What is the Reynolds Number of the Solar Wind?

Abstract

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.

A Detailed Survey of the Parallel Mean Free Path of Solar Energetic Particle Protons and Electrons

“…Evaluating these theoretical pMFP estimates requires various turbulence parameter values as inputs. As these have been observed to vary significantly, including variations as a function of the solar cycle (see, e.g., Isaacs et al 2015;Oughton et al 2015;Zhao et al 2018;Engelbrecht & Wolmarans 2020;Burger et al 2022;Cuesta et al 2022;Wrench et al 2024), an ensemble of the values of turbulence quantities relevant to the theoretical pMFP expressions considered here is constructed. These values are then used to ascertain the potential variation of pMFPs, and compared with the observed values for this quantity reported on here, including bestfit estimations.…”