Turbulent Field Research Articles (Page 2)

Abstract The difference between the assumed conditions and the actual engineering scenario leads to systematic theoretical error when the transit-time difference method is applied to measure the flow rate in turbulent field. This paper focuses on the theoretical error in the turbulent of such a geometric scale as the coal mine roadway. A three-dimensional coupled simulation model of ultrasonic propagation integrating pressure acoustics, computational fluid dynamics and ray acoustics was established. A large number of simulation cases were designed and the influencing factors of theoretical error were quantified using statistical analysis method. The results show that the theoretical error is positively correlated with flow rate and wall roughness, and negatively correlated with equivalent diameter of roadway section. Compared to the theoretically assumed uniform flow field, the propagation time of ultrasonic waves in the turbulent flow field is shorter in the downstream direction and longer in the upstream direction. The relative value of the theoretical error is about 2%, and the absolute value is described by the multiple regression prediction model. The high fitting degree of the model indicates that 96.9% of the variation in absolute error could be reliably explained, which is beneficial to improve the accuracy and engineering applicability of the transit-time difference method.

Under conditions of time-varying velocities, turbulent fields exhibiting non-uniform gradients external to the hypersonic vehicle interact with the optical dome, resulting in phenomena such as offset, jitter, blurring, and energy attenuation of target signals. This paper establishes a fluid-structure interaction model for a blunt bi-conic side-window vehicle, utilizing an air-to-air missile as the research context. Based on CFD numerical simulation under time-varying velocities, the aero-optical transmission effect evaluation index is quantitatively calculated utilizing a reverse ray tracing algorithm. This study evaluates the imaging performance of the optical system in terms of light deflection, wavefront transmission distortion, and imaging deviation. The results indicate that the flow field gradually stabilizes after an exposure time of 6s, while the optical dome gradually stabilizes after 11s. During the initial phase, the aero-optical transmission effect induced by the aero-optical flow field is the primary contributor to the degradation of imaging performance. As the exposure time increases, the aero-thermal effects within the structural domain intensify, leading to the aero-optical transmission effect caused by the optical window becoming the predominant factor.

Supercritical fluids operate above their critical point and are characterized by strong nonlinearities in the equation of state, highly non-ideal fluid behavior, and a tight coupling between thermodynamics and transport properties. As a result, supercritical fluid flows behave fundamentally different from their low-pressure counterparts. The thermodynamic space of supercritical fluids is commonly divided into two main regions separated by the pseudo-boiling region, where a second-order phase transition occurs. Transcritical flows—those crossing the pseudo-boiling line—undergo substantial variations in thermophysical properties. Additionally, near the pseudo-boiling line, smaller-than-Kolmogorov thermal scales are generated, which are tightly coupled with small velocity scales. The complex two-way interaction between pseudo-boiling phenomena and turbulence remains an open question, both from a fundamental physics perspective and for modeling efforts. In this regard, a database of homogeneous isotropic turbulence under various supercritical thermodynamic conditions in the vicinity of the pseudo-boiling line is presented. The dataset includes instantaneous three-dimensional turbulent flow fields and real-fluid thermophysical quantities, as well as Reynolds- and Favre-averaged data, enabling the study and modeling of transcritical fluid turbulence.

Model-based time super-sampling of turbulent flow field sequences

We investigate the influence of the Reynolds number on the spatial development of an incompressible planar jet. The study relies on direct numerical simulations (DNS) at inlet Reynolds numbers between $500 \leqslant Re \leqslant 13\,500$ , being the widest range and the largest values considered so far in DNS. At the lowest $Re$ , the flow is transitional and characterised by large quasi-two-dimensional vortices; at the largest $Re$ , the flow reaches a fully turbulent regime with a well-developed self-similar region. We provide a complete description of the flow, from the instabilities in the laminar near-inlet region, to the self-similar regime in the turbulent far field. At the inlet, the leading destabilisation mode is sinusoidal/asymmetric at low Reynolds number and varicose/symmetric at large Reynolds number, with both modes coexisting at intermediate $Re$ . In the far field, the mean and fluctuating statistics converge to self-similar profiles only for $Re\geqslant 4500$ ; the flow anisotropy, the budget of the Reynolds stresses and the energy spectra are addressed. The spreading of the jet is quantified via the turbulent–non-turbulent interface (TNTI). We find that the thickness of the turbulent region, and the shape and fractal dimension of the TNTI become $Re$ -independent for $Re \geqslant 4500$ . Comparisons with previous numerical and experimental works are provided whenever available.

Abstract Turbulence and magnetic fields are components of the interstellar medium and are interconnected through plasma processes. In particular, the magnetic flux transport in the presence of magneto-hydrodynamic (MHD) turbulence is an essential factor for understanding star formation. The theory of Reconnection Diffusion (RD), based on statistics of Alfvénic turbulence, predicts a dependence of the diffusion coefficient of the magnetic field on the Alfvénic Mach number MA. However, this theory does not consider the effects of compressibility which are important in the regime of supersonic MHD turbulence. In this work, we measure the diffusion coefficient of magnetic fields in sub-Alfvénic MHD turbulence, with different sonic Mach numbers MS. We perform numerical simulations of forced turbulence in periodic domains from the incompressible limit to the supersonic regime. We introduce two methods to extract the diffusion coefficient, based on the analysis of tracer particles. Our results confirm the RD assumption regarding the correspondence between the diffusion of magnetic field and that of fluid Lagrangian particles. The measured diffusion rate provided by incompressible turbulence agrees with the suppression predicted by the RD theory in the presence of strong magnetic fields: $D \propto M_A^3$. Our simulations also indicate an increase in RD efficiency when the turbulence is compressible. The dependency on MA and MS from the simulations can be described by the relation $D \propto M_A^{\alpha }$, where α(MS) ≈ 3/(1 + MS). This quantitative characterization of D is critical for modeling star formation in turbulent molecular clouds and evaluating the efficiency of this transport compared to other mechanisms.

Abstract The hydrophobicity and floatability of fine coal slime are severely diminished by surface coatings of gangue minerals, complicating coal–gangue separation in slurry systems. Traditional pulping methods struggle to efficiently remove fine mud from coal particles, reducing recovery efficiency. To address this, a self‐designed impact flow slurry conditioning device was developed to enhance reagent adsorption on coal surfaces. Combining computational fluid dynamics (CFD) simulations, reagent adsorption rate analysis, and contact angle measurements, this study optimized slurry impact velocity to evaluate flow field dynamics and conditioning mechanisms. Flotation experiments revealed that strain rate increased with impact velocity, peaking at 774 s−1 (5 m/s), while the minimum vortex scale reached 1.04 μm at 4 m/s. At 4 m/s, the collector adsorption rate and coal contact angle were maximized, achieving a combustible recovery rate of 98.18%, indicating optimal flotation performance. The impact flow method effectively strips surface gangue coatings, enhances coal‐gangue separation, and improves coal hydrophobicity and floatability. The device integrates a disturbing cone and plate to generate localized turbulence and shear fields, significantly boosting reagent adsorption efficiency and overcoming structural limitations of traditional stirring equipment. These innovations provide critical insights into shear‐driven adsorption mechanisms and advance coal slurry flotation technology, offering a scalable solution for industrial applications. This research establishes a foundation for developing efficient, high‐performance coal processing systems.

Achieving high-precision and efficient prediction of turbulent flow fields presents a significant challenge for the rapid design of complex flow channels. Traditional turbulent flow field calculation methods require solving the Navier–Stokes equations, which are computationally intensive and time-consuming. Other than the traditional method, a novel fast prediction method of two-dimensional flow is proposed in this study based on a deep attention network integrating physical information. First, the geometric information of flow channels is extracted based on a series of grayscale images, which are then embedded and input into a transformer encoder. The geometric parameters obtained from the transformer encoder, along with the Reynolds number, flow field coordinates, and distance field, are input into a multilayer perceptron to predict the flow field. To enhance the network's physical interpretability, a physical loss function is incorporated into the network. Additionally, a dynamic weight strategy is employed to balance the interaction between data loss terms and physical loss terms. Extensive quantitative comparison between the predicted and numerical simulation results of the back-step vortex field with varying geometric structures shows that 80% of data points have an absolute relative error below 0.02. The correlation coefficient between the predicted and computational fluid dynamics (CFD) values is greater than 0.97, with near-wall pressure values closely matching the CFD results. Additionally, the model requires no manual weight adjustments, and dynamic weighting reduces training losses while improving performance.

Abstract The turbulence in the liquid iron within the outer core of the Earth is responsible for the geomagnetic field generation, its sustainment and dynamical evolution. Here we revive Braginsky's idea of the Stratified Ocean at the top of the Core (SOC) and consider a non‐stationary turbulent wave field composed of Magnetic‐Archimedean‐Coriolis (MAC) waves inside the SOC. The non‐stationarity, hitherto ignored, implies non‐vanishing coupling of waves with distinct frequencies, in particular the effect of beating waves leading to formation of electromotive force slowly varying in time in the core. It is shown that the beating frequencies, that is small frequency differences between interacting MAC waves can lead to an Earth‐like behavior of the large‐scale magnetic field, exhibiting long periods of fairly stable field separated by short lived reversals or strong excursions, which appear to be random. Within such an approach the resulting reversals/excursions are simply manifestations of a chaotic turbulent flow inside the core, and no significant alterations of the large‐scale flow structures are necessary in order for reversals to occur. Such a dynamical picture seems highly desired since it has been a long‐standing puzzle that many previous numerical simulations of the Earth's core dynamo exhibiting magnetic field reversals reported no significant modifications of large‐scale flow structures during the process and only local variations in strength of the background small‐scale turbulence.

Abstract Cosmic rays (CRs) interact with turbulent magnetic fields in the interstellar medium (ISM), generating nonthermal emission. After many decades of studies, the theoretical understanding of their diffusion in the ISM continues to pose a challenge. This study numerically explores a recent prediction termed “mirror diffusion” and its synergy with the traditional diffusion mechanism based on gyroresonant scattering. Our study combines 3D MHD simulations of star-forming regions with test particle simulations to analyze CR diffusion. We demonstrate the significance of mirror diffusion in CR diffusion parallel to the magnetic field when the mirroring condition is satisfied. Our results support the theoretical expectation that the resulting particle propagation arising from mirror diffusion in combination with much faster diffusion induced by gyroresonant scattering resembles a Levy-flight-like propagation. Our study highlights the necessity to reevaluate the diffusion coefficients traditionally adopted in the ISM based on gyroresonant scattering alone. For instance, our simulations imply a diffusion coefficient ∼1027 cm2 s–1 for particles with a few hundred TeV within regions spanning a few parsecs around the source. This estimate is in agreement with gamma-ray observations, which show the relevance of our results for the understanding of gamma-ray emission in star-forming regions.

Abstract The unstable isotope 60Fe, with a half-life of 2.6 million years, is produced primarily in supernova explosions. The observed presence of 60Fe in cosmic rays and its detection in deep-sea crusts and sediments suggest two possible scenarios: either the direct acceleration of 60Fe from supernova ejecta or its enrichment in the circumstellar material surrounding supernova progenitors, which indicates cosmic ray production in clusters of supernovae. Focusing on the latter scenario, we consider an environment shaped by successive supernova explosions, reminiscent of the Local Bubble around the time of the most recent supernova explosion. We independently tracked the evolution of the 60Fe mass ratio within the Local Bubble using passive scalars. To investigate the spectra of protons and 60Fe, we explicitly modeled cosmic-ray acceleration and transport at the remnant of the last supernova by simultaneously solving the hydrodynamical equations for the supernova outflow and the transport equations for cosmic rays, scattering turbulence, and large-scale magnetic field, using the time-dependent acceleration code Radiation Acceleration Transport Parallel Code. The main uncertainty in our prediction of the local 60Fe flux at about pc = 1 GeV nuc−1 is the magnetic-field structure in the Local Bubble and the cosmic-ray diffusion beyond the approximately 100 kyr of evolution covered by our study. We found that if the standard galactic propagation applies, the local 60Fe flux would be around 3% of that measured. If there is a sustained reduction in the diffusion coefficient at and near the Local Bubble, then the expected 60Fe flux could be up to 30% of that measured.

The transport of energetic particles in the heliosphere is profoundly influenced by interactions with coherent structures in the turbulent magnetic field of the solar wind, particularly current sheets. While prior studies have largely relied on idealized turbulence models, this work quantifies the role of solar wind current sheets (quasi-1D plasma structures characterized by strong magnetic field gradients) in driving pitch-angle scattering. We present an analytical Hamiltonian framework coupled with test particle simulations, informed by observational data from the ARTEMIS and Wind missions, to model particle dynamics through current sheets with realistic parameters. Our results demonstrate that the scattering efficiency depends critically on the current sheet's shear angle, the relative magnitude of the magnetic field component directed along the normal to the current sheet surface, and the ratio of the particle gyroradius to the current sheet thickness. Large pitch-angle jumps, arising from nonadiabatic separatrix crossings in phase space, lead to rapid chaotization, whereas diffusive scattering broadens the pitch-angle distributions. Statistical analysis of solar wind current sheets at 1 AU reveals significant scattering rates for 100 keV to 1 MeV protons, with implications for particle transport mechanisms. The derived diffusion rates enable the inclusion of coherent structures into global transport models for a more accurate modeling of energetic particle dynamics in the heliosphere. These findings underscore the importance of current sheets in shaping energetic particle spatial distributions and provide practical methods for incorporating them in space and astrophysical plasmas.

Abstract Optimal arrangements of turbulent pipe systems strongly depend on branch patterns, and turbulence fields typically cause involved multimodality in the solution space. These features hinder gradient-based structural optimization frameworks from finding promising solutions for turbulent pipe systems. In this article, we propose a multi-stage framework that integrates data-driven morphological exploration and evolutionary shape optimization to address the challenges posed by the complexity of turbulent pipe systems. Our framework begins with data-driven morphological exploration, aiming to find promising morphologies. It results in the shapes for selecting a reasonable number of candidates for the next shape refinement stage. Herein, we employ data-driven topology design, a gradient-free, and multi-objective optimization methodology incorporating a deep generative model and the concept of evolutionary algorithms to generate promising arrangements. Subsequently, a deep clustering strategy extracts representative shapes. The final stage involves refining these shapes through shape optimization using a genetic algorithm. Applying the framework to a two-dimensional turbulent pipe system with a minimax objective shows its effectiveness in delivering high-performance solutions for the turbulent flow optimization problem with branching.

In this study, a computational thermo-fluid dynamics simulation of a wide-slot jet impingement heating process is performed. The present configuration consists of a turbulent incompressible air jet impinging orthogonally on an isothermal cold plate at a Reynolds number of around 11,000. The two-dimensional mean turbulent flow field is numerically predicted by solving Reynolds-averaged Navier–Stokes (RANS) equations, where the two-equation eddy viscosity k-ω model is utilized for turbulence closure. As the commonly used shear stress transport variant overpredicts heat transfer at the plate due to excessive turbulent diffusion, the recently developed generalized k-ω (GEKO) model is considered for the present analysis, where the primary model coefficients are suitably tuned. Through a comparative analysis of the various solutions against one another, in addition to reference experimental and numerical data, the effectiveness of the generalized procedure in predicting both the jet flow characteristics and the heat transfer at the plate is thoroughly evaluated, while determining the optimal set of model parameters. By improving accuracy within the RANS framework, the importance of model adaptability and parameter tuning for this specific fluid engineering application is demonstrated. This study offers valuable insights for improving predictive capability in turbulent jet simulations with broad engineering implications, particularly for industrial heating or cooling systems relying on wide-slot jet impingement.

Interstellar magnetic fields play an important role in the dynamics and evolution of galaxies. The nearby spiral galaxy M 31 is an ideal laboratory for extensive studies of magnetic fields. We measure the strength and distribution separately for the various magnetic field components: total, ordered, regular, isotropic turbulent, and, for the first time, anisotropic turbulent. Based on radio continuum observations of M 31 at 3.6,cm and 6.2,cm wavelengths with the Effelsberg 100--m telescope, plus combined observations with the VLA and Effelsberg telescopes at 20.5,cm, the intensities of total, linearly polarized, and unpolarized synchrotron emission are measures of the strengths of total, ordered, and isotropic turbulent fields in the sky plane. We used two assumptions about equipartition between the energy densities of total magnetic fields and total cosmic rays, i.e. local equipartition and overall equipartition on the scale of order 10,kpc and more. Faraday rotation measures (RMs) provided a model of the regular field. The quadratic difference between ordered and regular field strengths yields the strength of the anisotropic turbulent field. The average equipartition strengths of the magnetic field in the emission torus, between 8,kpc and 12,kpc radius in the galaxy plane, are $(6.3±0.2),μG for the total, (5.4±0.2),μ$G for the isotropic turbulent, and $(3.2±0.3),μ$G for the ordered field in the sky plane. The total, isotropic turbulent, and ordered field strength decrease exponentially with radial scale lengths of ≃14--15,kpc. The average strength of the axisymmetric regular field, B_ derived from the RMs in the emission torus, is $(2.0±0.5),μ$G and remains almost constant between 7,kpc and 12,kpc radius. Quadratic subtraction of the component B_ in the sky plane from the ordered field, B_ yields the strength of the anisotropic turbulent field, B_ which is $(2.7±0.7),μ$G on average in the emission torus. Our test with an extreme non-equipartition case assuming constant CREs along the torus enhances the magnetic field fluctuations. The average strength of the regular field between 7,kpc and 12,kpc radius is about 40% smaller than the equipartition strength of the ordered field (containing regular and anisotropic turbulent fields). As those two quantities were measured with independent methods, our results are consistent with the assumption of equipartition. Furthermore, our estimate of the diffusion length of cosmic-ray electrons (CREs) emitting at of łesssim 0.34,kpc in the sky plane sets the lower limit for the validity of the equipartition assumption. The average magnetic energy density in the emission torus is about five times larger than the thermal energy density of the diffuse warm ionized gas, while the magnetic energy density is similar to the kinetic energy density of turbulent motions of the neutral gas. Magnetic fields are a primary dynamical agent in the interstellar medium of M 31. The ratio between regular and isotropic turbulent fields is a measure of the relative efficiencies of the large-scale and the small-scale dynamos. The average value of ≃0.39, almost constant with azimuth in the emission torus as well with radius in the range 7--12,kpc, is consistent with present-day dynamo models. The ratio between anisotropic and isotropic turbulent fields is ≃0.57 on average and is almost constant with the azimuth in the emission torus as well as with the radius in the range 7--10,kpc. This indicates that anisotropic turbulent fields are generated by the shearing of isotropic turbulent fields.

Abstract The light curves of radioactive transients, such as supernovae and kilonovae, are powered by the decay of radioisotopes, which release high-energy leptons through β+ and β− decays. These leptons deposit energy into the expanding ejecta. As the ejecta density decreases during expansion, the plasma becomes collisionless, with particle motion governed by electromagnetic forces. In such environments, strong or turbulent magnetic fields are thought to confine particles, though the origin of these fields and the confinement mechanism have remained unclear. Using fully kinetic particle-in-cell (PIC) simulations, we demonstrate that plasma instabilities can naturally confine high-energy leptons. These leptons generate magnetic fields through plasma streaming instabilities, even in the absence of pre-existing fields. The self-generated magnetic fields slow lepton diffusion, enabling confinement and transferring energy to thermal electrons and ions. Our results naturally explain the positron trapping inferred from late-time observations of thermonuclear and core-collapse supernovae. Furthermore, they suggest potential implications for electron dynamics in the ejecta of kilonovae. We also estimate synchrotron radio luminosities from positrons for Type Ia supernovae and find that such emission could only be detectable with next-generation radio observatories from a Galactic or local-group supernova in an environment without any circumstellar material.

The solar wind is a medium characterized by strong turbulence and significant field fluctuations on various scales. Recent observations have revealed that magnetic turbulence exhibits a self-similar behavior. Similarly, high-resolution measurements of the proton density have shown comparable characteristics, prompting several studies of the multifractal properties of these density fluctuations. This work aims to investigate whether low-resolution measurements of the solar wind proton density exhibit nonlinear and multifractal structures. We also aim to interpret these features within the framework of non-extensive statistical mechanics. We performed a systematic analysis of hourly resolution proton density data obtained from various spacecraft located at the Lagrange point L1, recorded over 17 years. We analyzed the multifractal nature of the fluctuations and tested for consistency with the ( q )-triplet formalism from non-extensive statistical mechanics. We find that low-resolution solar wind proton density data also display nonlinear and multifractal signatures. Our analysis provides a validation of the ( q )-triplet predicted by non-extensive statistical theory. To the best of our knowledge, this represents the most rigorous and systematic validation to date of the ( q )-triplet in the solar wind.

ABSTRACT The wind shear, coherence, and turbulence intensity define the turbulent wind field. While it is evident that a floating offshore wind turbine (FOWT) will exhibit a distinct behavior in turbulent wind, the specific impact of the wind shear and the turbulence intensities lacks an in-depth investigation. The present study examines how wind shear and turbulence intensity affect the dynamic reactions of a Submerged Tension Leg FOWT platform in terms of the rotor thrust force, coupled motion responses, the forces, and moments at the tower base. The modeling of Submerged Tension Leg Platform (STLP) supporting a 5 MW wind turbine, which incorporates the interaction of aerodynamics, hydrodynamics, and structural dynamics, is conducted in the time domain using the simulation tool FAST by NREL. The outcomes based on the study depict that the wind field with high turbulence intensity may result in significant responses, particularly for above-rated wind speed, which may lead to the amplification of the structural loads. Further, the coupled dynamic performance of the STLP FOWT system is studied with emphasis on the effect of the wind-wave misalignment. This study on wind wave misalignment depicts the critical wave heading angle where the response of the STLP is amplified.

Abstract Suprathermal electrons are routinely observed in interplanetary space. At higher energies, there are in-situ evidences that shocks, both interplanetary shocks, often driven by fast coronal mass ejections, and terrestrial bow shocks, can accelerate electrons up to transrelativistic energies (∼MeVs). The acceleration mechanism responsible for these energetic electrons is still under debate. In this work, we study the effects of large-scale shock ripples on electron acceleration at a quasi-perpendicular shock in a 2D system. For tractability of the numerical simulation, we consider the scenario where the magnetic field line contains ripples, and the shock is assumed planar and piecewise. The propagation of gyrophase-averaged electrons is governed by the focused transport equation, where the effect of the turbulent magnetic field is modeled by the pitch-angle diffusion, described by the quasi-linear theory. A Monte Carlo simulation on the equivalent time-forward Itô stochastic differential equation is performed within a periodic box to obtain the phase-space distribution function of the accelerated electrons. Our model predicts power-law energy spectra with a cutoff at high-energy ends, whereas their spectral indices are softer than those predicted by the diffusive shock acceleration theory. We demonstrate that, with a suitable choice of pitch-angle diffusion strength, a small fraction of electrons can experience magnetic traps in multiple ripples along the shock surface, boosting their energies to ∼MeVs. Our results therefore provide a framework for a better understanding of relativistic electron events associated with shocks within the heliosphere.

Abstract We statistically analyze the power spectral density (PSD) of magnetic field turbulence in the upstream solar wind of the Martian bow shock by investigating the data from Tianwen-1 and Mars Atmosphere and Volatile Evolution (MAVEN) during 2021 November 13 and December 31. The spectral indices and break frequencies of these PSDs are automatically identified. According to the profiles of the PSDs, we find that they could be classified into three types: A, B, and C. Only less than a quarter of the events exhibit characteristics similar to the 1 au PSDs (Type A). We observe the energy injection in more than one-third of the events (Type B), and the injected energy usually results in the steeper spectral indices of the dissipation ranges. We find the absence of the dissipation range in over one third of the PSDs (Type C), which is likely due to the dissipation occurring at higher frequencies rather than proton cyclotron resonant frequencies. We also find that the two spacecraft observed different types of PSDs in more than half of the investigated episodes, indicating significant variability upstream of the Martian bow shock. For example, the Type-B PSDs are more often seen by Tianwen-1, which was near the flank of the bow shock, than by MAVEN near the nose. This statistical study demonstrates the complicated turbulent environment of the solar wind upstream of the Martian bow shock.