impose periodic boundary conditions in the plane perpendicular to the background magnetic field B₀. RMHD turbulence is driven by outward-propagating Alfvén waves (z⁺ fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfvén waves (z^- fluctuations). Nonlinear interactions between z⁺ and z^- then cause fluctuation energy to cascade from large scales to small scales and dissipate. We present ten simulations with different values of the correlation time τ⁺_c⊙ and perpendicular correlation length L_⊥⊙ of outward-propagating Alfvén waves (AWs) at the coronal base. We find that between 15% and 33% of the z⁺ energy launched into the corona dissipates between the coronal base and Alfvén critical point, which is at r_A = 11.1R_⊙ in our model solar wind. Between 33% and 40% of this input energy goes into work on the solar-wind outflow, and between 22% and 36% escapes as z⁺ fluctuations through the simulation boundary at r=r_A. Except in the immediate vicinity of r=R_⊙, the z^× power spectra scale like k_⊥^-α×, where k_⊥ is the wavenumber in the plane perpendicular to B₀. In our simulation with the smallest value of τ⁺_c⊙ (~2 min) and largest value of L_⊥⊙ (~2×10⁴ km), we find that α⁺ decreases approximately linearly with increasing ln(r), reaching a value of~1.3 at r=11.1R_⊙. Our simulations with larger values of τ⁺_c⊙ exhibit alignment between the contours of constant Φ^× and Ω^×, where Φ^× are the Elsässer potentials and Ω^× are the outer-scale parallel Elsässer vorticities. This alignment reduces the efficiency of nonlinear interactions at r≥2R_⊙ to a degree that increases with increasing τ⁺_c⊙.