arXiv subjects

Sean Oughton

Publications and source records attributed to Sean Oughton.

At least 19 recordsLinked to original sources

arXiv2026

Energy transfer and conversion in Strongly Anisotropic Magnetohydrodynamic Turbulence

In homogeneous magnetohydrodynamic (MHD) turbulence without a background magnetic field driven by mechanical forces, an exact decomposition of the energy fluxes (D. Capocci et al., Journal of Plasma Physics, 91(1), E11 (2025)) has shown that current-sheet thinning is the dominant physical mechanism responsible for transferring energy from large to small scales. In contrast, mechanisms that are characteristic of hydrodynamic turbulence, such as vortex stretching and strain self-amplification, are strongly suppressed. Here, we extend this analysis to MHD turbulence in the presence of weak and strong imposed magnetic field, as previously driven by mechanical forces, and confirm that current-sheet thinning remains the leading process driving the energy cascade toward smaller scales in these more realistic configurations, and find enhanced scale invariance in the subfluxes. In addition to that, a decomposition of the contributions from the fluctuating and the background magnetic field to the conversion between kinetic and magnetic energies shows that the background-field-dependent contribution results in a nonlinear dynamo, that is an effective kinetic-to-magnetic conversion at large and intermediate scales. However, at small scales, it has the opposite effect, resulting in a net conversion of magnetic to kinetic energy.

physics.plasm-ph↗

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

Angular dependence of third-order law in anisotropic MHD turbulence

In solar wind turbulence, the energy transfer/dissipation rate is typically estimated using MHD third-order structure functions calculated using spacecraft observations. However, the inherent anisotropy of solar wind turbulence leads to significant variations in structure functions along different observational directions, thereby affecting the accuracy of energy-dissipation rate estimation. An unresolved issue is how to optimise the selection of observation angles under limited directional sampling to improve estimation precision. We conduct a series of MHD turbulence simulations with different mean magnetic field strengths, $ B_0 $. Our analysis of the third-order structure functions reveals that the global energy dissipation rate estimated around a polar angle of $ θ= 60^\circ$ agrees reasonably with the exact one for $ 0 \le B_0/b_{rms} \le 5 $, where $b_{rms}$ denotes the root-mean-square magnetic field fluctuation. The speciality of $60^\circ$ polar angle can be understood by the Mean Value Theorem of Integrals, since the spherical integral of the polar-angle component ($\widetilde{T_θ}$) of the divergence of Yaglom flux is zero, and $\widetilde{T_θ}$ changes sign around 60$^\circ$. Existing theory on the energy flux vector as a function of the polar angle is assessed, and supports the speciality of $60^\circ$ polar angle. The angular dependence of the third-order structure functions is further assessed with virtual spacecraft data analysis. The present results can be applied to measure the turbulent dissipation rates of energy in the solar wind, which are of potential importance to other areas in which turbulence takes place, such as laboratory plasmas and astrophysics.

physics.space-ph↗

arXiv2025

Estimation of Effective Viscosity to Quantify Collisional Behavior in Collisionless Plasma

While dissipation in collisional plasma is defined in terms of viscosity and resistivity, the exact functional form of dissipation i.e., the so-called dissipation function in nearly collisionless plasma is unknown. Nevertheless, previous studies have suggested that there exists viscous-like energy conversion in collisionless plasma with scaling characteristics analogous to collisional plasma, and in particular that the average dissipation is proportional to the square of the rate of strain as in hydrodynamics. In this study, using 2.5D kinetic particle-in-cell (PIC) simulation of collisionless plasma turbulence, we provide an estimate of effective viscosity at each scale, obtained via a scale-filtering approach. We then compare the turbulent dynamics of the PIC simulation with that from MHD and two-fluid simulations in which with the viscosity is equal to the effective viscosity estimate obtained from the PIC simulation. We find that the global behavior in these MHD and two-fluid simulations has a striking similarity with that in its kinetic/PIC counterpart. In addition, we explore the scale dependence of the effective viscosity, and discuss implications of this approach for space plasmas.

physics.plasm-ph↗

arXiv2025

Radial Basis Operator Networks

Operator networks are designed to approximate nonlinear operators, which provide mappings between infinite-dimensional spaces such as function spaces. These networks are playing an increasingly important role in machine learning, with their most notable contributions in the field of scientific computing. Their significance stems from their ability to handle the type of data often encountered in scientific applications. For instance, in climate modeling or fluid dynamics, input data typically consists of discretized continuous fields (like temperature distributions or velocity fields). We introduce the radial basis operator network (RBON), which represents a significant advancement as the first operator network capable of learning an operator in both the time domain and frequency domain when adjusted to accept complex-valued inputs. Despite the small, single hidden-layer structure, the RBON boasts small $L^2$ relative test error for both in- and out-of-distribution data (OOD) of less than $1\times 10^{-7}$ in some benchmark cases. Moreover, the RBON maintains small error on OOD data from entirely different function classes from the training data.

cs.LG↗

arXiv2024

Power spectrum estimation methods on intracluster medium surface brightness fluctuations

Accurate estimation of galaxy cluster masses is a central problem in cosmology. Turbulence is believed to introduce significant deviations from the hydrostatic mass estimates. Estimation of turbulence properties is complicated by projection of the 3D cluster onto the 2D plane of the sky, and is commonly done in the form of indirect probes from fluctuations in the X-ray surface brightness and Sunyaev-Zeldovich effect maps. In this paper, we address this problem using simulations. We examine different methods for estimating the power spectrum on 2D projected fluctuation data, emulating data projected onto a 2D plane of the sky, and comparing them to the original, expected 3D power spectrum. Noise can contaminate the power spectrum of ICM observations, so we also briefly compare a few methods of reducing noise in the images for better spectral estimation.

astro-ph.CO↗

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

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

New Exact Betchov-like Relation for the Helicity Flux in Homogeneous Turbulence

In homogeneous and isotropic turbulence, the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020), J. Fluid Mech. 922, A3(2021)). We extend the formalism to the transfer of kinetic helicity across scales, important in the presence of large-scale mirror breaking mechanisms, to identify physical processes resulting in helicity transfer and quantify their contributions to the mean flux in the inertial range. All subfluxes transfer helicity from large to small scales. About 50% of the mean flux is due to the scale-local vortex flattening and vortex twisting. We derive a new exact relation between these effects, similar to the Betchov relation for the energy flux, revealing that the mean contribution of the former is three times larger than that of the latter. Multi-scale effects account for the remaining 50% of the mean flux, with approximate equipartition between multi-scale vortex flattening, twisting and entangling.

physics.flu-dyn↗

arXiv2022

The essential role of multi-point measurements in investigations of turbulence, three-dimensional structure, and dynamics: the solar wind beyond single scale and the Taylor Hypothesis

Space plasmas are three-dimensional dynamic entities. Except under very special circumstances, their structure in space and their behavior in time are not related in any simple way. Therefore, single spacecraft in situ measurements cannot unambiguously unravel the full space-time structure of the heliospheric plasmas of interest in the inner heliosphere, in the Geospace environment, or the outer heliosphere. This shortcoming leaves numerous central questions incompletely answered. Deficiencies remain in at least two important subjects, Space Weather and fundamental plasma turbulence theory, due to a lack of a more complete understanding of the space-time structure of dynamic plasmas. Only with multispacecraft measurements over suitable spans of spatial separation and temporal duration can these ambiguities be resolved. We note that these characterizations apply to turbulence across a wide range of scales, and also equally well to shocks, flux ropes, magnetic clouds, current sheets, stream interactions, etc. In the following, we will describe the basic requirements for resolving space-time structure in general, using turbulence' as both an example and a principal target or study. Several types of missions are suggested to resolve space-time structure throughout the Heliosphere.

physics.space-ph↗

arXiv2022

Strategies for determining the cascade rate in MHD turbulence: isotropy, anisotropy, and spacecraft sampling

``Exact'' laws for evaluating cascade rates, tracing back to the Kolmogorov ``4/5'' law, have been extended to many systems of interest including magnetohydrodynamics (MHD), and compressible flows of the magnetofluid and ordinary fluid types. It is understood that implementations may be limited by the quantity of available data and by the lack of turbulence symmetry. Assessment of the accuracy and feasibility of such ``third-order'' (or Yaglom) relations is most effectively accomplished by examining the von Karman-Howarth equation in increment form, a framework from which the third-order laws are derived as asymptotic approximations. Using this approach, we examine the context of third-order laws for incompressible MHD in some detail. The simplest versions rely on the assumption of isotropy and the presence of a well-defined inertial range, while related procedures generalize the same idea to arbitrary rotational symmetries. Conditions for obtaining correct and accurate values of the dissipation rate from these laws based on several sampling and fitting strategies are investigated using results from simulations. The questions we address are of particular relevance to sampling of solar wind turbulence by one or more spacecraft.

physics.space-ph↗

arXiv2022

Turbulence in the outer heliosphere

The solar wind (SW) and local interstellar medium (LISM) are turbulent media. Their interaction is governed by complex physical processes and creates heliospheric regions with significantly different properties in terms of particle populations, bulk flow and turbulence. Our knowledge of the solar wind turbulence \nature and dynamics mostly relies on near-Earth and near-Sun observations, and has been increasingly improving in recent years due to the availability of a wealth of space missions, including multi-spacecraft missions. In contrast, the properties of turbulence in the outer heliosphere are still not completely understood. In situ observations by Voyager and New Horizons, and remote neutral atom measurements by IBEX strongly suggest that turbulence is one of the critical processes acting at the heliospheric interface. It is intimately connected to charge exchange processes responsible for the production of suprathermal ions and energetic neutral atoms. This paper reviews the observational evidence of turbulence in the distant SW and in the LISM, advances in modeling efforts, and open challenges.

physics.space-ph↗

arXiv2020

On the Generation of Compressible Mirror-mode Fluctuations in the Inner Heliosheath

Measurements made with the Voyager 1 spacecraft indicate that significant levels of compressive fluctuations exist in the inner heliosheath. Some studies have already been performed with respect to the mirror-mode instability in the downstream region close to the solar wind termination shock, and here we extend the investigation to the whole inner heliosheath. We employ quasilinear theory and results from a global magnetohydrodynamic model of the heliosphere to compute the time evolution of both the temperature anisotropy and the energy density of the corresponding magnetic fluctuations, and we demonstrate their likely presence in the inner heliosheath. Furthermore, we compute the associated, locally generated density fluctuations. The results can serve as inputs for future models of the transport of compressible turbulence in the inner heliosheath.

physics.space-ph↗

arXiv2020

Critical Balance and the Physics of MHD Turbulence

A discussion of the advantages and limitations of the concept of critical balance, as employed in turbulence phenomenologies, is presented. The incompressible magnetohydrodynamic (MHD) case is a particular focus. The discussion emphasizes the status of the original Goldreich & Sridhar (1995) critical balance conjecture relative to related theoretical issues and models in an MHD description of plasma turbulence. Issues examined include variance and spectral anisotropy, influence of a mean magnetic field, local and nonlocal effects, and the potential for effects of external driving. Related models such as Reduced MHD provide a valuable context in the considerations. Some new results concerning spectral features and timescales are presented in the course of the discussion. Also mentioned briefly are some adaptations and variations of critical balance.

physics.plasm-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↗

arXiv2019

Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence

In an earlier paper (Wan et al. 2012), the authors showed that a similarity solution for anisotropic incompressible 3D magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\vB_0$, exists if the ratio of parallel to perpendicular (with respect to $\vB_0$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor--Kármán-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, DC field strength, and cross-helicity, on the nature of similarity decay is discussed.

physics.flu-dyn↗

arXiv2019

[Plasma 2020 Decadal] The essential role of multi-point measurements in turbulence investigations: the solar wind beyond single scale and beyond the Taylor Hypothesis

This paper briefly reviews a number of fundamental measurements that need to be made in order to characterize turbulence in space plasmas such as the solar wind. It has long been known that many of these quantities require simultaneous multipoint measurements to attain a proper characterization that would reveal the fundamental physics of plasma turbulence. The solar wind is an ideal plasma for such an investigation, and it now appears to be technologically feasible to carry out such an investigation, following the pioneering Cluster and MMS missions. Quantities that need to be measured using multipoint measurements include the two-point, two-time second correlation function of velocity, magnetic field and density, and higher order statistical objects such as third and fourth order structure functions. Some details of these requirements are given here, with a eye towards achieving closure on fundamental questions regarding the cascade rate, spectral anisotropy, characteristic coherent structures, intermittency, and dissipation mechanisms that describe plasma turbuelence, as well as its variability with plasma parameters in the solar wind. The motivation for this discussion is the current planning for a proposed Helioswarm mission that would be designed to make these measurements,leading to breakthrough understanding of the physics of space and astrophysical turbulence.

physics.space-ph↗

arXiv2019

Cross-helically forced and decaying hydromagnetic turbulence

We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find weak inverse transfer of kinetic energy toward the smallest wavenumber. This is plausibly explained by the finiteness of scale separation between the injection wavenumber and the smallest wavenumber of the domain, which here is a factor of 15. In the decaying case, there is a slight increase at the smallest wavenumber, which is probably explained by the dominance of kinetic energy over magnetic energy at the smallest wavenumbers. Within a range of wavenumbers covering almost an order of magnitude the decay is purely exponential, which is argued to be a consequence of a suppression of nonlinearity due to the presence of strong cross helicity.

physics.flu-dyn↗