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The Reynolds number, Re , is an important quantity for describing a turbulent flow. It tells us about the bandwidth over which energy can cascade from large scales to smaller ones, prior to the onset of dissipation. However, calculating it for nearly collisionless plasmas like the solar wind is challenging. Previous studies have used formulations of an “effective” Reynolds number, expressing Re as a function of the correlation scale and either the Taylor scale or a proxy for the dissipation scale. We find that the Taylor scale definition of the Reynolds number has a sizable prefactor of approximately 27, which has not been employed in previous works. Drawing from 18 years of data from the Wind spacecraft at 1 au, we calculate the magnetic Taylor scale directly and use both the ion inertial length and the magnetic spectrum break scale as approximations for the dissipation scale, yielding three distinct Re estimates for each 12 hr interval. Average values of Re range between 116,000 and 3,406,000 within the general distribution of past work. We also find considerable disagreement between the methods, with linear associations of between 0.38 and 0.72. Although the Taylor scale method is arguably more physically motivated, due to its dependence on the energy cascade rate, more theoretical work is needed in order to identify the most appropriate way of calculating effective Reynolds numbers for kinetic plasmas. As a summary of our observational analysis, we make available a data product of 28 years of 1 au solar wind and magnetospheric plasma measurements from Wind.

We present a time-dependent, three-dimensional single-fluid model for the transport of magnetohydrodynamic (MHD) turbulence that is self-consistently evolving with a dynamic large-scale solar wind in the outer heliosphere. The emphasis is on the region beyond the termination shock, where the solar wind expands subsonically, as well as sub-Alfvénically and nonradially. In extension of earlier work, we refine the treatment of turbulence by considering, in addition to the Elsässer energies, a nonconstant energy difference (or residual energy) and by allowing each of these quantities its own characteristic correlation length scale. While the nonlinear effects in the equations for the Elsässer energies and their length scales are implemented using familiar von Kármán–Howarth style modeling of homogeneous MHD turbulence, the energy difference, which is not conserved in the absence of dissipation, and its length scale are modeled using distinct approaches. We also clarify the impact of the choice of measurement direction for correlation functions associated with two-dimensional fluctuations in transport models. Finally, we illustrate and study the solutions of the resulting six-equation model in detail.

Solar wind fluctuations admit well-documented anisotropies of the variance matrix, or polarization, related to the mean magnetic field direction. Typically, one finds a ratio of perpendicular variance to parallel variance of the order of 9:1 for the magnetic field. Here we study the question of whether a kinetic plasma spontaneously generates and sustains parallel variances when initiated with only perpendicular variance. We find that parallel variance grows and saturates at about 5% of the perpendicular variance in a few nonlinear times irrespective of the Reynolds number. For sufficiently large systems (Reynolds numbers) the variance approaches values consistent with the solar wind observations. [ABSTRACT FROM AUTHOR]