Turbulent Heating in the Accelerating Region Using a Multishell Model

Abstract

Recent studies of turbulence-driven solar winds indicate that fast winds are obtained only at the price of unrealistic bottom boundary conditions: too large wave amplitudes and small frequencies. In this work, the incompressible turbulent dissipation is modeled with a large-scale von Karman–Howarth–Kolmogorov-like phenomenological expression ($Q_{\text{K41}}^{0}$). An evaluation of the phenomenology is thus necessary to understand if unrealistic boundary conditions result from physical or model limitations. To assess the validity of the Kolmogorov-like expression, $Q_{\text{K41}}^{0}$, one needs to compare it to exact heating, which requires describing the cascade in detail. This has been done in the case of homogeneous MHD turbulence, including expansion, but not in the critical accelerating region. To assess the standard incompressible turbulent heating in the accelerating region, we use a reduced MHD model (multishell model) in which the perpendicular turbulent cascade is described by a shell model, allowing to reach a Reynolds number of $10^{6}$. We first consider the homogeneous and expanding cases, and find that primitive MHD and multishell equations give remarkably similar results. We thus feel free to use the multishell model in the accelerating region. The results indicate that the large-scale phenomenology is inaccurate and it overestimates the heating by a factor at least 20, thus invalidating earlier studies of winds driven by incompressible turbulence. We conclude that realistic 1D wind models cannot be based solely on incompressible turbulence, but probably need an addition of compressible turbulence and shocks to increase the wave reflection and thus the heating.