Effective Magnetic Reynolds Number Research Articles

Measurement of the Taylor Microscale and the Effective Magnetic Reynolds Number in the Solar Wind With Cluster

AbstractWe use magnetic field data from the Cluster mission to estimate the value of the Taylor microscale and the effective magnetic Reynolds number in the interplanetary solar wind. Turbulent cascades can be characterized by the spatial scale at which dissipation begins to impact the local energy transfer, estimated by the Taylor microscale, as well as the separation between the injection and dissipation scales, estimated by the effective magnetic Reynolds number. Estimating the Taylor microscale requires measurements of the autocorrelation function at small separations. The Cluster spacecraft have exceptionally sensitive search coil magnetometers with high time resolution, making them ideal for measuring the Taylor microscale. We obtain a value of km; smaller than most previous measurements. We interpret this value as being smaller due to the higher time resolution, enabling the curvature of the autocorrelation function to be measured closer to the origin, giving a more accurate measurement. Combining the Taylor Microscale's computed value with concurrent correlation length measurements, we obtain a value of for the effective magnetic Reynolds number, which compares well to other observations. The four spacecraft of Cluster also allow directions transverse to the flow to be surveyed. The small separations (7 km) of Clusters 3 and 4 show that the Taylor microscale may vary as a function of direction to the mean magnetic field direction. The observed differences are small, requiring more observations to confirm this anisotropy.

The Variation of the Solar Wind Correlation Scale and Taylor Scale Upstream of Mars Observed by MAVEN

The correlation scale and Taylor scale, which characterize the turbulence and dissipation levels, of the solar wind upstream of Mars are determined using the Mars atmosphere and volatile evolution magnetic field data from 2015 to 2020, which covers half of a solar cycle from the solar maximum to the solar minimum. Our analysis suggests that the correlation scale varies between 10 and 20 hr and the Taylor scale between 0.3 and 1 s. Applying the frozen-in flow approximation, we convert the two temporal scales to the two spatial scales, which are about (1.5–3.0) × 107 km and 150–500 km, respectively. We further compare the correlation scale and Taylor scale to the sunspot number (SSN) to study the impacts of solar activity. The highest correlation coefficient between the correlation scale and the SSN is 0.78, where the two data sets are shifted by 16 months with the correlation scale behind the SSN. For the Taylor scale, the highest correlation coefficient is 0.52 with the time lag of 17 months. We also analyze the effective magnetic Reynolds number that is the square of the ratio of the two scales. It is more than 3 × 109, suggesting the good assumption of the frozen-in flow. However, its correlation with the SSN is weak.

The Solar-cycle Variations of the Anisotropy of Taylor Scale and Correlation Scale in the Solar Wind Turbulence

Abstract The field-aligned anisotropy of the solar wind turbulence, which is quantified by the ratio of the parallel to the perpendicular correlation (and Taylor) length scales, is determined by simultaneous two-point correlation measurements during the time period 2001–2017. Our results show that the correlation scale along the magnetic field is the largest, and the correlation scale in the field-perpendicular directions is the smallest, at both solar maximum and solar minimum. However, the Taylor scale reveals inconsistent results for different stages of the solar cycles. During the years 2001–2004, the Taylor scales are slightly larger in the field-parallel directions, while during the years 2004–2017, the Taylor scales are larger in the field-perpendicular directions. The correlation coefficient between the sunspot number and the anisotropy ratio is employed to describe the effects of solar activity on the anisotropy of solar wind turbulence. The results show that the correlation coefficient regarding the Taylor scale anisotropy (0.65) is larger than that regarding the correlation scale anisotropy (0.43), which indicates that the Taylor scale anisotropy is more sensitive to the solar activity. The Taylor scale and the correlation scale are used to calculate the effective magnetic Reynolds number, which is found to be systematically larger in the field-parallel directions than in the field-perpendicular directions. The correlation coefficient between the sunspot number and the magnetic Reynolds number anisotropy ratio is −0.75. Our results will be meaningful for understanding the solar wind turbulence anisotropy and its long-term variability in the context of solar activity.

Transition from hydrodynamic turbulence to magnetohydrodynamic turbulence in von Kármán flows

AbstractThe influence of an externally applied magnetic field on flow turbulence is investigated in liquid-gallium von-Kármán (VK) swirling flows. Time-resolved measurements of global variables (such as the flow power consumption) and local recordings of the induced magnetic field are made. From these measurements, an effective Reynolds number is introduced as ${\mathit{Rm}}_{\mathit{eff}} = \mathit{Rm}(1\ensuremath{-} \ensuremath{\alpha} \sqrt{N} )$, so as to take into account the influence of the interaction parameter $N$. This effective magnetic Reynolds number leads to unified scalings for both global variables and the locally induced magnetic field. In addition, when the flow rotation axis is perpendicular to the direction of the applied magnetic field, significant flow and induced magnetic field fluctuations are observed at low interaction parameter values, but corresponding to an Alfvèn speed ${v}_{A} $ of the order of the fluid velocity fluctuations ${u}_{\mathit{rms}} $. This strong increase in the flow fluctuations is attributed to chaotic changes between hydrodynamic and magnetohydrodynamic velocity profiles.

MHD simulations of the magnetorotational instability in a shearing box with zero net flux

Aims. We study the properties of MHD turbulence driven by the magnetorotational instability (MRI) in accretion disks. To do this we perform a series of numerical simulations for which the resolution is gradually increased. Methods. We adopt the local shearing box model and focus on the special case for which the initial magnetic flux threading the disk vanishes. We employ the finite difference code ZEUS to evolve the ideal MHD equations. Results. Performing a set of numerical simulations in a fixed computational domain with increasing resolution, we demonstrate that turbulent activity decreases as resolution increases. The highest resolution considered is 256 grid cells per scale height. We quantify the turbulent activity by measuring the rate of angular momentum transport through evaluating the standard a parameter. We find a = 0.004 when (N x , N Y , N z ) = (64,100,64), a = 0.002 when (N x , N y , N z ) = (128,200,128) and a = 0.001 when (N x , N y , N z ) = (256,400, 256). This steady decline is an indication that numerical dissipation, occurring at the grid scale is an important determinant of the saturated form of the MHD turbulence. Analysing the results in Fourier space, we demonstrate that this is due to the MRI forcing significant flow energy all the way down to the grid dissipation scale. We also use our results to study the properties of the numerical dissipation in ZEUS. Its amplitude is characterised by the magnitude of an effective magnetic Reynolds number Re M which increases from 10 4 to 10 5 as the number of grid points is increased from 64 to 256 per scale height. Conclusions. The simulations we have carried out do not produce results that are independent of the numerical dissipation scale, even at the highest resolution studied. Thus it is important to use physical dissipation, both viscous and resistive, and to quantify contributions from numerical effects, when performing numerical simulations of MHD turbulence with zero net flux in accretion disks at the resolutions normally considered.

Taylor scale and effective magnetic Reynolds number determination from plasma sheet and solar wind magnetic field fluctuations

Cluster data from many different intervals in the magnetospheric plasmas sheet and the solar wind are employed to determine the magnetic Taylor microscale from simultaneous multiple point measurements. For this study we define the Taylor scale as the square root of the ratio of the mean square magnetic field (or velocity) fluctuations to the mean square spatial derivatives of their fluctuations. The Taylor scale may be used, in the assumption of a classical Ohmic dissipation function, to estimate effective magnetic Reynolds numbers, as well as other properties of the small scale turbulence. Using solar wind magnetic field data, we have determined a Taylor scale value of 2400 ± 100 km, which is used to obtain an effective magnetic Reynolds number of about 260,000 ± 20,000, and in the plasma sheet we calculated a Taylor scale of 1900 ± 100 km, which allowed us to obtain effective magnetic Reynolds numbers in the range of about 7 to 110. The present determination makes use of a novel extrapolation technique to derive a statistically stable estimate from a range of small scale measurements. These results may be useful in magnetohydrodynamic modeling of the solar wind and the magnetosphere and may provide constraints on kinetic theories of dissipation in space plasmas.

Depolarization canals and interstellar turbulence

Recent radio polarization observations have revealed a plethora of unexpected features in the polarized Galactic radio background that arise from propagation effects in the random (turbulent) interstellar medium. The canals are especially striking among them, a random network of very dark, narrow regions clearly visible in many directions against a bright polarized Galactic synchrotron background. There are no obvious physical structures in the ISM that may have caused the canals, and so they have been called Faraday ghosts. They evidently carry information about interstellar turbulence but only now is it becoming clear how this information can be extracted. Two theories for the origin of the canals have been proposed; both attribute the canals to Faraday rotation, but one invokes strong gradients in Faraday rotation in the sky plane (specifically, in a foreground Faraday screen) and the other only relies on line-of-sight effects (differential Faraday rotation). In this review we discuss the physical nature of the canals and how they can be used to explore statistical properties of interstellar turbulence. This opens studies of magnetized interstellar turbulence to new methods of analysis, such as contour statistics and related techniques of computational geometry and topology. In particular, we can hope to measure such elusive quantities as the Taylor microscale and the effective magnetic Reynolds number of interstellar MHD turbulence.

Dynamics of helicity transport and Taylor relaxation

A simple model of the dynamics of Taylor relaxation is derived using symmetry principles alone. No statistical closure approximations are invoked or detailed plasma model properties assumed. Notably, the model predicts several classes of nondiffusive helicity transport phenomena, including traveling nonlinear waves and superdiffusive turbulent pulses. A universal expression for the scaling of the effective magnetic Reynolds number of a system undergoing Taylor relaxation is derived. Some basic properties of intermittency in helicity transport are examined.

Saturation and Thermalization of the Magnetorotational Instability: Recurrent Channel Flows and Reconnections

The nonlinear evolution and the saturation mechanism of the magnetorotational instability (MRI) are investigated using three-dimensional resistive MHD simulations. A local shearing box is used for our numerical analysis and the simulations begin with a purely vertical magnetic field. We find that the magnetic stress in the nonlinear stage of the MRI is strongly fluctuating. The time evolution shows the quasi-periodic recurrence of spike-shape variations typically for a few orbits which correspond to the rapid amplification of the magnetic field by the nonlinear growth of a two-channel solution followed by the decay through magnetic reconnections. The increase rate of the total energy in the shearing box system is analytically related to the volume-averaged torque in the system. We find that at the saturated state this energy gain of the system is balanced with the increase of the thermal energy mostly due to the joule heating. The spike-shape time evolution is a general feature of the nonlinear evolution of the MRI in the disks threaded by vertical fields and can be seen if the effective magnetic Reynolds number is larger than about unity.

Nonlinear magnetic reconnection with collisionless dissipation

An analytical model of two-dimensional collisionless reconnection in an X-type magnetic geometry is presented. The conversion of magnetic energy to the kinetic energy of accelerated ions takes place in the vicinity of the neutral line. The structure of this dissipation region and the magnetic energy release rate have been investigated both for linear and nonlinear regimes of collisionless reconnection. A simple model of global reconnection flow has been constructed, assuming an incompressible ideal magnetohydrodynamics approximation outside the dissipation region. The corresponding scaling for the external Mach number (Me) is found, which predicts a maximum reconnection rate Me=1/2R̃m −1/2, where R̃m≊(Le/λi)2≫1 is the effective magnetic Reynolds number for collisionless reconnection (Le is the global size of the system and λi is the ion inertial skin depth).

Magnetic ropes in the solar wind

The generation of magnetic fluctuations by MHD turbulence in the solar wind is discussed. An estimate of the effective magnetic Reynolds number in the solar wind based on a width of the inertial range of the turbulence is proposed. Dynamo activity is predicted to lead to generation of magnetic ropes whose length is of the order of the energy range scale, 2.5 × 1011 cm, and whose thickness can be as low as 5 × 108 cm. Experimental detection of the ropes would require determination of two‐point and higher correlation functions for the magnetic fluctuations in the solar wind.

On turbulent diffusion of magnetic fields and the loss of magnetic flux from stars

The turbulent diffusion of magnetic fields in astrophysical objects, and the processes leading to magnetic field flux loss from such objects are discussed with attention to the suppression of turbulent diffusion by back-reaction of magnetic fields on small spatial scales, and on the constraint imposed on magnetic flux loss by flux-freezing within stars. Turbulent magnetic diffusion can be suppressed even for very weak large-scale magnetic fields, so that 'standard' turbulent diffusion is incapable of significant magnetic flux destruction within a star. Finally, magnetic flux loss via winds is shown to be generally ineffective, no matter what the value of the effective magnetic Reynolds number is.

Fluid motions due to an electric current source

A concentrated electric current enters a region of fluid through an interface. It is shown that the magnetic field due to the current in general gives rise to rotational magnetic forces which must cause motions of the fluid. In particular the paper solves the axisymmetric non-linear problem in which a concentrated current enters a semi-infinite region of inviscid conducting fluid of constant density, inducing an inwards flow along the wall and a jet away from the wall opposite the current source. The case treated is the practically realistic one in which the effective magnetic Reynolds number is small and the current flows isotropically from the source. The first-order perturbation of this current distribution by electromagnetic induction is also calculated.An analytical solution is possible because the non-linear equation of motion happens to be a linear equation in the square of the Stokes stream function. The motion is analytically related to viscous jet flows discussed by Slezkin, Landau and Squire.