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

TL;DR

This study uses advanced numerical simulations to explore how inhomogeneous reduced MHD turbulence driven by Alfvén waves evolves from the Sun to the Alfvén critical point, revealing energy dissipation, spectral scaling, and wave alignment effects.

Contribution

First simulations to include solar wind outflow velocity and radial inhomogeneity without approximating nonlinear terms in RMHD turbulence.

Findings

15-33% of $z^+$ energy dissipates before the Alfvén point.

33-40% of input energy drives solar wind outflow.

Power spectra scale as $k_ot^{- ext{alpha}^ ext{pm}}$, with alpha decreasing with radius.

Abstract

We present direct numerical simulations of inhomogeneous reduced magnetohydrodynamic (RMHD) turbulence between the Sun and the Alfv\'en 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 Alfv\'en waves ($z^+$ fluctuations) launched from the Sun, which undergo partial non-WKB reflection to produce sunward-propagating Alfv\'en waves ($z^-$ fluctuations). We present ten simulations with different values of the correlation time $\tau_{\rm c\,\sun}^+$ and perpendicular correlation length $L_{\perp \sun}$ of outward-propagating Alfv\'en 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 Alfv\'en 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 $k_\perp^{-\alpha^\pm}$, where $k_\perp$ is the wavenumber in the plane perpendicular to $\vec{B}_0$. In our simulation with the smallest value of $\tau_{\rm c\,\sun}^+$ ($\sim 2 \mbox{min}$) and largest value of $L_{\perp \sun}$ ($2\times 10^4 \mbox{km}$), we find that $\alpha^+$ 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 $\tau_{\rm c\,\sun}^+$ exhibit alignment between the contours of constant $\phi^+$, $\phi^-$, $\Omega_0^+$, and $\Omega_0^-$, where $\phi^\pm$ are the Els\"asser potentials and $\Omega_0^\pm$ are the outer-scale parallel Els\"asser vorticities.