Dynamical Age of Alfv\'enic Turbulence in the Solar Wind

Abstract

An evolving turbulent flow such as the solar wind can be meaningfully characterized by its "turbulence age" -- an estimate of the number of nonlinear times that have elapsed during a plasma parcel's propagation from the Sun to a given point in space. Recent observations of the near-Sun solar wind by the \textit{Parker Solar Probe} (\textit{PSP}) indicate high correlation between velocity and magnetic fluctuations (i.e., cross helicity, $\sigma_c$), which is known to impede development of magnetohydrodynamic (MHD) turbulence. Here we propose a new formulation of the turbulence age ($A_\text{t}$) of the solar wind that explicitly accounts for the Alfv\'enic nature of the fluctuations in the inner heliosphere. $A_\text{t}$ is then evaluated for slow and fast wind streams using a variety of data sources -- observations from the \textit{PSP, Advanced Composition Explorer}, and \textit{Voyager} missions, and a global solar wind simulation that includes turbulence transport. Compared to the formulation employed in previous work that neglected Alfv\'enicity, the present approach yields smaller values of $A_\text{t}$ in medium-to-high $\sigma_c$ solar wind; similar turbulence ages are then obtained for slow and fast wind in the ecliptic. The radial evolution of $A_\text{t}$ between heliocentric distances of $r\sim 0.2$ to 40 AU is examined. The rate of increase of $A_\text{t}$ is found to decrease until $\sim 5$ AU, indicating a gradual slowing of the \textit{in situ} development of turbulence in the inner heliosphere. Beyond $\sim 5$ AU this rate begins to increase, likely due to turbulence driving by pick-up ions. This paper highlights the important role of cross helicity in modulating MHD turbulence, and the results will aid in further interpretations of observations of the radial evolution of various turbulence parameters in the solar wind.