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Empirical Results on the Magnetic Prandtl Number in the Slow Solar Wind Based on In Situ Measurements.

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Title: Empirical Results on the Magnetic Prandtl Number in the Slow Solar Wind Based on In Situ Measurements.
Authors: Hand, T. J. E.1 (AUTHOR) teh14@aber.ac.uk, Roberts, O. W.1 (AUTHOR), Li, X.1 (AUTHOR), Knight, T.1 (AUTHOR), Narita, Y.2,3 (AUTHOR), Vörös, Z.4 (AUTHOR), Pitňa, A.5 (AUTHOR)
Source: Journal of Geophysical Research. Space Physics. Mar2026, Vol. 131 Issue 3, p1-12. 12p.
Subject Terms: Reynolds number, Dimensionless numbers, Measurement, Turbulence, Diffusion kinetics, Solar wind, Plasma diffusion
Abstract: The magnetic Prandtl number in the slow solar wind is estimated by using magnetic and velocity Reynolds numbers. The Prandtl number quantifies the ratio of kinetic to magnetic diffusion rates in a plasma, and indicates which process dominates the transport dynamics in a fluid. We use a combination of the correlation scale and the Taylor microscale to estimate the Reynolds numbers. We find Reynolds numbers of Re=1,500,000±260,000 $\mathrm{R}\mathrm{e}=1,500,000\pm 260,000$ and Rem=910,000±170,000 ${\mathrm{R}\mathrm{e}}_{m}=910,000\pm 170,000$. The magnetic Prandtl number is the ratio of kinetic to magnetic Reynolds numbers and is found to be: Prm=0.6±0.15 ${\mathrm{P}\mathrm{r}}_{m}=0.6\pm 0.15$ at 1 au. This novel result suggests the ratio of magnetic/kinetic diffusion is approximately unity in the slow wind, implying that the energy held by magnetic and velocity fields, for similar wavenumber ranges, is approximately equal, consistent with the approximately Alfvénic nature of the interval. Plain Language Summary: The solar wind is a turbulent, near‐collisionless system, as collisions between ions and electrons are negligible. Consequently, many classical characteristics of a turbulent system are difficult to define, such as viscosity and magnetic resistivity. Two characteristics of interest are the Reynolds number (a measure of the turbulent state of a system), and the magnetic Prandtl number (a measure of kinetic to magnetic diffusion). In this paper, we present measurements of the Reynolds number and the magnetic Prandtl number in the slow solar wind, employing techniques that do not require direct measurements of either viscosity or magnetic resistivity. Instead, two length scales are considered to establish the kinetic and magnetic Reynolds numbers: the correlation scale (size of the largest structures within a turbulent system) and the Taylor microscale (the size of structures where dissipation begins, prior to critical damping). These Reynolds numbers then lead to a final estimation of the magnetic Prandtl number. Key Points: Kinetic and magnetic effective Reynolds numbers are calculated at 1au using in situ dataEmpirical measurement of the magnetic Prandtl number is performed for the first timeResults show that the magnetic Prandtl number in the solar wind is close to unity [ABSTRACT FROM AUTHOR]
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Abstract:The magnetic Prandtl number in the slow solar wind is estimated by using magnetic and velocity Reynolds numbers. The Prandtl number quantifies the ratio of kinetic to magnetic diffusion rates in a plasma, and indicates which process dominates the transport dynamics in a fluid. We use a combination of the correlation scale and the Taylor microscale to estimate the Reynolds numbers. We find Reynolds numbers of Re=1,500,000±260,000 $\mathrm{R}\mathrm{e}=1,500,000\pm 260,000$ and Rem=910,000±170,000 ${\mathrm{R}\mathrm{e}}_{m}=910,000\pm 170,000$. The magnetic Prandtl number is the ratio of kinetic to magnetic Reynolds numbers and is found to be: Prm=0.6±0.15 ${\mathrm{P}\mathrm{r}}_{m}=0.6\pm 0.15$ at 1 au. This novel result suggests the ratio of magnetic/kinetic diffusion is approximately unity in the slow wind, implying that the energy held by magnetic and velocity fields, for similar wavenumber ranges, is approximately equal, consistent with the approximately Alfvénic nature of the interval. Plain Language Summary: The solar wind is a turbulent, near‐collisionless system, as collisions between ions and electrons are negligible. Consequently, many classical characteristics of a turbulent system are difficult to define, such as viscosity and magnetic resistivity. Two characteristics of interest are the Reynolds number (a measure of the turbulent state of a system), and the magnetic Prandtl number (a measure of kinetic to magnetic diffusion). In this paper, we present measurements of the Reynolds number and the magnetic Prandtl number in the slow solar wind, employing techniques that do not require direct measurements of either viscosity or magnetic resistivity. Instead, two length scales are considered to establish the kinetic and magnetic Reynolds numbers: the correlation scale (size of the largest structures within a turbulent system) and the Taylor microscale (the size of structures where dissipation begins, prior to critical damping). These Reynolds numbers then lead to a final estimation of the magnetic Prandtl number. Key Points: Kinetic and magnetic effective Reynolds numbers are calculated at 1au using in situ dataEmpirical measurement of the magnetic Prandtl number is performed for the first timeResults show that the magnetic Prandtl number in the solar wind is close to unity [ABSTRACT FROM AUTHOR]
ISSN:21699380
DOI:10.1029/2026JA035053