arXiv subjects

Tulasi N. Parashar

Publications and source records attributed to Tulasi N. Parashar.

At least 19 recordsLinked to original sources

arXiv2026

Direct power spectral density estimation from structure functions without Fourier transforms

Second-order structure functions and power spectral densities are popular tools in the study of statistical properties across scales, particularly for the analysis of turbulent flows. Although intimately related, analyses primarily use one or the other. We introduce a framework for estimating the power spectrum using the second-order structure function without applying Fourier transforms -- enabling one to take advantage of the real-space structure function calculations. We validate and showcase this method, comparing it to classical Fourier power spectrum estimates determined from analytical calculations, fractional Brownian motion, turbulence simulations, and space-physics and astrophysical observations of turbulence. We show that this method is able to robustly obtain the expected power law behaviour where we use turbulence ranges as test-cases.

physics.flu-dyn↗

arXiv2025

De-Biasing Structure Function Estimates From Sparse Time Series of the Solar Wind: A Data-Driven Approach

Structure functions, which represent the moments of the increments of a stochastic process, are essential complementary statistics to power spectra for analysing the self-similar behaviour of a time series. However, many real-world environmental datasets, such as those collected by spacecraft monitoring the solar wind, contain gaps, which inevitably corrupt the statistics. The nature of this corruption for structure functions remains poorly understood - indeed, often overlooked. Here we simulate gaps in a large set of magnetic field intervals from Parker Solar Probe in order to characterize the behaviour of the structure function of a sparse time series of solar wind turbulence. We quantify the resultant error with regards to the overall shape of the structure function, and its slope in the inertial range. Noting the consistent underestimation of the true curve when using linear interpolation, we demonstrate the ability of an empirical correction factor to de-bias these estimates. This correction, "learnt" from the data from a single spacecraft, is shown to generalize well to data from a solar wind regime elsewhere in the heliosphere, producing smaller errors, on average, for missing fractions >25%. Given this success, we apply the correction to gap-affected Voyager intervals from the inner heliosheath and local interstellar medium, obtaining spectral indices similar to those from previous studies. This work provides a tool for future studies of fragmented solar wind time series, such as those from Voyager, MAVEN, and OMNI, as well as sparsely-sampled astrophysical and geophysical processes more generally.

astro-ph.SR↗

arXiv2024

Scale Separation Effects on Simulations of Plasma Turbulence

Understanding plasma turbulence requires a synthesis of experiments, observations, theory, and simulations. In the case of kinetic plasmas such as the solar wind, the lack of collisions renders the fluid closures such as viscosity meaningless and one needs to resort to higher order fluid models or kinetic models. Typically, the computational expense in such models is managed by simulating artificial values of certain parameters such as the ratio of the Alfvén speed to the speed of light ($v_A/c$) or the relative mass ratio of ions and electrons ($m_i/m_e$). Although, typically care is taken to use values as close as possible to realistic values within the computational constraints, these artificial values could potentially introduce unphysical effects. These unphysical effects could be significant at sub-ion scales, where kinetic effects are the most important. In this paper, we use the ten-moment fluid model in the Gkeyll framework to perform controlled numerical experiments, systematically varying the ion-electron mass ratio from a small value down to the realistic proton-electron mass ratio. We show that the unphysical mass ratio has a significant effect on the kinetic range dynamics as well as the heating of both the plasma species. The dissipative process for both ions and electrons become more compressive in nature, although the ions remain nearly incompressible in all cases. The electrons move from being dominated by incompressive viscous like heating/dissipation, to very compressive heating/dissipation dominated by compressions/rarefactions. While the heating change is significant for the electrons, a mass ratio of $m_i/m_e \sim 250$ captures the asymptotic behaviour of electron heating.

physics.plasm-ph↗

arXiv2024

Higher-order nonequilibrium term: Effective power density quantifying evolution towards or away from local thermodynamic equilibrium

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A forefront research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here, we introduce the ``higher-order non-equilibrium term'' (HORNET) effective power density that quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, namely magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, $\rm{Pi-D}$, and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8\% and 35\% for electrons and ions, respectively, for reconnection; up to 67\% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed.

physics.plasm-ph↗

arXiv2023

Scale and Time Dependence of Alfvénicity in the Solar Wind as Observed by {\it Parker Solar Probe}

Alfvénicity is a well-known property, common in the solar wind, characterized by a high correlation between magnetic and velocity fluctuations. Data from the Parker Solar Probe (PSP) enable the study of this property closer to the Sun than ever before, as well as in sub-Alfvénic solar wind. We consider scale-dependent measures of Alfvénicity based on second-order functions of the magnetic and velocity increments as a function of time lag, including the normalized cross-helicity $σ_c$ and residual energy $σ_r$. Scale-dependent Alfvénicity is strongest for lags near the correlation scale and increases when moving closer to the Sun. We find that $σ_r$ typically remains close to the maximally negative value compatible with $σ_c$. We did not observe significant changes in measures of Alfvénicity between sub-Alfvénic and super-Alfvénic wind. During most times, the solar wind was highly Alfvénic; however, lower Alfvénicity was observed when PSP approached the heliospheric current sheet or other magnetic structures with sudden changes in the radial magnetic field, non-unidirectional strahl electron pitch angle distributions, and strong electron density contrasts. These results are consistent with a picture in which Alfvénic fluctuations generated near the photosphere transport outward forming highly Alfvénic states in the young solar wind and subsequent interactions with large scale structures and gradients leads to weaker Alfvénicity, as commonly observed at larger heliocentric distances.

astro-ph.SR↗

arXiv2023

Statistics of Turbulence in the Solar Wind. I. What is the Reynolds Number of the Solar Wind?

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 "effective" Reynolds number formulations, 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 sizeable 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-hour 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.

physics.plasm-ph↗

arXiv2023

Scale Filtering Analysis of Kinetic Reconnection and its Associated Turbulence

Previously, using an incompressible von Kármán-Howarth formalism, the behavior of cross-scale energy transfer in magnetic reconnection and turbulence was found to be essentially identical to each other, independent of an external magnetic (guide) field, in the inertial and energy-containing ranges (Adhikari et al., Phys. Plasmas 30, 082904, 2023). However, this description did not account for the energy transfer in the dissipation range for kinetic plasmas. In this letter, we adopt a scale-filtering approach to investigate this previously unaccounted-for energy transfer channel in reconnection. Using kinetic particle-in-cell (PIC) simulations of antiparallel and component reconnection, we show that the pressure-strain (PS) interaction becomes important at scales smaller than the ion inertial length, where the nonlinear energy transfer term drops off. Also, the presence of a guide field makes a significant difference in the morphology of the scale-filtered energy transfer. These results are consistent with kinetic turbulence simulations, suggesting that the pressure strain interaction is the dominant energy transfer channel between electron scales and ion scales.

physics.plasm-ph↗

arXiv2023

Effective Viscosity, Resistivity, and Reynolds Number in Weakly Collisional Plasma Turbulence

We examine dissipation and energy conversion in weakly collisional plasma turbulence, employing in situ observations from the Magnetospheric Multiscale (MMS) mission and kinetic Particle-in-Cell (PIC) simulations of proton-electron plasma. A previous result indicated the presence of viscous-like and resistive-like scaling of average energy conversion rates -- analogous to scalings characteristic of collisional systems. This allows for extraction of collisional-like coefficients of effective viscosity and resistivity, and thus also determination of effective Reynolds numbers based on these coefficients. The effective Reynolds number, as a measure of the available bandwidth for turbulence to populate various scales, links macro turbulence properties with kinetic plasma properties in a novel way.

physics.plasm-ph↗

arXiv2023

Statistics of Pressure Fluctuations in Turbulent Kinetic Plasmas

In this study we explore the statistics of pressure fluctuations in kinetic collisionless turbulence. A 2.5D kinetic particle-in-cell (PIC) simulation of decaying turbulence is used to investigate pressure balance via the evolution of thermal and magnetic pressure in a plasma with beta of order unity. We also discuss the behavior of thermal, magnetic and total pressure structure functions and their corresponding wavenumber spectra. The total pressure spectrum exhibits a slope of -7/3 extending for about a decade in the ion-inertial range. In contrast, shallower -5/3 spectra are characteristic of the magnetic pressure and thermal pressure. The steeper total pressure spectrum is a consequence of cancellation caused by density-magnetic field magnitude anticorrelation. Further, we evaluate higher order total pressure structure functions in an effort to discuss intermittency and compare the power exponents with higher order structure functions of velocity and magnetic fluctuations. Finally, applications to astrophysical systems are also discussed.

physics.plasm-ph↗

arXiv2023

Effect of a guide field on the turbulence like properties of magnetic reconnection

The effect of an external guide field on the turbulence-like properties of magnetic reconnection is studied using five different 2.5D kinetic particle-in-cell (PIC) simulations. The magnetic energy spectrum is found to exhibit a slope of approximately -5/3 in the inertial range, independent of the guide field. On the contrary, the electric field spectrum, in the inertial range steepens more with the guide field and approaches a slope of -5/3. In addition, spectral analysis of the different terms of the generalized Ohm's law is performed and found to be consistent with PIC simulations of turbulence and MMS observations. Finally, guide field effect on the energy transfer behavior is examined using von-Kármán Howarth (vKH) equation based on incompressible Hall-MHD. The general characteristics of the vKH equation with constant rate of energy transfer in the inertial range, is consistent in all the simulations. This suggests that the qualitative behavior of energy spectrum, and energy transfer in reconnection is similar to that of turbulence, indicating that reconnection fundamentally involves an energy cascade.

physics.plasm-ph↗

arXiv2022

Interplay of Turbulence and Proton-Microinstability Growth in Space Plasmas

Numerous prior studies have shown that as proton beta increases, a narrower range of proton temperature anisotropy values is observed. This effect has often been ascribed to the actions of kinetic microinstabilities because the distribution of observational data aligns with contours of constant instability growth rates in the beta-anisotropy plane. However, the linear Vlasov theory of instabilities assumes a uniform background in which perturbations grow. The established success of linear-microinstability theories suggests that the conditions in regions of extreme temperature anisotropy may remain uniform for a long enough time so that the instabilities have the chance to grow to sufficient amplitude. Turbulence, on the other hand, is intrinsically non-uniform and non-linear. Thin current sheets and other coherent structures generated in a turbulent plasma, may destroy the uniformity fast enough. It is therefore not a-priori obvious whether the presence of intermittency and coherent structures favors or disfavors instabilities. To address this question, we examined the statistical distribution of growth rates associated with proton temperature-anisotropy driven microinstabilities and local nonlinear time scales in turbulent plasmas. Linear growth rates are, on average, substantially less than the local nonlinear rates. However, at the regions of extreme values of temperature anisotropy, near the "edges" of the populated part of the proton temperature anisotropy-parallel beta plane, the instability growth rates are comparable or faster than the turbulence time scales. These results provide a possible answer to the question as to why the linear theory appears to work in limiting plasma excursions in anisotropy and plasma beta.

physics.space-ph↗

arXiv2022

Exploring the potential of neural networks to predict statistics of solar wind turbulence

Time series datasets often have missing or corrupted entries, which need to be ignored in subsequent data analysis. For example, in the context of space physics, calibration issues, satellite telemetry issues, and unexpected events can make parts of a time series unusable. Various approaches exist to tackle this problem, including mean/median imputation, linear interpolation, and autoregressive modeling. Here we study the utility of artificial neural networks (ANNs) to predict statistics, particularly second-order structure functions, of turbulent time series concerning the solar wind. Using a dataset with artificial gaps, a neural network is trained to predict second-order structure functions and then tested on an unseen dataset to quantify its performance. A small feedforward ANN, with only 20 hidden neurons, can predict the large-scale fluctuation amplitudes better than mean imputation or linear interpolation when the percentage of missing data is high. Although, they perform worse than the other methods when it comes to capturing both the shape and fluctuation amplitude together, their performance is better in a statistical sense for large fractions of missing data. Caveats regarding their utility, the optimisation procedure, and potential future improvements are discussed.

astro-ph.SR↗

arXiv2022

Observations of Cross Scale Energy Transfer in the Inner Heliosphere by Parker Solar Probe

The solar wind, a continuous flow of plasma from the sun, not only shapes the near Earth space environment but also serves as a natural laboratory to study plasma turbulence in conditions that are not achievable in the lab. Starting with the Mariners, for more than five decades, multiple space missions have enabled in-depth studies of solar wind turbulence. Parker Solar Probe (PSP) was launched to explore the origins and evolution of the solar wind. With its state-of-the-art instrumentation and unprecedented close approaches to the sun, PSP is starting a new era of inner heliospheric exploration. In this review we discuss observations of turbulent energy flow across scales in the inner heliosphere as observed by PSP. After providing a quick theoretical overview and a quick recap of turbulence before PSP, we discuss in detail the observations of energy at various scales on its journey from the largest scales to the internal degrees of freedom of the plasma. We conclude with some open ended questions, many of which we hope that PSP will help answer.

physics.space-ph↗

arXiv2022

Isotropization and Evolution of Energy-Containing Eddies in Solar Wind Turbulence: Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1

We examine the radial evolution of correlation lengths perpendicular ($λ_C^{\perp}$) and parallel ($λ_C^{\parallel}$) to the magnetic-field direction, computed from solar wind magnetic-field data measured by Parker Solar Probe (PSP) during its first eight orbits, Helios 1, Advanced Composition Explorer (ACE), WIND, and Voyager 1 spacecraft. Correlation lengths are grouped by an interval's alignment angle; the angle between the magnetic-field and solar wind velocity vectors ($Θ_{\rm BV}$). Parallel and perpendicular angular channels correspond to angles $0^{\circ}~<~Θ_{\rm BV}~<~40^{\circ}$ and $50^{\circ}~<~Θ_{\rm BV}~<~90^{\circ}$, respectively. We observe an anisotropy in the inner heliosphere within 0.40~au, with $λ_C^{\parallel} / λ_C^{\perp} \approx 0.75$ at 0.10~au. This anisotropy reduces with increasing heliocentric distance and the correlation lengths roughly isotropize within 1~au. Results from ACE and WIND support a reversal of the anisotropy, such that $λ_C^{\parallel} /λ_C^{\perp} \approx 1.29$ at 1~au. The ratio does not appear to change significantly beyond 1~au, although the small number of parallel intervals in the Voyager dataset precludes unambiguous conclusions from being drawn. This study provides insights regarding the radial evolution of the large, most energetic interacting turbulent fluctuations in the heliosphere. We also emphasize the importance of tracking the changes in sampling direction in PSP measurements as the spacecraft approaches the Sun, when using these data to study the radial evolution of turbulence. This can prove to be vital in understanding the more complex dynamics of the solar wind in the inner heliosphere and can assist in improving related simulations.

astro-ph.SR↗

arXiv2022

Intermittency in the Expanding Solar Wind: Observations from Parker Solar Probe (0.16au), Helios 1 (0.3-1au), and Voyager 1 (1-10au)

We examine statistics of magnetic field vector components to explore how intermittency evolves from near sun plasma to radial distances as large as 10 au. Statistics entering the analysis include auto-correlation, magnetic structure functions of order n (SFn), and scale dependent kurtosis (SDK), each grouped in ranges of heliocentric distance. The Goddard Space Flight Center Space Physics Data Facility (SPDF) provides magnetic field measurements for resolutions of 6.8ms for Parker Solar Probe, 6s for Helios, and 1.92s for Voyager 1. We compute SF2 to determine the scales encompassing the inertial range and examine SDK to investigate degree of non-Gaussianity. Auto-correlations are used to resolve correlation scales. Correlation lengths and ion inertial lengths provide an estimate of effective Reynolds number (Re). Variation in Re allows us to examine for the first time the relationship between SDK and Re in an interplanetary plasma. A conclusion from this observed relationship is that regions with lower Re at a fixed physical scale have on average lower kurtosis, implying less intermittent behavior. Kolmogorov refined similarity hypothesis is applied to magnetic SFn and kurtosis to calculate intermittency parameters and fractal scaling in the inertial range. A refined Voyager 1 magnetic field dataset is generated.

physics.space-ph↗

arXiv2020

A Detailed Examination of Anisotropy and Timescales in Three-dimensional Incompressible Magnetohydrodynamic Turbulence

When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the magnetic field, relative to the direction along the field. This anisotropy of the spectrum is deeply connected with anisotropy of estimated timescales for dynamical processes, and requires reconsideration of basic issues such as scale locality and spectral transfer. Here analysis of high-resolution three-dimensional simulations of unforced magnetohydrodynamic turbulence permits quantitative assessment of the behavior of theoretically relevant timescales in Fourier wavevector space. We discuss the distribution of nonlinear times, Alfvén times, and estimated spectral transfer rates. Attention is called to the potential significance of special regions of the spectrum, such as the two-dimensional limit and the "critical balance" region. A formulation of estimated spectral transfer in terms of a suppression factor supports a conclusion that the quasi two-dimensional fluctuations (characterized by strong nonlinearities) are not a singular limit, but may be in general expected to make important contributions.

physics.plasm-ph↗

arXiv2020

Statistics of Kinetic Dissipation in Earth's Magnetosheath -- MMS Observations

A familiar problem in space and astrophysical plasmas is to understand how dissipation and heating occurs. These effects are often attributed to the cascade of broadband turbulence which transports energy from large scale reservoirs to small scale kinetic degrees of freedom. When collisions are infrequent, local thermodynamic equilibrium is not established. In this case the final stage of energy conversion becomes more complex than in the fluid case, and both pressure-dilatation and pressure strain interactions (Pi-D $\equiv -Π_{ij} D_{ij}$) become relevant and potentially important. Pi-D in plasma turbulence has been studied so far primarily using simulations. The present study provides a statistical analysis of Pi-D in the Earth's magnetosheath using the unique measurement capabilities of the Magnetospheric Multiscale (MMS) mission. We find that the statistics of Pi-D in this naturally occurring plasma environment exhibit strong resemblance to previously established fully kinetic simulations results. The conversion of energy is concentrated in space and occurs near intense current sheets, but not within them. This supports recent suggestions that the chain of energy transfer channels involves regional, rather than pointwise, correlations.

physics.plasm-ph↗

arXiv2020

Intermittency and Ion Temperature-Anisotropy Instabilities: Simulation and Magnetosheath Observation

Weakly collisional space plasmas are rarely in local thermal equilibrium and often exhibit non-Maxwellian electron and ion velocity distributions that lead to the growth of microinstabilities, that is, enhanced electric and magnetic fields at relatively short wavelengths. These instabilities play an active role in the evolution of space plasmas, as does ubiquitous broadband turbulence induced by turbulent structures. This study compares certain properties of a 2.5 dimensional Particle-In-Cell (PIC) simulation for the forward cascade of Alfvenic turbulence in a collisionless plasma against the same properties of turbulence observed by the Magnetospheric Multiscale Mission spacecraft in the terrestrial magnetosheath. The PIC simulation is of decaying turbulence which develops both coherent structures and anisotropic ion velocity distributions with the potential to drive kinetic scale instabilities. The uniform background magnetic field points perpendicular to the plane of the simulation. Growth rates are computed from linear theory using the ion temperature anisotropies and ion beta values for both the simulation and the observations. Both the simulation and the observations show that strong anisotropies and growth rates occur highly intermittently in the plasma, and the simulation further shows that such anisotropies preferentially occur near current sheets. This suggests that, though microinstabilities may affect the plasma globally , they act locally and develop in response to extreme temperature anisotropies generated by turbulent structures. Further studies will be necessary to understand why there is an apparent correlation between linear instability theory and strongly intermittent turbulence.

physics.space-ph↗