Dynamical Age of Alfvénic 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, $σ_c$), 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 Alfvénic 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 Alfvénicity, the present approach yields smaller values of $A_\text{t}$ in medium-to-high $σ_c$ 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.

Figures (4)

• Figure 1: The function $f(\sigma_c)$ [Eq. \ref{['eq:f_sigc']}].
• Figure 2: Joint pdfs of turbulence age and solar wind speed, computed from 25 years of ACE observations at 1 AU. Bins with fewer than 5 counts are neglected. The pdf of each "column", or speed bin, has been normalized by the total counts in that bin. Cyan circles and vertical bars show mean and $1\sigma$ of $A_\text{t}$ within slow ($U< 400$), medium ($400 \le U< 600$), and fast ($U\ge 600$) intervals. Left and right panels show $A_\text{t}$ computed using Eqs. \ref{['eq:At1']} and \ref{['eq:At2']}, respectively, with 1 AU observations (see text). The relative decrease in $A_\text{t}$ for medium and fast wind when accounting for $\sigma_c$ (right panel) is evident.
• Figure 3: Left: Radial evolution of $A_\text{t}$ in slow and fast solar wind, evaluated from PSP as described in the text. Right: Radial evolution of $A_\text{t}$ in simulation, at low (blue) and high (red) heliolatitudes. In both panels $A_\text{t1}$ and $A_\text{t2}$ are evaluated using Eqs. \ref{['eq:At1']} and \ref{['eq:At2']}, respectively, with the latter accounting for $\sigma_c$.
• Figure 4: Radial evolution of turbulence age between $\sim 0.2$ and 40 AU. PSP, ACE, and global simulation results are computed using Eq. \ref{['eq:At2']}, while Voyager 1 result is adapted from Matthaeus et al. 1998. Top: Solid dark-red curve shows $A_\text{t2}$ computed from PSP observations averaged in radial bins. Tan-shaded region (between 0.2 and 0.8 AU) represents the statistical spread in $A_\text{t2}$ computed from PSP. See text for details. Blue circle at 1 AU marks $A_\text{t2}$ computed from ACE, with vertical bars marking the $1\sigma$ spread. Pale-green shaded region between 0.2 and 40 AU shows $A_\text{t2}$ computed from the Usmanov et al. (2025) solar wind model in the ecliptic region, with upper and lower bounds of the shaded area corresponding to heliolatitudes of $7\degree$ and $0\degree$, respectively. Dashed curves show $A_\text{t}$ adapted from Fig. 2 of Matthaeus et al. (1998); their result has been shifted upwards by ad-hoc amounts (constant in $r$) to "line up" at 1 AU with the trends from PSP and the global simulation (see text). Bottom: Rate of change of $A_\text{t}$: $\frac{dA_\text{t}}{dt}=U\frac{dA_\text{t}}{dr}$ (see text).