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Direct Numerical Simulations of Reflection-Driven, Reduced MHD Turbulence from the Sun to the Alfven 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. 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). We present ten simulations with different values of the correlation time $τ_{\rm c\,\sun}^+$ and perpendicular correlation length $L_{\perp \sun}$ 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. 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 $r=r_{\rm A}$. The $z^\pm$ power spectra scale like $k_\perp^{-α^\pm}$, where $k_\perp$ is the wavenumber in the plane perpendicular to $\vec{B}_0$. In our simulation with the smallest value of $τ_{\rm c\,\sun}^+$ ($\sim 2 \mbox{min}$) and largest value of $L_{\perp \sun}$ ($2\times 10^4 \mbox{km}$), we find that $α^+$ decreases approximately linearly with increasing $\ln(r)$, reaching a value of 1.3 at $r=11.1 R_{\sun}$. Our simulations with larger values of $τ_{\rm c\,\sun}^+$ exhibit alignment between the contours of constant $ϕ^+$, $ϕ^-$, $Ω_0^+$, and $Ω_0^-$, where $ϕ^\pm$ are the Elsässer potentials and $Ω_0^\pm$ are the outer-scale parallel Elsässer vorticities.