Turbulent Field Research Articles

Predicting the measurable statistical properties of density fluctuations in a supersonic compressible turbulent flow is a major challenge in physics. In 1951, Chandrasekhar derived an invariant under the assumption of the statistical homogeneity and isotropy of the turbulent density field and stationarity of the background density. Recently, Jaupart and Chabrier [] extended this invariant to nonisotropic flows in a time-evolving background and showed that it has the dimension of a mass. This invariant Minv is defined by Minv=E(ρ)Var(ρE(ρ))(lcρ)3, where ρ is the density field and lcρ is the correlation length. In this article, we perform numerical simulations of homogeneous and isotropic compressible turbulence to test the validity of this invariant in a medium subject to isotropic decaying turbulence. We study several input configurations, namely different Mach numbers, injection lengths of turbulence, and equations of state. We confirm that Minv remains constant during the decaying phase of turbulence. Furthermore, we develop a theoretical model of the density field statistics which predicts without any free parameter the evolution of the correlation length with the variance of the log-density field beyond the assumption of the Gaussian field for the log density. Noting that Minv is independent of the Mach number, we show that this invariant can be used to relate the non-Gaussian evolution of the log-density probability distribution function to its variance with no free parameters.

ABSTRACT The early evolution of protostellar, star-forming discs, including their density structure, turbulence, magnetic dynamics, and accretion variability, remains poorly understood. We present high-resolution magnetohydrodynamic simulations, using adaptive mesh refinement to capture detailed disc dynamics down to sub-au scales. Starting from initial conditions derived from a molecular cloud simulation, we model the collapse of a dense core into a protostellar disc over 10 000 yr following sink particle (star) formation, achieving a maximum effective resolution of 0.63 au. This simulation traces the evolution of the disc density, accretion rates, turbulence, and magnetic field structures. We find that the protostellar disc grows to a diameter of approximately 100 au, with mass accretion occurring in episodic bursts influenced by the turbulence of the core from which the disc builds up. The disc is highly turbulent with a sonic Mach number of $\sim 2$. Episodic accretion events within the disc cause intermittent increases in mass and magnetic energy density, resulting in an equipartition of the thermal and magnetic pressure, i.e. leading to an Alfvén Mach number of $\sim 2$. Some regions above and below the disc mid-plane show sub-Alfvénic conditions with intermittent outflow activity. The disc density profiles steepen over time, following a power law consistent with observed young stellar discs and the minimum mass solar nebula. These results underscore the role of turbulence in early accretion variability and offer new insights into the physical and magnetic structure of young protostellar discs, especially with respect to their turbulent components.

Numerical simulation of flow field and radon concentration distribution in large-scale roadways during drivage.

Obtaining highly accurate turbulent flow fields is a challenging and resource-consuming process in research tasks and practical engineering applications. In this paper, we propose a Swin-Transformer-based model called Multi-Scale Swin Transformer (MSST) to reconstruct high-resolution flow fields by learning features from low-resolution fields. The hierarchical architecture of MSST enables the model to capture features at different levels, making it well suited for multi-scale feature extraction. Forced isotropic turbulence and turbulent channel flow are used as datasets. A loss function based on physical constraints is embedded in MSST, which improves the super-resolution reconstruction accuracy. The reconstructed instantaneous flow fields are comprehensively analyzed and compared. The results show that MSST performs well in the evaluation metrics and can reconstruct the turbulent flow field with high resolution in complex flow field situations, especially on turbulent channel flow.

Context. An increasing number of observations have indicated the existence of slow diffusion phenomena in astrophysical environments, such as around the supernova remnants and pulsar γ-ray halos, where the diffusion coefficient of cosmic rays (CRs) near the source region is significantly smaller than that far away from the source region. The inhomogeneous diffusion indicates the existence of multiple diffusion mechanisms. Aims. Comparing the CR mirror diffusion with the scattering diffusion, our aim is to explore their diffusion characteristics in different magnetohydrodynamic (MHD) turbulence regimes and understand the effect of different MHD modes on mirror and scattering diffusion. Methods. We performed numerical simulations with the test particle method. Within the global frame of reference, we first measured parallel and perpendicular CR diffusion and then determined the mean free path of CRs with varying energies. Results. Our main results demonstrate that (1) CRs experience a transition from superdiffusion to normal diffusion; (2) mirror diffusion is more important than scattering diffusion in confining CRs; (3) CR diffusion strongly depends on the properties of MHD turbulence; and (4) magnetosonic and Alfvén modes respectively dominate the parallel and perpendicular diffusion of CR particles. Conclusions. The diffusion of CRs is a complex problem of mixing the mirror diffusion and scattering diffusion. The property of turbulent magnetic fields influences CR diffusion. The CR slow diffusion due to the presence of magnetic mirrors in turbulence has important implications for explaining observations near a CR source.

It is shown that the generation of magnetic islands by pressure-gradient-driven turbulence is common across a wide range of conditions. The interaction among the turbulence, the magnetic island, and other large scale structures, namely, the zonal flow and the zonal current, largely determines the dynamics of the overall system. The turbulence takes a background role, providing energy to the large-scale structures, without influencing their evolution directly. It is found that the growth of the zonal current is linearly related to that of the magnetic island, while the zonal flow has a strongly sheared region where the island has its maximum radial extension. The zonal current is found to slow down the formation of large-scale magnetic islands, while the zonal flow is needed to have the system move its energy to larger and larger scales. The driving instability in the system is the fluid kinetic ballooning mode (KBM) instability at high β, while the tearing mode is kept stable. The formation of magnetic-island-like structures at the spatial scale of the fluid KBM instability is observed quite early in the non-linear phase for most cases studied, and a slow coalescence process evolves the magnetic structures toward larger and larger scales. Cases, which did neither show this coalescence process nor show the formation of the small scale island-like structures, were seen to have narrower mode structures for comparable instability growth rates, which was achieved by varying the magnetic shear. The islands often end up exceeding the radial box size late in the non-linear phase, showing unbounded growth. The impact on the pressure profile of turbulence driven magnetic islands is not trivial, showing flattening of the pressure profile only far from the resonance, where the zonal flow is weaker, and the appearance of said flattening is slow, after the island has reached a sufficiently large size, when compared with collisional time scales.

Reconstructing high-resolution turbulent flow fields from sparse low-resolution data remains a significant challenge for conventional data-driven methods, primarily due to the added difficulty of resolving the spatiotemporally coupled multi-scale dynamics inherent in turbulence. We propose a novel framework, named as Cascaded PhyFormer-SRNet, that provides a comprehensive solution through improved model architecture design, imposition of physical constraints, and a method for enhanced fine-scale refinement. First, an end-to-end spatiotemporal transformer-based super-resolution model is developed to integrate spatial feature extraction and attention mechanism for temporal enhancement. Unlike conventional methods that separately construct spatial and temporal super-resolution models, a unified architecture enables simultaneous spatiotemporal super-resolution, allowing more effective learning of the spatiotemporal multi-scale interactions present in turbulence. Second, finite difference-based physical constraints are imposed on the reconstructed flow fields to ensure physically consistent predictions of fine-scale turbulence characteristics. Building on the proposed physics-informed transformer-based super-resolution model, a cascaded refinement strategy to improve multi-scale spectral reconstruction is further applied to complete our proposed Cascaded PhyFormer-SRNet framework. Through these three innovations, the Cascaded PhyFormer-SRNet achieves superior spectral accuracy across scales and facilitates high-fidelity turbulence reconstruction in space and time. Experiments show that our framework outperforms conventional methods in reconstructing multi-scale channel turbulence from highly compressed data, even at compression ratios over 99%. Separate experiments show effective reconstruction of Kolmogorov flow from both regularly and randomly distributed noisy observations, with a reduction in reconstruction error exceeding 32% for the former compared to conventional methods.

Abstract This study addresses the technical bottlenecks of conventional artificial lift technologies under high‐pressure conditions in deep well operations, utilizing CFD methods to investigate gas–liquid two‐phase flow characteristics in downhole jet pumps based on actual operating conditions. The research employs Solidworks for modelling, ANSYS ICEM for mesh generation, and the k‐ε turbulence model for numerical simulation analysis. Experimental results demonstrate that jet pump performance characteristics are primarily influenced by key structural parameters including area ratio, nozzle‐throat gap distance, throat length, and diffuser angle, with area ratio showing the most significant impact on hydraulic efficiency. Through the combination of theoretical design empirical formulas and field production data, along with in‐depth numerical simulation optimization, optimal design ranges were established: nozzle‐throat area ratio of 0.23–0.28, nozzle‐throat gap distance of 2–3 times nozzle diameter, throat length of 7–8 times throat diameter, and diffuser angle of 6°. The scientific validity and reliability of these parameters were verified through systematic comparative analysis of pressure distribution characteristics, velocity field evolution patterns, and turbulent field variation characteristics under different working conditions. This research elucidates the complex flow mechanisms in jet pump operations and establishes a theoretical framework for structural optimization and performance enhancement, thereby contributing to improved deep well lifting efficiency and economic viability of production operations.

Abstract Rectangular structures subjected to turbulent flows are subject to vortex shedding, which induces dynamic forces that depend on the flow conditions and structural motion. Structures with rotational and transverse structural modes may be excited by vortex shedding to oscillate, inducing vibration and fatigue problems. This work investigates the coupled torsional and transverse vibration of a rectangular cross-section with an aspect ratio of 4. To illustrate the effect of mode coupling, three cases are considered: rotation only, rotation and transverse vibration with the same natural frequencies, and rotation and transverse vibration with different natural frequencies. Results show that allowing the structure to vibrate with the two modes with the same natural frequency results in higher vibration amplitudes. Flow fields indicate that higher vibration amplitudes are associated with a wider wake, a distinctive vortex shedding pattern, a widespread turbulent field, and a longer vortex reattachment length on the side of the structure.

The interplay between drift-wave coherence and particle transport in plasmas is investigated through a truncated Hasegawa–Mima model coupled with a drift-wave Hamiltonian model. By reducing the system to a three-wave interaction, we identify regimes of periodic and chaotic wave amplitudes and link them to the emergence or suppression of zonal flows. Numerical simulations reveal two distinct transport regimes: hyperballistic motion under periodic waves, where coherent zonal flows channel particles poloidally, and superdiffusive spreading under chaotic waves, where non-periodic fields disrupt directional coherence. Particle tracking indicates that periodic waves enhance radial confinement while enabling rapid poloidal transport, whereas chaotic fluctuations suppress large-scale migration through chaotic scattering. These results highlight the critical role of wave-field coherence in determining transport efficiency and offer a conceptual framework for turbulence control, highlighting that manipulating the coherence of the turbulent field, in addition to its amplitude, is a key strategy for controlling plasma transport. The findings connect reduced-order models with fully turbulent systems, offering insights into harnessing self-organized structures, such as zonal flows, for improved plasma confinement.

Abstract Shocks associated with interplanetary coronal mass ejections are known to energize charged particles and give rise to solar energetic particles. Many of these energetic particles move ahead of the shock to create a foreshock region. The foreshock region primarily consists of solar wind plasma, exhibiting turbulent velocity and magnetic fields. Such turbulent behavior results from inherent solar wind turbulence modified by energetic particles. We analyze magnetic field data from six such ICME shocks observed by the Wind spacecraft. The analysis of the shock upstream shows that the magnetic power spectral density (PSD) maintains a power-law slope of −5/3. We also identify clear intermittent peaks in the PSD. After characterizing these peaks, we investigate various possibilities for their generation. Our analysis indicates that these peaks in the PSD are due to the resonant interaction of Alfvén waves with the bulk solar wind protons and protons with energy up to 10 keV. However, evidence of Alfvén wave interaction with highly energetic protons is not evident in our analysis, and we anticipate that such evidence is obscured by the prevailing solar wind turbulence in the shock upstream.

Abstract The motion of energetic particles such as cosmic rays is complicated due to their interaction with turbulent magnetic fields. In particular, an analytical description of such interactions is difficult to achieve due to their stochastic and nonlinear nature. Therefore, transport equations are used to describe the motion of energetic particles. In phase-space, where the particle distribution function depends on position, time, and velocity, one uses a Fokker-Planck partial differential equation. While the general case of such a transport equation is too complicated to solve analytically, we consider the special case of a constant pitch-angle scattering coefficient. For this special case we explore analytical solutions of the Fokker-Planck equation by using Airy functions. We also develop an N-dimensional subspace method for this case corresponding to a semi-analytical approach. We compare the different methods, obtained results, and computational times needed with each other. We also determine different expectation values which are relevant for applications in particle transport theory.

We employ well-known concepts from statistical physics, quantum field theories, and general topology to study magnetic reconnection and topology change and their connection in incompressible flows in the context of an effective field theory without appealing to magnetic field lines. We consider the dynamical system corresponding to wave packets moving with Alfvén velocity x[over ̇](t):=V_{A}(x,t) whose trajectories x(t) define pathlines, which naturally provides a mathematical way to estimate the rate of magnetic topology change. A considerable simplification is attained, in fact, by directly employing well-known concepts from hydrodynamic turbulence without appealing to the complicated notion of magnetic field lines moving through plasma, which may prove even more useful in the relativistic regime. Continuity conditions for magnetic field allow rapid but continuous divergence of pathlines, shown to imply reconnection, but not discontinuous divergence, which would change topology. Thus, topology can change only due to time-reversal symmetry breaking, e.g., by dissipative effects. In laminar and even chaotic flows, the separation of pathlines at all times remains proportional to their initial separation, argued to correspond to slow reconnection, and topology changes by dissipation with a rate proportional to resistivity. In turbulence, pathlines diverge superlinearly with time independent of their initial separation, i.e., fast reconnection, and magnetic topology changes by turbulent dissipation with a rate independent of small-scale plasma effects. The crucial role of turbulence in enhancing topology change and reconnection rates originates from its ability to break time-reversal invariance and make the flow superchaotic. In fact, due to the loss of Lipschitz continuity of the magnetic field in turbulence, pathlines separate superlinearly even if their initial separation tends to vanish, unlike deterministic chaos. This superchaotic behavior is an example of spontaneous stochasticity in statistical physics, sometimes called the real butterfly effect in chaos theory to distinguish it from the butterfly effect, in which trajectories can diverge exponentially only if initial separation remains finite. If 3D reconnection is defined as magnetic topology change, it can be fast only in turbulence where both reconnection and topology change are driven by spontaneous stochasticity, independent of any plasma effects. Our results strongly support the Lazarian-Vishniac theory of turbulent reconnection.

Abstract X-ray polarization is a unique new probe of the particle acceleration in astrophysical jets made possible through the Imaging X-ray Polarimetry Explorer. Here we report on the first dense X-ray polarization monitoring campaign on the blazar Mrk 421. Our observations were accompanied by an even denser radio and optical polarization campaign. We find significant short-timescale variability in both X-ray polarization degree and angle, including an ∼90° angle rotation about the jet axis. We attribute this to random variations of the magnetic field, consistent with the presence of turbulence but also unlikely to be explained by turbulence alone. At the same time, the degree of lower-energy polarization is significantly lower and shows no more than mild variability. Our campaign provides further evidence for a scenario in which energy-stratified shock-acceleration of relativistic electrons, combined with a turbulent magnetic field, is responsible for optical to X-ray synchrotron emission in blazar jets.

This study investigates the use of viscous dampers (VDs) to reduce the vibration of a deepwater offshore platform under joint wind, wave, and earthquake action. A finite element model was established based on the Opensees software (version 3.7.1), incorporating soil–structure interaction simulated by the nonlinear Winkler springs and simulating hydrodynamic loads via the Morison equation. Turbulent wind fields were generated using the von Kármán spectrum, and irregular wave profiles were synthesized from the JONSWAP spectrum. The 1995 Kobe earthquake record served as seismic input. The time-history dynamic response for the deepwater offshore platform was evaluated under two critical scenarios: isolated seismic excitation and the joint action of wind, wave, and seismic loading. The results demonstrate that VDs configured diagonally at each structural level effectively suppress platform vibrations under both isolated seismic and wind–wave–earthquake conditions. Under seismic excitation, the VD system reduced maximum deck acceleration, velocity, displacement, and base shear force by 9.95%, 22.33%, 14%, and 31.08%, respectively. For combined environmental loads, the configuration achieved 15.87%, 21.48%, 13.51%, and 34.31% reductions in peak deck acceleration, velocity, displacement, and base shear force, respectively. Moreover, VD parameter analysis confirms that increased damping coefficients enhance control effectiveness.

This study presents a comprehensive numerical framework for Background-Oriented Schlieren (BOS) to systematically evaluate its performance and reconstructive capabilities under complex flow conditions. This framework integrates two stages: forward modeling, using ray tracing to simulate image degradation, and inverse processing, using optical flow and a conjugate gradient algorithm to extract displacements and reconstruct phase information. This method is first validated using turbulent flow fields in the Johns Hopkins Turbulence Database, where the reconstructed phase screens closely match the original data, with relative errors below 4% and structural similarity indices above 0.75 in all cases, providing a possible restoration method for degraded flow field images. It is then applied to shock wave fields with varying Mach numbers; this method achieves meaningful reconstruction at short ranges but fails under long-range imaging due to severe wavefront distortions. However, even in degraded conditions, the extracted optical flow fields preserve structural features correlated with the underlying shock patterns, indicating potential for BOS-based target recognition. These findings highlight both the capabilities and limitations of BOS and suggest new pathways for extending its use beyond traditional flow visualization.

Abstract We investigate the role of interplanetary (IP) shocks in solar wind turbulence using observations of Solar Orbiter, Parker Solar Probe, and Wind. Employing statistical analysis of quasi-perpendicular fast forward (FF) and fast reverse (FR) shocks, we revisit evolution of magnetic field turbulence across IP shocks. Our previous work indicates that the spectral properties of magnetic fluctuations are statistically conserved across different types of IP shocks, except FR shocks in the transition range of frequencies. We focus on the spectral index in the transition range ( α tr ) using 1 minute sliding windows at 10 s intervals to probe the turbulent dissipation near shocks. We address the influence of key turbulence parameters, particularly cross helicity (σ c) and fluctuation amplitude (σ B), on α tr . Our results demonstrate (1) an immediate change in α tr across the shock with no evidence for further gradual or asymptotic evolution over extended intervals, and this implies that shock universally serves as a thin boundary separating two turbulence states; (2) the dominant factor forming the steepness of α tr is σ c, rather than σ B; and (3) the statistically shallower downstream α tr of FR shocks results from a systematic reduction in σ c across shocks. These findings suggest that the observed spectral modification is primarily governed by changes in turbulence Alfvénicity, not directly by dissipation processes related to the shock, and can be commonly observed toward extensive heliospheric distances.

ABSTRACT Radio broad-band spectro-polarimetric observations are sensitive to the spatial fluctuations of the Faraday depth (FD) within the telescope beam. Such FD fluctuations are referred to as ‘Faraday complexity’, and can unveil small-scale magneto-ionic structures in both the synchrotron-emitting and the foreground volumes. We explore the astrophysical origin of the Faraday complexity exhibited by 191 polarized extragalactic radio sources (EGSs) within $5^\circ$ from the Galactic plane in the longitude range of $20^\circ$–$52^\circ$, using broad-band data from the Karl G. Jansky Very Large Array presented by a previous work. A new parameter called the FD spread is devised to quantify the spatial FD fluctuations. We find that the FD spread of the EGSs (i) demonstrates an enhancement near the Galactic mid-plane, most notable within Galactic latitude of $\pm 3^\circ$, (ii) exhibits hints of modulations across Galactic longitude, (iii) does not vary with the source size across the entire range of $2.5$–$300\,\,\mathrm{ arcsec}$, and (iv) has an amplitude higher than expected from magneto-ionic structures of extragalactic origin. All these suggest that the primary cause of the Faraday complexity exhibited by our target EGSs is $< 2.5\,\,\mathrm{ arcsec}$-scale magneto-ionic structures in the Milky Way. We argue that the anisotropic turbulent magnetic fields generated by galactic-scale shocks and shears, or the stellar feedback-driven isotropic turbulent magnetic fields, are the most likely candidates. Our work highlights the use of broad-band radio polarimetric observations of EGSs as a powerful probe of multiscale magnetic structures in the Milky Way.

ABSTRACTWe discuss charged particle transport in a turbulent magnetic field. The pitch angle diffusion is essential to the transport processes of energetic particles in real and momentum spaces. We integrate particle trajectories in time under the influence of the turbulent magnetic field given as a superposition of parallel‐propagating magnetohydrodynamic waves (“slab‐turbulence”). As in the standard theory for cosmic ray transports, the small wave amplitude and the random phase approximation are the fundamental assumptions of the quasi‐linear theory. In the presence of large amplitude waves, our numerical study shows the anomalous pitch angle diffusion of the energetic particles. In the presence of waves with strong phase correlation, where the MHD turbulence is represented as intermittent wave packets, the particles are transported in the momentum space due to the mirror reflections rather than the pitch angle diffusion. The particle motions are mostly ballistic and occasionally reflected by the intermittent wave packets; thus, the spatial transport of the energetic particles can be super‐diffusive in the presence of large amplitude MHD waves with strong phase correlation.

Abstract The interstellar medium (ISM) consists of multiphase gas, including the warm neutral medium (WNM), the unstable neutral medium (UNM), and the cold neutral medium (CNM). While significant attention has been devoted to understanding the WNM and CNM, the formation of a substantial fraction of the UNM, with temperatures ranging from a few hundred to a few thousand Kelvin, remains less well understood. In this study, we present 3D hydrodynamical and magnetohydrodynamic simulations of the turbulent multiphase ISM to investigate the roles of turbulence and magnetic fields in regulating the multiphase ISM. Our results confirm that turbulence is crucial in redistributing energy and producing the UNM. The turbulent mixing effect smooths the phase diagram, flattens the pressure–density relationship, and increases the fraction of gas in the UNM. We find magnetic fields not only contribute to sustaining the UNM but also influence the dynamics and distribution of gas across all phases. Magnetic fields introduce anisotropy to the turbulent cascade, reducing the efficiency of turbulent mixing in the direction perpendicular to the magnetic field. We find the anisotropy results in a less flat phase diagram compared to hydrodynamical cases. Furthermore, the inclusion of magnetic fields shallows the second-order velocity structure functions across multiple ISM phases, suggesting that more small-scale fluctuations are driven. These fluctuations contribute to the formation of the UNM by altering the energy cascade and thermodynamic properties of the gas. Our findings suggest that the combined effects of turbulence and magnetic fields are important in regulating the multiphase ISM.