An extended structure-function model and its application to the analysis of solar wind intermittency properties

An extended structure-function model is developed by including the new effect in the p-model of Meneveau and Sreenivasan which shows that the averaged energy cascade rate changes with scale, a situation which has been found to prevail in nonfullydeveloped turbulence in the inner solar wind. This model is useful for the small-scale fluctuations in the inner heliosphere, where the turbulence is not fully developed and cannot be explained quantitatively by any of the previous intermittency turbulence models. With two model parameters, the intrinsic index of the energy spectrum <alpha>, and the fragmentation fraction P ₁, the model can fit, for the first time, all the observed scaling exponents of the structure functions, which are calculated for time lags ranging from 81 s to 0.7 h from the Helios solar wind data. From the cases we studied we cannot establish for P ₁ either a clear radial evolution trend, or a solar-wind-speed or stream-structure dependence or a systematic anisotropy for both the flow velocity and magnetic field component fluctuations. Generally, P ₁ has values between 0.7 and 0.8. However, in some cases in low-speed wind P ₁ has somewhat higher values for the magnetic components, especially for the radial component. In high-speed wind, the inferred intrinsic spectral indices (<alpha>) of the velocity and magnetic field components are about equal, while the experimental spectral indices derived from the observed power spectra differ. The magnetic index is somewhat larger than the index of the velocity spectrum. For magnetic fluctuations in both high- and low-speed winds, the intrinsic exponent <alpha> has values which are near 1.5, while the observed spectral exponent has much higher values. In the solar wind with considerable density fluctuations near the interplanetary current sheet near 1 AU, it is found that P ₁ has a comparatively high value of 0.89 for V _x . The impact of these results on the understanding of the nature of solar wind fluctuations is discussed, and the limitations in using structure functions to study intermittency are also described.     

Intermittency analysis and spatial dependence of magnetic field disturbances in the fast solar wind

Based on Helios measurements, seven quantities of normalized PDF (Probability Distribution Function) associated with magnetic field and its disturbances are utilized to characterize the intermittency in the fast solar wind using Castaing distributions and the idea of “Flatness”. The magnetic field fluctuations are found to be more intermittent at farther distances from the sun. The “Flatness” decreases with increasing time scales, with the corresponding PDF eventually approaching Gaussian distributions. Such a transition occurs at a relatively small time scale for the perpendicular component of perturbed field. The increase in “Flatness” with decreasing time scale is more apparent farther from the sun. By examining how the relative energy density of magnetic disturbances at various time scales changes with the mean field, our study supports the idea that the perturbed fields in the fast solar wind in the frequency range considered are consistent with cross-scale redistribution of wave energy favoring larger scales.     

Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. Using present experimental technology in solar wind measurements we cannot directly measure the real volumetric dissipation rate, <varepsilon>(t), but are constrained to represent it by its surrogate the energy flux near the dissipation range at the proton gyro scale. There is evidence for the multifractal nature of the so defined dissipation field <varepsilon>(t), a result derived from the scaling exponents of its statistical moments. The generalized dimension D _q has been determined and reveals that the dissipation field has a multifractal structure, which is not compatible with a scale-invariant cascade. The related multifractal spectrum f(<alpha>) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D _q can for turbulence in high-speed streams be fitted well by the functional dependence of the p-model with a comparatively large parameter p ₁=0.87, indicating a strongly intermittent multifractal energy cascade. The experimental value for D _p/3 used in the scaling exponent s(p) of the velocity structure function gives an exponent that can describe some of the observations. The scaling exponent <mu> of the autocorrelation function of <varepsilon>(t) has also been directly evaluated, being 0.37. Finally, the mean dissipation rate was determined, which could be used in solar wind heating models.     

Small and large scale fluctuations in atmospheric wind speeds

Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences, no matter what location is considered. The shape of these PDFs is found to be robust over a wide range of scales which seems to contradict the mathematical concept of stability where a Gaussian distribution should be the limiting one. Motivated by the non-stationarity of atmospheric winds it is shown that the intermittent distributions can be understood as a superposition of different subsets of isotropic turbulence. Thus we suggest a simple stochastic model to reproduce the measured statistics of wind speed fluctuations.     

Intermittency of the solar wind density near the interplanetary shock

The properties of turbulent fluctuations of the solar wind plasma near the interplanetary shock observed at September 12, 2014 by the BMSW instrument are considered. The spectra of the density fluctuations in the solar wind and their statistical characteristics up-and downstream of the shock front are analyzed. They are compared with each other and with characteristics corresponding to different turbulence models. It is shown that the spectral and statistical characteristics of the density fluctuations in the solar wind conserve their basic properties after the arrival of an interplanetary shock. Intermittency is observed both before and after the front, but its level increases on average in the second case. In both regions, the scaling of the structure functions of the density fluctuations in the solar wind differ from the scaling of the classical Kolmogorov model and can be described by the log-Poisson turbulence model. Parameterization of the scaling of the structure functions revealed the presence of filamentary structures in the solar wind plasma, which provide the density intermittency in the studied space regions.     

Investigation of the amplitude features of high-latitude magnetic impulse events

The features of the amplitude distributions of magnetic impulse events have been investigated using the observations from a number of high-latitude observatories in the Northern and Southern hemispheres. It has been shown that the tails of the statistical distribution functions of the impulse amplitudes are approximated by a power law of the form f(A) = A ^−α, where A is the impulse amplitude and α is the exponent. Therefore, the magnetic-impulse generation regime corresponds to the features of the on-off intermittency model. The distribution of the magnetic impulse amplitudes has been analyzed for various geomagnetic latitudes, local times, seasons, solar activity cycle phases, and interplanetary conditions. It has been found that most statistical distributions of magnetic impulse amplitudes have the exponent α larger than 2, which is typical of the chaotic regimes called “strong turbulence.” In some cases, the exponent α is close to 1, which is typical of the regimes generated in a weakly turbulent medium. Qualitative estimates of the plasma wave turbulence level in the high-latitude magnetosphere have been obtained.     

Impact of interplanetary shock on parameters of plasma turbulence in the Earth’s magnetosheath

Data from the BMSW spectrometer, which measures the ion flux value and sometimes plasma parameters with a time resolution of 31 ms, allow the study of the parameters of turbulence of the solar wind and magnetosheath plasma on kinetic scales. In this work, the frequency spectra of the ion flux fluctuations before and after recording the interplanetary shock front in the Earth’s magnetosheath are compared based on these data. It is shown that, in contrast to the solar wind, where the exponential decay of the spectrum often occurs after the shock front on the kinetic scales, no such phenomenon is observed in the magnetosheath: the spectrum on these scales can be approximated by a power function in all the cases considered. In half of these cases, the spectrum slope on the kinetic scales does not change during the interplanetary shock propagation. The results indicate a weak impact of interplanetary shock waves on the parameters of the plasma turbulence. In addition, it is shown that an interplanetary shock does not change the level of intermittency of the ion flux in the magnetosheath at both low and high level before the front.     

Effect of the solar wind and IMF parameters on the formation of long-period irregular pulsation burst regimes

The excitation of long-period irregular pulsations in the 2.0–6.0 mHz range (ipcl pulsation series) in the Earth’s magnetosphere, depending on the set of solar wind plasma and IMF parameters, has been studied experimentally. It has been found that burst regimes are observed when the solar wind dynamic pressure and velocity are higher than V ∼ 320 km/s and P ∼ 1 nPa, respectively. It has been indicated that the dynamics of the ipcl pulsation intensity and fractal structure largely depend on the solar wind plasma velocity and magnetic pressure, respectively. An analysis of the relationship between the appearance of ipcl pulsation burst series and large-scale solar wind streams and polar coronal holes made it possible to identify solar geoeffective regions, which can cause solar wind streams and Alfvén waves that promote the generation of burst regimes. On the basis of the studied conditions of the interplanetary medium, favourable for the excitation of ipcl pulsation burst series, and generalization of morphological patterns, the possible mechanisms of their generation have been considerded. It has been demonstrated that ipcl burst regimes are most probably generated as wind instability in hydrodynamics (the Miles-Phillips mechanism). The Miles-Phillips instability is related to different factors in the solar wind stream, among which turbulence, the threshold velocity value, and pressure fluctuations play a defining role. Precisely these regularities are typical of the ipcl burst regime generation conditions.     

Solar wind velocity distribution on the heliospheric current sheet during Carrington rotations 1787-1795

The solar wind velocity distribution in the heliosphere is best represented using a v-map, where velocity contours are plotted in heliographic latitude-longitude coordinates. It has already been established that low-speed regions of the solar wind on the source surface correspond to the maximum bright regions of the K-corona and the neutral line of the coronal magnetic field. In this analysis, v-maps on the source surface for Carrington rotations (CRs) 1787-1795, during 1987, have been prepared using the interplanetary scintillation measurements at Research Institute of Atmospherics (RIA), Nagoya Univ., Japan. These v-maps were then used to study the time evolution of the low-speed (\leq450 km s⁻¹) belt of the solar wind and to deduce the distribution of solar wind velocity on the heliospheric current sheet. The low-speed belt of the solar wind on the source surface was found to change from one CR to the next, implying a time evolution. Instead of a slow and systematic evolution, the pattern of distribution of solar wind changed dramatically at one particular solar rotation (CR 1792) and the distributions for the succeeding rotations were similar to this pattern. The low-speed region, in most cases, was found to be close to the solar equator and almost parallel to it. However, during some solar rotations, they were found to be organised in certain longitudes, leaving regions with longitudinal width greater than 30^○ free of low-speed solar wind, i.e. these regions were occupied by solar wind with velocities greater than 450 km s⁻¹. It is also noted from this study that the low-speed belt, in general, followed the neutral line of the coronal magnetic field, except in certain cases. The solar wind velocity on the heliospheric current sheet (HCS) varied in the range 300–585 km s⁻¹ during the period of study, and the pattern of velocity distribution varied from rotation to rotation.     

Variations in the amplitude of the chandler wobble

It is shown that within the framework of the Kolmogorov model the “energy” of the pole E(t) = x ₁² + x ₂² can be interpreted as a Markovian process. The exact analytical expression has been obtained for the density of the conditional probability of the quantity E(t) and the problem of the first passage time of the process E(t) has been analyzed. It was shown that the available data on the swing of the function E(t) are not at variance with the Kolmogorov model and a short-period drop of the amplitude of the Chandler wobble in the early 20th century fits this model at Q = 50–200 too; values of Q > 350 are less reasonable.     

Injection and acceleration of H+ and He2+ at Earth’s bow shock

We have performed a number of one-dimensional hybrid simulations (particle ions, massless electron fluid) of quasi-parallel collisionless shocks in order to investigate the injection and subsequent acceleration of part of the solar wind ions at the Earth’s bow shock. The shocks propagate into a medium containing magnetic fluctuations, which are initially superimposed on the background field, as well as generated or enhanced by the electromagnetic ion/ion beam instability between the solar wind and backstreaming ions. In order to study the mass (M) and charge (Q) dependence of the acceleration process He²⁺ is included self-consistently. The upstream differential intensity spectra of H⁺ and He²⁺ can be well represented by exponentials in energy. The e-folding energy E_c is a function of time: E_c increases with time. Furthermore the e-folding energy (normalized to the shock ramming energy E_p) increases with increasing Alfvén Mach number of the shock and with increasing fluctuation level of the initially superimposed turbulence. When backstreaming ions leave the shock after their first encounter they exhibit already a spectrum which extends to more than ten times the shock ramming energy and which is ordered in energy per charge. From the injection spectrum it is concluded that leakage of heated downstream particles does not contribute to ion injection. Acceleration models that permit thermal particles to scatter like the non-thermal population do not describe the correct physics.     

The α-effect in 2D fast dynamos

We look at the large-scale dynamo properties of spatially periodic, time dependent, helical 2D flows of the form u(x, t)?=?(? _y ?ψ?(x, y, t), ?? _x ?ψ?(x, y, t), ?ψ (x, y, t). These flows act as kinematic fast dynamos and are able to generate a mean magnetic field uniform and constant in the xy-plane but whose direction varies periodically along z with wavenumber k. Using Mean Field Electrodynamics, the generation mechanism can be understood in terms of a k-dependent α-effect, which depends on the magnetic Reynolds number, R _m . We calculate this effect for different motions and investigate how its limit as k?→?0 depends on R _m and on the properties of the flows such as their spatial structure or correlation time. This work generalises earlier studies based on 2D steady flows to motions with time dependence.     

Effects of variations of river stage and hydraulic conductivity on temporal scaling of groundwater levels: numerical simulations

It was found in previous studies that groundwater levels may fluctuate as a temporal fractal. In this study numerical simulations of groundwater level fluctuations in an unconfined aquifer near a river were conducted to investigate the effects of aquifer heterogeneity and river stage variations on the fractal behavior of the water levels, h(t). Groundwater recharge was taken to be a white-noise process. The aquifer heterogeneity was simulated with a second-order stationary field of hydraulic conductivity (K) with an exponential variogram model. The results showed that groundwater levels fluctuate as a temporal fractal in both homogeneous and heterogeneous aquifers as long as K is less than 10 m/d. Most aquifers may indeed act as a fractal filter which takes a random non-fractal recharge inputs and produces a fractal responses of groundwater level fluctuations. A crossover in temporal scaling of h(t) may appear in more permeable aquifers. Fluctuations of the groundwater level in a homogeneous aquifer are dominated by the recharge process when the river stage is constant or by the river stage variations when the river stage varies in highly permeable aquifers. Heterogeneity plays an important role in the temporal scaling of h(t) in more permeable aquifers: the stronger the heterogeneity, the stronger the temporal scaling of h(t).     

Properties of electric turbulence in the polar cap ionosphere

Small-scale (scales of ∼0.5–256 km) electric fields in the polar cap ionosphere are studied on the basis of measurements of the Dynamics Explorer 2 (DE-2) low-altitude satellite with a polar orbit. Nineteen DE-2 passes through the high-latitude ionosphere from the morning side to the evening side are considered when the IMF z component was southward. A rather extensive polar cap, which could be identified using the ɛ-t spectrograms of precipitating particles with auroral energies, was formed during the analyzed events. It is shown that the logarithmic diagrams (LDs), constructed using the discrete wavelet transform of electric fields in the polar cap, are power law (μ ∼ s ^α). Here, μ is the variance of the detail coefficients of the signal discrete wavelet transform, s is the wavelet scale, and index α characterizes the LD slope. The probability density functions P(δE, s) of the electric field fluctuations δE observed on different scales s are non-Gaussian and have intensified wings. When the probability density functions are renormalized, that is constructed of δE/s ^γ, where γ is the scaling exponent, they lie near a single curve, which indicates that the studied fields are statistically self-similar. In spite of the fact that the amplitude of electric fluctuations in the polar cap is much smaller than in the auroral zone, the quantitative characteristics of field scaling in the two regions are similar. Two possible causes of the observed turbulent structure of the electric field in the polar cap are considered: (1) the structure is transferred from the solar wind, which is known to have turbulent properties, and (2) the structure is generated by convection velocity shears in the region of open magnetic field lines. The detected dependence of the characteristic distribution of turbulent electric fields over the polar cap region on IMF B _y and the correlation of the rms amplitudes of δE fluctuations with IMF B _z and the solar wind transfer function (B _y ² + B _z ²)^1/2sin(θ/2), where θ is the angle between the geomagnetic field and IMF reconnecting on the dayside magnetopause when IMF B _z < 0, together with the absence of dependence on the IMF variability are arguments for the second mechanism.     

ANN forecast of hourly averaged AE index based on L1 IMF and plasma measurements

The AE index has two components: one driven by the solar wind and one related to the magnetotail unloading process. We recall some past findings on this issue and present a new ANN algorithm for the AE forecasting at 5 and 60 min time scales, built by adding to a previous algorithm a further layer with a hyperbolic tangent transfer function and two more inputs, the output at time t and the difference between the input at time t and the output at time t - 1. We show that, at the 60 min time scale and for AE > 400 nT, the new algorithm performs better than the former one, while no improvement is obtained at the 5 min time scale. This result confirms that the AE component driven by the solar wind can be forecast, at least partially, while the unloading component may not be reproduced from solar wind inputs.     

Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small but finite inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,?v,?t), x and v being the particle position and velocity, respectively. For arbitrary inertia, position and velocity variables are coupled, with the result that p(x,?v,?t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small (but nevertheless finite) inertia, (x,?v)-variables decouple and the determination of p(x,?v,?t) is reduced to solve a system of two standard forced advection–diffusion equations in the space variables x. The latter equations are derived here from first principles, i.e., from the well-known Lagrangian evolution equations for position and particle velocity.