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.