Turbulent Field Research Articles

LEMDA: A Lagrangian‐Eulerian Multiscale Data Assimilation Framework

AbstractLagrangian trajectories are widely used as observations for recovering the underlying flow field via Lagrangian data assimilation (DA). However, the strong nonlinearity in the observational process and the high dimensionality of the problems often cause challenges in applying standard Lagrangian DA. In this paper, a Lagrangian‐Eulerian multiscale DA (LEMDA) framework is developed. It starts with exploiting the Boltzmann kinetic description of the particle dynamics to derive a set of continuum equations, which characterize the statistical quantities of particle motions at fixed grids and serve as Eulerian observations. Despite the nonlinearity in the continuum equations and the processes of Lagrangian observations, the time evolution of the posterior distribution from LEMDA can be written down using closed analytic formulas after applying the stochastic surrogate model to describe the flow field. This offers an exact and efficient way of carrying out DA, which avoids using ensemble approximations and the associated tunings. The analytically solvable properties also facilitate the derivation of an effective reduced‐order Lagrangian DA scheme that further enhances computational efficiency. The Lagrangian DA part within the framework has advantages when a moderate number of particles is used, while the Eulerian DA part can effectively save computational costs when the number of particle observations becomes large. The Eulerian DA part is also valuable when particles collide, such as using sea ice floe trajectories as observations. LEMDA naturally applies to multiscale turbulent flow fields, where the Eulerian DA part recovers the large‐scale structures, and the Lagrangian DA part efficiently resolves the small‐scale features in each grid cell via parallel computing. Numerical experiments demonstrate the skillful results of LEMDA and its two components.

Active flow control for bluff body under high Reynolds number turbulent flow conditions using deep reinforcement learning

This study employs deep reinforcement learning for active flow control in a turbulent flow field of high Reynolds numbers at Re = 274 000. That is, an agent is trained to obtain a control strategy that can reduce the drag of a cylinder while also minimizing the oscillations of the lift. Probes are placed only around the surface of the cylinder, and a proximal policy optimization (PPO) agent controls nine zero-net mass flux jets on the downstream side of the cylinder. The trained PPO agent effectively reduces drag by 29% and decreases lift oscillations by 18% of amplitude, with the control effect demonstrating good repeatability. Control tests of this agent within the Reynolds number range of Re = 260 000 to 288 000 show that the agent's control strategy possesses a certain degree of robustness, with very similar drag reduction effects under different Reynolds numbers. Analysis using power spectral energy reveals that the agent learns specific flow frequencies in the flow field and effectively suppresses low-frequency, large-scale structures. Graphically visualizing the policy, combined with pressure, vorticity, and turbulent kinetic energy contours, reveals the mechanism by which jets achieve drag reduction by influencing reattachment vortices. This study successfully implements robust active flow control in realistically significant high Reynolds number turbulent flows, minimizing time costs (using two-dimensional geometrical models and turbulence models) and maximally considering the feasibility of future experimental implementation.

Optimization and experimental validation of a high-efficiency oil–water cyclone separator for well testing conditions

The performance of surface oil–water cyclone separators impacts the measurement accuracy of crude oil produced from exploration and appraisal wells, thereby influencing the formulation of exploration and development plans. To obtain the optimal structural configuration for cyclone oil–water separators, this study optimizes the design of a high-efficiency oil–water cyclone separator suitable for special conditions in well testing. A numerical simulation was performed using the discrete phase model to analyze the three-dimensional turbulent swirl field of the oil–water phases within the separator. Separation efficiency and pressure drop were used as evaluation criteria. The Plackett–Burman experimental method was employed to evaluate six factors affecting separation performance, with oil outlet diameter and cyclone chamber cone angle identified as significant factors. Mathematical models for separation efficiency and pressure drop were developed based on these factors. The central composite design method was then applied to investigate the interactive effects of oil outlet diameter and cyclone chamber cone angle on separation efficiency and pressure drop. The optimal parameter combination was determined: oil outlet diameter of 4.241 mm and cyclone chamber cone angle of 9.622°. The predicted separation efficiency was 93.870%, and the predicted pressure drop was 48.287 kPa. Field tests of the optimized cyclone separator verified the rationality of these optimized parameters, achieving a separation efficiency of 92.9%. This research offers a foundation for optimizing the design of oil–water cyclone separators.

Quantum-inspired fluid simulation of two-dimensional turbulence with GPU acceleration

Tensor network algorithms can efficiently simulate complex quantum many-body systems by utilizing knowledge of their structure and entanglement. These methodologies have been adapted recently for solving the Navier-Stokes equations, which describe a spectrum of fluid phenomena, from the aerodynamics of vehicles to weather patterns. Within this quantum-inspired paradigm, velocity is encoded as matrix product states (MPS), effectively harnessing the analogy between interscale correlations of fluid dynamics and entanglement in quantum many-body physics. This particular tensor structure is also called quantics tensor train (QTT). By utilizing NVIDIA's cuQuantum library to perform parallel tensor computations on GPUs, our adaptation speeds up simulations by up to 12.1 times. This allows us to study the algorithm in terms of its applicability, scalability, and performance. By simulating two qualitatively different but commonly encountered 2D flow problems at high Reynolds numbers up to 1×107 using a fourth-order time stepping scheme, we find that the algorithm has a potential advantage over direct numerical simulations in the turbulent regime as the requirements for grid resolution increase drastically. In addition, we derive the scaling χ=O(poly(1/ε)) for the maximum bond dimension χ of MPS representing turbulent flow fields, with an error ε, based on the spectral distribution of turbulent kinetic energy. Our findings motivate further exploration of related quantum algorithms and other tensor network methods. Published by the American Physical Society 2025

Anisotropic diffusion of high-energy cosmic rays in magnetohydrodynamic turbulence

The origin of cosmic rays (CRs) and how they propagate remain unclear. Studying the propagation of CRs in magnetohydrodynamic (MHD) turbulence can help to comprehend many open issues related to CR origin and the role of turbulent magnetic fields. To comprehend the phenomenon of slow diffusion in the near-source region, we study the interactions of CRs with the ambient turbulent magnetic field to reveal their universal laws. We numerically study the interactions of CRs with the ambient turbulent magnetic field, considering pulsar wind nebula as a general research case. Taking the magnetization parameter and turbulence spectral index as free parameters, together with radiative losses, we perform three group simulations to analyze the CR spectral, spatial distributions, and possible CR diffusion types. Our studies demonstrate that (1) CR energy density decays with both its effective radius and kinetic energy in the form of power-law distributions; (2) the morphology of the CR spatial distribution strongly depends on the properties of magnetic turbulence and the viewing angle; (3) CRs suffer a slow diffusion near the source and a fast or normal diffusion away from the source; (4) the existence of a power-law relationship between the averaged CR energy density and the magnetization parameter is independent of both CR energy and radiative losses; and (5) radiative losses can suppress CR anisotropic diffusion and soften the power-law distribution of CR energy density. The distribution law established between turbulent magnetic fields and CRs presents an intrinsic property, providing a convenient way to understand complex astrophysical processes related to turbulence cascades.

Improving MRI turbulence quantification by addressing the measurement errors caused by the derivatives of the turbulent velocity field - Sequence development and in-vitro validation.

To improve the current method for MRI turbulence quantification which is the intravoxel phase dispersion (IVPD) method. Turbulence is commonly characterized by the Reynolds stress tensor (RST) which describes the velocity covariance matrix. A major source for systematic errors in MRI is the sequence's sensitivity to the variance of the derivatives of velocity, such as the acceleration variance, which can lead to a substantial measurement bias. We developed a Cartesian phase contrast sequence with fast velocity encoding and two separately measured partial echoes with opposite readout directions. This design aims to reduce the high-order gradient moments that are responsible for the described measurement error. Velocity encoding directions follow the ICOSA6 scheme to capture the full RST. Turbulence data is reconstructed using the intra-voxel phase dispersion (IVPD) technique. We validated this sequence in vitro using a periodic hill flow benchmark with highly anisotropic turbulence. MRI data underwent extensive averaging, with multiple velocity encoding values employed to reduce noise and isolate systematic effects. The RST data obtained from the new sequence agree well with the ground truth. Compared to a state-of-the-art sequence, the maximum errors were reduced by factor five. Simple adjustments to current MRI protocols can greatly enhance turbulence measurement accuracy through the reduction of high-order gradient moments. The proposed measures include applying fast velocity encoding, high readout bandwidth, and a highly asymmetric readout. Ringing artifacts due to the asymmetric readout can be removed via a second, inverted readout.

The effects of wall proximity on the turbulent flow field in a square duct structured with detached divergent ribs on one wall

The effect of the wall proximity of detached 60∘ divergent ribs applied on one wall in a square duct on the turbulent flow field was investigated. Laser Doppler anemometry (LDA) measurements were conducted for different clearance-to-rib-height ratios in the range of 0.1–1.0 at a Reynolds number (based on the rib height and mean bulk velocity) of 5000. Mean velocities, Reynolds stresses, triple velocity correlations as well as skewness and kurtosis were determined and yield deep insights into the turbulent flow field. The results showed that a geometry-induced secondary fluid motion occurred above and below the rib. The variations in the highly three-dimensional flow field close to the ribs and the geometry-induced secondary flow motion with the clearance-to-rib-height ratio determined the development of the wall-bounded flows and separating shear layers. Large recirculation regions on the bottom duct wall were prevented by the fluid exiting the gap below the detached ribs and separated shear layers pivoted upward in lateral direction. With decreasing wall proximity, lower mean vertical flow velocities above the ribs and the increasing upward fluid flow originating from the flow in the gap attenuated an intense interaction of the separated shear layers with the wall-bounded flow within the inter-rib spacing. Since turbulent structures originated in the shear layers, distributions of high-order statistic moments depend strongly on the shear layer development. Reynolds stresses and triple velocity correlations increased in the direction of the side walls near the rib due to the lateral flow motion, and their peak regions moved away from the wall with increasing clearance-to-rib-height ratios.

Submesoscale Eddy Contribution to Ocean Vertical Heat Flux Diagnosed From Airborne Observations

AbstractSubmesoscale eddies (those smaller than 50 km) are ubiquitous throughout the ocean, as revealed by satellite infrared images. Diagnosing their impact on ocean energetics from observations remains a challenge. This study analyzes a turbulent field of submesoscale eddies using airborne observations of surface currents and sea surface temperature, with high spatial resolution, collected during the S‐MODE experiment in October 2022. Assuming surface current divergence and temperature are homogeneous down to 30 m depth, we show that more than 80% of the upward vertical heat fluxes, reaching 227 W , is explained by the smallest resolved eddies, with a size smaller than 15 km. This result emphasizes the contribution of small‐scale eddies, poorly represented in numerical models, to the ocean heat budget and, therefore, to the climate system.

Static deep stall analysis augmented by numerically constrained turbulent flows

As computational resources have advanced, scale-resolving methods like large eddy simulation (LES) have gained popularity in the aerodynamic design particularly in predicting massively separated flow regions. The limitations of traditional Reynolds-averaged Navier–Stokes (RANS) are evident in this regime, given the importance of the intrinsic unsteadiness and the strong three-dimensionality of the flow. This research focuses on wall-resolved implicit large eddy simulation (ILES) for airfoil flows in deep stall with a focus on its dynamics. Moreover, it is also of interest to understand how the spanwise extent of the computational domain affects the resolved aerodynamic forces and flow dynamics. The simulations in this study analyzed various spanwise extents (lz ranging from 0.10c to 2c) under specific conditions: a chord Reynolds number Re=105, an asymptotic Mach number M∞=0.15, and an angle of attack α = 20 degrees. Significant differences were found in aerodynamic coefficients and flow dynamics when the smallest spanwise extent was used. Specifically, spectral proper orthogonal decomposition showed that a small span failed to capture critical low-frequency dynamics necessary for predicting adequate stall behavior. Additionally, the turbulence field in the small span case remained largely rod-like, unlike the three-dimensional turbulence seen in larger spans. The current work propose the nondimensional spanwise integral length scale (SILS/lz) as a metric for determining the sufficiency of spanwise extent, using two-point correlations for the streamwise velocity. Findings suggest that a spanwise extent of lz=1c is sufficient, with minimal differences observed between lz=1c and lz=2c. The results emphasize the importance of adequate spanwise resolution to accurately capture deep-stall flow structures and their unsteady behavior.

The robustness of skyrmion numbers of structured optical fields in atmospheric turbulence

The robustness of skyrmion numbers of structured optical fields in atmospheric turbulence

Suppression of photospheric velocity fluctuations in strongly magnetic O stars in radiation-magnetohydrodynamic simulations

O stars generally show clear signs of strong line broadening (in addition to rotational broadening) in their photospheric absorption lines (typically referred to as macroturbulence), believed to originate in a turbulent sub-surface zone associated with enhanced opacities due to the recombination of iron-group elements (at T ∼ 150-200 kK). O stars with detected global magnetic fields also display such macroturbulence; the sole exception to this is NGC 1624-2, which also has the strongest (by far) detected field of the known magnetic O stars. It has been suggested that this lack of additional line broadening is due to NGC 1624-2's exceptionally strong magnetic field, which might be able to suppress the turbulent velocity field generated in the iron opacity peak zone. We tested this hypothesis based on two-dimensional (2D), time-dependent, radiation magnetohydrodynamical (RMHD) box-in-a-star simulations for O stars that encapsulate the deeper sub-surface atmosphere (down to T ∼ 400 kK), the stellar photosphere, and the onset of the supersonic line-driven wind in one unified approach. To study the potential suppression of atmospheric velocity fluctuations, we extended our previous non-magnetic O star radiation-hydrodynamic (RHD) simulations to include magnetic fields of varying strengths and orientations. We used MPI-AMRVAC which is a Fortran 90 based publically available parallel finite volume code that is highly modular. We used the recently added RMHD module to perform all our simulations here. For moderately strong magnetic cases (∼ 1 kG), the simulated atmospheres are highly structured and characterised by large root-mean-square velocities, and our results are qualitatively similar to those found in previous non-magnetic studies. By contrast, we find that a strong horizontal magnetic field in excess of 10 kG can indeed suppress the large velocity fluctuations, and can thus stabilise (and thereby also inflate) the atmosphere of a typical early O star in the Galaxy. On the other hand, an equally strong radial field is only able to suppress horizontal motions, and as a consequence these models exhibit significant radial fluctuations. Our simulations provide an overall physical rationale as to why NGC 1624-2 with its strong ∼ 20 kG dipolar field lacks the large macroturbulent line broadening that all other known slowly rotating early O stars exhibit. However, our simulations also highlight the importance of field geometry for controlling the atmospheric dynamics in massive and luminous stars that are strongly magnetic, tentatively suggesting latitudinal dependence of macroturbulence and basic photospheric parameters.

ИССЛЕДОВАНИЕ ПРИМЕНИМОСТИ МЕТОДОВ ИДЕНТИФИКАЦИИ КОГЕРЕНТНЫХ ВИХРЕВЫХ СТРУКТУР В МОДЕЛЬНЫХ ЭКСПЕРИМЕНТАХ

Stable in time vortices, which can be considered as coherent vortex structures (CVSs), highly influence processes of momentum, heat and mass transfer in any fluid, including an atmosphere and an ocean. They affect all scales of motion, as a consequence, vortices of all scales play a crucial role in climatological system of Earth. Nowadays the most studied processes in geophysics are large vortices (cyclones), while mesoscale and submesoscale processes in the atmosphere and ocean remain at “gray zone”, especially little information on their impact on the climate scale. Climate assessment requires the ability to automatically identify CVS in spatial data (for example, in numerical modeling data). The main limitation in development of this direction is the lack of strict mathematical definition of a vortex. Some developments in this direction have been carried out in the field of small-scale turbulence, where a number of criteria have been developed. The main advantage of this methodology is the ability to identify vortex motions of any scale and in any continuous medium, the minimum size of the vortex is determined exclusively by the spatial resolution of the data used. The paper examines applicability of these vortex identification methods (VIMs) to significantly largerscale geophysical data. For analysis, the most proven Eulerian methods of vortex identification were chosen, which are Q, Δ, λ2, λci and Rortex criteria. The paper demonstrates the comparison of three generations of VIMs in application to idealized two- and three-dimensional vortices. The study showed that Rortex criterion is the most promising in the case of identification of atmospheric mesoscale processes: it most reliably identifies the CVS, and also provides information about the direction of rotation. The DBSCAN method, used in the study for clustering of individual coherent structures, makes it possible to estimate the geometric properties and various vortex statistics. The developed approach can be used for climate analysis of the dynamics of mesoscale vortices.

Airborne observations of fast-evolving ocean submesoscale turbulence

Ocean images collected by astronauts onboard the Apollo spacecraft more than 50 years ago revealed a large number of ocean eddies, with a size between 1 and 20 km. Since then, satellite infrared, ocean color, sun glitter and synthetic aperture radar images, with high spatial resolution, have confirmed the ubiquitous presence of these small eddies in all oceans. However, observing the dynamical characteristics and evolution of these eddies has remained challenging. An experiment was recently carried out in the California Current system using the new airborne Doppler Scatterometer (National Aeronautics and Space Administration-Jet Propulsion Laboratory DopplerScatt) instrument that observes surface velocities. Here, with DopplerScatt, we mapped a 30 × 100 km domain over multiple days to unveil numerous 1–20 km ocean eddies, called submesoscale eddies, that evolve over a period of a few hours. The strong interactions between eddies generate horizontal velocity divergence, implying vertical velocities reaching 250 m day−1 at 40 m depth. The velocity field also produces horizontal dispersion of particles over a distance of 50 km within 12 h, which rapidly fills the turbulent eddy field. These observations suggest that submesoscale ocean turbulence may profoundly affect the vertical transport of heat, carbon, and important climatic gases between the atmosphere and the ocean interior, as well as the horizontal dispersion of tracers and particles. As such, submesoscale ocean eddies are a critical element of Earth’s climate system.

A comparative study of turbulent flow fields in the wake of an isolated boulder, vegetation patch, and wooden log

A comparative study of turbulent flow fields in the wake of an isolated boulder, vegetation patch, and wooden log

EFFECT OF COLOR RANDOMIZATION ON pT BROADENING OF FAST PARTONS IN TURBULENT QUARK-GLUON PLASMA

We analyze the effect of the parton color randomization on pT broadening in the quark-gluon plasma with turbulent color fields. We calculate the transport coefficient for a simplified model of fluctuating color fields in the form of alternating sequential transverse layers with homogenous transverse chromomagnetic fields with random orientation in the SU(3) group and gaussian distribution in the magnitude. Our numerical results show that the color randomization can lead to a sizable reduction of the turbulent contribution to ˆq. The magnitude of the effect grows with increasing ratio of the electric and magnetic screening masses.

Hidden field discovery of turbulent flow over porous media using physics-informed neural networks

This study utilizes physics-informed neural networks (PINNs) to analyze turbulent flow passing over fluid-saturated porous media. The fluid dynamics in this configuration encompass complex features, including leakage, channeling, and pulsation at the pore-scale, which pose challenges for detailed flow characterization using conventional modeling and experimental approaches. Our PINN model integrates (i) implementation of domain decomposition in regions exhibiting abrupt flow changes, (ii) parameterization of the Reynolds number in the PINN model, and (iii) Reynolds Averaged Navier–Stokes (RANS) k−ε turbulence model within the PINN framework. The domain decomposition method, distinguishing between non-porous and porous regions, enables turbulent flow reconstruction with a reduced training dataset dependency. Furthermore, Reynolds number parameterization in the PINN model facilitates the inference of hidden first and second-order statistics flow fields. The developed PINN approach tackles both the reconstruction of turbulent flow fields (forward problem) and the prediction of hidden turbulent flow fields (inverse problem). For training the PINN algorithm, computational fluid dynamics (CFD) data based on the RANS approach are deployed. The findings indicate that the parameterized domain-decomposed PINN model can accurately predict flow fields while requiring fewer internal training datasets. For the forward problem, when compared to the CFD results, the relative L2 norm errors in PINN predictions for streamwise velocity and turbulent kinetic energy are 5.44% and 18.90%, respectively. For the inverse problem, the predicted velocity magnitudes at the hidden low and high Reynolds numbers in the shear layer region show absolute relative differences of 8.55% and 4.39% compared to the CFD results, respectively.

An Evaluation of Different Numerical Methods to Calculate the Pitch-angle Diffusion Coefficient from Full-orbit Simulations: Disentangling a Rope of Sand

The pitch-angle diffusion coefficient (PADC) quantifies the effect of pitch-angle scattering on charged particles propagating through turbulent magnetic fields and is a key ingredient in understanding the diffusion of these particles along the background magnetic field. Despite its significance, only a limited number of studies have calculated the PADC from test-particle simulations in synthetic magnetic turbulence, employing various, often quite different, techniques for this purpose. In this study, we undertake a comparative analysis of nine different methods for calculating the PADC from full-orbit simulations. Our objective is to find the strengths and limitations of each method and to determine the most reliable approach. Although all nine methods should theoretically yield comparable results, certain methods may be ill-suited for numerical investigations, while others may not be applicable under conditions of strong turbulence. Through this investigation, we aim to provide recommendations for best practices when employing these methods in future numerical studies of pitch-angle scattering.

Wind loads on square lattice towers with tubular members based on wind tunnel test and numerical simulation

The square lattice tower with tubular members (SLTTM) is widely used in civil engineering. Wind load is the primary factor affecting the stability of these structures. This paper presents the wind loads of the SLTTM at different Reynolds numbers (Re) through wind tunnel testing and large eddy simulation (LES). A series of wind tunnel tests with four segment models were first conducted to discuss the effects of wind direction, turbulence intensity, and solidity ratio on the aerodynamic force under low and subcritical Reynolds numbers. The LES method was subsequently employed to determine the aerodynamic force coefficient at Re = 191–1.34 × 106 in both the smooth and uniform turbulent wind fields. The results from wind tunnel tests indicate that the mean and fluctuating drag coefficients at low Reynolds numbers are somewhat different from those at subcritical Reynolds numbers. The solidity ratio and wind direction exert a notable influence on the mean drag coefficient, whereas their impact on the fluctuating drag coefficient is relatively minimal. As the turbulence intensity increases, both the mean and fluctuating drag coefficients exhibit a notable rise. The results of the LES at Re = 191–1.34 × 106 show that an increase in turbulence intensity can markedly elevate the fluctuating drag coefficient. However, the effect on the mean drag coefficient is found to depend on the Reynolds number range. The Reynolds number effect on the mean and fluctuating drag coefficients of the SLTTM may be primarily attributed to the members without and with a shielding effect, respectively.

Data-Driven Turbulent Prandtl Number Modeling for Hypersonic Shock–Boundary-Layer Interactions

We develop a neural-network-based variable turbulent Prandtl number model for the k–ϵ turbulence model for improved wall heating predictions in hypersonic shock–boundary-layer interactions (SBLIs). The model is developed by performing a finite-dimensional field inference for a spatially varying turbulent Prandtl number on six canonical SBLIs: three compression ramps at Mach 8 and three impinging shocks at Mach 5. The inference results identify a turbulent Prandtl number that reduces wall heating by systematically directing heat transfer away from the wall. An ensemble of Lipschitz-continuous neural networks is then trained on the inferred turbulent Prandtl number fields to develop a predictive model. We evaluate the resulting variable turbulent Prandtl number model on a suite of test cases, including the hollow cylinder flare and HIFiRE ground test experiments. The machine-learning-augmented model systematically increases Prt near the wall to reduce negative turbulent heat flux while decreasing Prt away from the wall to enhance positive turbulent heat flux, collectively reducing overall heat transfer to the surface. Results show that the learned model consistently improves peak heating predictions by 40–70% compared to the baseline k–ϵ model, a k–ϵ model augmented with various high-speed corrections, and the shear stress transport model across a range of conditions.

LES study of turbulent flow fields over a three-dimensional steep hill considering the effects of thermal stratification

LES study of turbulent flow fields over a three-dimensional steep hill considering the effects of thermal stratification