Turbulent Dynamics Research Articles

Oscillation mechanism and predictive model of explosion load for natural gas in confined tube

Gas explosion in confined space often leads to significant pressure oscillation. It is widely recognized that structural damage can be severe when the oscillation frequency of the load resonates with the natural vibration frequency of the structure. To reveal the oscillation mechanism of gas explosion load, the experiment of gas explosion was conducted in a large-scale confined tube with the length of 30 m, and the explosion process was numerically analyzed using FLACS. The results show that the essential cause of oscillation effect is the reflection of the pressure wave. In addition, due to the difference in the propagation path of the pressure wave, the load oscillation frequency at the middle position of the tunnel is twice that at the end position. The average sound velocity can be used to calculate the oscillation frequency of overpressure accurately, and the error is less than 15%. The instability of the flame surface and the increase of flame turbulence caused by the interaction between the pressure wave and the flame surface are the main contributors to the increase in overpressure and amplitude. The overpressure peaks calculated by the existing flame instability model and turbulence disturbance model are 31.7% and 34.7% lower than the numerical results, respectively. The turbulence factor model established in this work can describe the turbulence enhancement effect caused by flame instability and oscillatory load, and the difference between the theoretical and numerical results is only 4.6%. In the theoretical derivation of the overpressure model, an improved model of dynamic turbulence factor is established, which can describe the enhancement effect of turbulence factor caused by flame instability and self-turbulence. Based on the one-dimensional propagation theory of pressure wave, the oscillatory effect of the load is derived to calculate the frequency and amplitude of pressure oscillation. The average error of amplitude and frequency is less than 20%.

Symmetries of the Electromagnetic Turbulence in a Tokamak Edge

We construct the low-frequency formulation of the turbulence characterizing the plasma in a Tokamak edge. Under rather natural assumptions, we demonstrate that, even in the presence of poloidal magnetic fluctuations, it is possible to deal with a reduced model for turbulence dynamics. This model relies on a single equation for the electric potential from which all the physical turbulent properties can be calculated. The main result of the present analysis concerns the existence of a specific Fourier branch for the dynamics which demonstrate the attractive character of the two-dimensional turbulence with respect to non-axisymmetric fluctuations. The peculiar nature of this instability, affecting the non-axially symmetric modes, is discussed in some detail by recovering two different physical regimes.

Personal Recollections on Jack Herring and Developments in Theory of Turbulence, Atmospheric Sciences, and Computational Fluid Dynamics

The majority of articles in this Special Issue illuminate various aspects of Jack Herring’s contributions to the theory of turbulence, atmospheric sciences, and computational fluid dynamics (CFD), be it through his publications, presentations, collaborations, work with colleagues and students, or personal contacts [...]

Geometric frustration and pairing-order transition in confined bacterial vortices

Dense systems of active matter exhibit highly dynamic collective motion characterized by intermingled vortices, referred to as active turbulence. The interaction between these vortices is key to controlling turbulent dynamics, and a promising approach for revealing the rules governing their interaction is geometric confinement. In this study, we investigate the vortex-pairing patterns in confined bacterial suspensions as a model frustrated system in which a perfect antiferromagnetic state is prohibited. We find that three-body vortex interactions exhibit anomalous pairing-order transition from corotational vortex pairing to counterrotating patterns with frustration. Although an active matter system is in nonequilibrium, our theory based on bending energy accounts for significant features, including pattern transition and a shift of the transition point in frustrated systems. Moreover, the interplay between the chirality in collective motion and frustration in vortex pairing creates a collective rotational flow under the broad geometric conditions of a confined space. Our results show that frustrated vortex patterning promotes a geometric approach for arranging active turbulence in microfluidic systems. Published by the American Physical Society 2024

Holographic turbulence from a random gravitational potential

We study the turbulent dynamics of a relativistic (2 + 1)-dimensional fluid placed in a stochastic gravitational potential. We demonstrate that the dynamics of the fluid can be obtained using a dual holographic description realized by an asymptotically Anti-de Sitter black brane driven by a random boundary metric. Using the holographic duality we study the energy power spectrum of a fluid with an inverse energy cascade and show that it is compatible with that of a compressible fluid flow. We calculate the local energy dissipation and the local fluid velocity distribution which provide other measures of the holographic fluid turbulence.

Turbulent Exchange in Unsteady Air-Sea Interaction at Small and Submesoscales

An adequate description of the interaction between the atmosphere and ocean remains one of the most important problems of modern oceanology and climatology. An extremely wide variety of physical processes occurring in the coupled layers, a large range of scales, a moving boundary, all this factors significantly complicates the creation of models that would allow calculating the physical characteristics in both media with the necessary accuracy. In this paper the temporal variability of dynamic parameters in the driving layer of the atmosphere and in the near-surface layer of the sea on small and sub-mesoscales from one to several tens of hours is considered. The collected experimental data show a very high correlation between the dynamic wind speed and turbulence intensity in the upper sea layer on all scales recorded. An important distinguishing feature of all measured physical quantities in both media is the presence of quasi-periodic oscillations with different periods. For a more accurate description of momentum and energy fluxes from the atmosphere a non-stationary model of turbulent exchange in the near-surface layer of the sea is proposed. The model takes into account quasi-periodicity in the intensity of dynamic interaction between the atmosphere and the sea at these scales. In the model we use the equations of momentum and turbulent energy balance, the system of equations is solved numerically, the calculation results are compared with other models and with experimental data. It is shown that taking into account the non-stationarity of the wind strain improves the correspondence between the calculations and the experimental data. It is noted that in the nonstationary case, the energy and momentum flux from the atmosphere and the turbulence intensity increases compared to the action of a constant average wind of the same duration. Therefore, the strong averaging often used in global models may markedly underestimate the intensity of the dynamic interaction between the atmosphere and ocean.

Effect of Model Fidelity on High-Speed Aeroelastic Behavior of a Cantilever Plate

Turbulence, flow separation, and shock dynamics challenge the modeling and analysis of high-speed aeroelastic behavior. Motivated by this, the importance of modeling the fidelity of the flow is explored in the aeroelastic response of a cantilever plate in an Ma=2.0 separating turbulent flow using unsteady Reynolds-averaged Navier–Stokes (URANS) and URANS-enriched local piston theory (LPT). Structural modeling assumptions are also evaluated using both linear and nonlinear representations. Close agreement in the predicted aeroelastic steady state is observed. However, large discrepancies in the dynamic aeroelastic response predictions are found and ultimately linked to the neglect of deformation-induced cavity pressure fluctuations and dynamic flow separation in the LPT model. Interestingly, the dynamic flow separation induces a fluid-driven limit cycle oscillation in the postflutter regime. Furthermore, structural nonlinearity is not found to have a strong impact on the conditions and configurations considered.

Causal analysis among azimuthal Fourier modes in linear plasma based on multivariate time series models

This study investigates the causal relationships among azimuthal Fourier modes in linear plasma turbulence using multivariate time series models. We elucidate the dynamics of mode interactions in magnetized plasmas by employing the vector autoregressive model and Granger causality analysis. Our analysis, based on data from the plasma assembly for nonlinear turbulence analysis, reveals significant variations in causality with changing pressure conditions. Modes form weakly coupled clusters at lower pressures, while higher pressures lead to stronger coupling and larger clusters. The impulse response function further provides insights into the temporal propagation and nature of influences between modes. These findings enhance the understanding of spatial pattern formation in magnetized plasmas and offer a quantitative framework for analyzing plasma turbulence dynamics.

Turbulent Ice–Ocean Boundary Layers in the Well-Mixed Regime: Insights from Direct Numerical Simulations

Abstract The meltwater mixing line (MML) model provides a theoretical prediction of near-ice water mass properties that is useful to compare with observations. If oceanographic measurements reported in a temperature–salinity diagram overlap with the MML prediction, then it is usually concluded that the local dynamics are dominated by the turbulent mixing of an ambient water mass with near-ice meltwater. While the MML model is consistent with numerous observations, it is built on an assumption that is difficult to test with field measurements, especially near the ice boundary, namely, that the effective (turbulent and molecular) salt and temperature diffusivities are equal. In this paper, this assumption is tested via direct numerical simulations of a canonical model for externally forced ice–ocean boundary layers in a uniform ambient. We focus on the well-mixed regime by considering an ambient temperature close to freezing and run the simulations until a statistical steady state is reached. The results validate the assumption of equal effective diffusivities across most of the boundary layer. Importantly, the validity of the MML model implies a linear correlation between the mean salinity and temperature profiles normal to the interface that can be leveraged to construct a reduced ice–ocean boundary layer model based on a single scalar variable called thermal driving. We demonstrate that the bulk dynamics predicted by the reduced thermal driving model are in good agreement with the bulk dynamics predicted by the full temperature–salinity model. Then, we show how the results from the thermal driving model can be used to estimate the interfacial heat and salt fluxes and the melt rate. Significance Statement We investigate the turbulent dynamics and thermodynamical properties of water masses below ice shelves using new data from high-resolution simulations. This is important because there are currently too few observations of ice–ocean boundary layer dynamics to construct reliable models of ice-shelf melting as a function of ocean conditions. Our results demonstrate that the turbulent diffusivities of salt and temperature are approximately equal in the well-mixed regime. This implies a linear correlation between the mean temperature and salinity profiles, consistent with the meltwater mixing line prediction that is often used to interpret polar observations. We take advantage of this correlation to propose a reduced model of ice–ocean boundary layers that can predict ice-shelf melt rates at relatively low computational cost.

A Detailed Survey of the Parallel Mean Free Path of Solar Energetic Particle Protons and Electrons

In this work, more than a dozen solar energetic particle (SEP) events are identified where the source region is magnetically well connected to at least one spacecraft at 1 au. The observed intensity–time profiles, for all available proton and electron energy channels, are compared to results computed using a numerical one-dimensional SEP transport model in order to derive the parallel mean free paths (pMFPs) as a function of energy (or rigidity) at 1 au. These inversion results are then compared to theoretical estimates of the pMFP, using observed turbulence quantities with observationally motivated variations as input. For protons, a very good comparison between inversion and theoretical results is obtained. It is shown that the observed inter-event variations in the inversion pMFP values can be explained by natural variations in the background turbulence values. For electrons, there is relatively good agreement with pMFPs derived assuming the damping model of dynamical turbulence, although the theoretical values are extremely sensitive to the details of the turbulence dissipation range, which themselves display a high level of variation.

Statistical Dynamics and Subgrid Modelling of Turbulence: From Isotropic to Inhomogeneous

Turbulence is the most important, ubiquitous, and difficult problem of classical physics. Feynman viewed it as essentially unsolved, without a rigorous mathematical basis to describe the statistical dynamics of this most complex of fluid motion. However, the paradigm shift came in 1959, with the formulation of the Eulerian direct interaction approximation (DIA) closure by Kraichnan. It was based on renormalized perturbation theory, like quantum electrodynamics, and is a bare vertex theory that is manifestly realizable. Here, we review some of the subsequent exciting achievements in closure theory and subgrid modelling. We also document in some detail the progress that has been made in extending statistical dynamical turbulence theory to the real world of interactions with mean flows, waves and inhomogeneities such as topography. This includes numerically efficient inhomogeneous closures, like the realizable quasi-diagonal direct interaction approximation (QDIA), and even more efficient Markovian Inhomogeneous Closures (MICs). Recent developments include the formulation and testing of an eddy-damped Markovian anisotropic closure (EDMAC) that is realizable in interactions with transient waves but is as efficient as the eddy-damped quasi-normal Markovian (EDQNM). As a similarly efficient closure, the realizable eddy-damped Markovian inhomogeneous closure (EDMIC) has been developed. Moreover, we present subgrid models that cater for the complex interactions that occur in geophysical flows. Recent progress includes the determination of complete sets of subgrid terms for skilful large-eddy simulations of baroclinic inhomogeneous turbulent atmospheric and oceanic flows interacting with Rossby waves and topography. The success of these inhomogeneous closures has also led to further applications in data assimilation and ensemble prediction and generalization to quantum fields.

Physics-informed neural network for turbulent flow reconstruction in composite porous-fluid systems

This study explores the implementation of physics-informed neural networks (PINNs) to analyze turbulent flow in composite porous-fluid systems. These systems are composed of a fluid-saturated porous medium and an adjacent fluid, where the flow properties are exchanged across the porous-fluid interface. The segregated PINN model employs a novel approach combining supervised learning and enforces fidelity to flow physics through penalization by the Reynolds-averaged Navier-Stokes (RANS) equations. Two cases were simulated for this purpose: solid block, i.e. porous media with zero porosity, and porous block with a defined porosity. The effect of providing internal training data on the accuracy of the PINN predictions for prominent flow features, including flow leakage, channeling effect and wake recirculation was investigated. Additionally, L2 norm error, which evaluates the prediction accuracy for flow variables was studied. Furthermore, PINN training time in both cases with internal training data was considered in this study. Results showed that the PINN model predictions with second-order internal training data achieved high accuracy for the prominent flow features compared to the RANS data, within a 20% L2 norm error of second-order statistics in the solid block case. In addition, for the porous block case, providing training data at the porous-fluid interface showed errors of 18.04% and 19.94% for second-order statistics, representing an increase in prediction accuracy by 7% compared to without interface training data. The study elucidates the impact of the internal training data distribution on the PINN training in complex turbulent flow dynamics, underscoring the necessity of turbulent second-order statistics variables in PINN training and an additional velocity gradient treatment to enhance PINN prediction.

Resolution analysis of magnetically arrested disc simulations

ABSTRACT Polarization measurements by the Event Horizon Telescope from M87* and Sgr A* suggest that there is a dynamically strong, ordered magnetic field, typical of what is expected of a magnetically arrested accretion disc (MAD). In such discs, the strong poloidal magnetic field can suppress the accretion flow and cause episodic flux eruptions. Recent work shows that general relativistic magnetohydrodynamic (GRMHD) MAD simulations feature dynamics of turbulence and mixing instabilities that are becoming resolved at higher resolutions. We perform a convergence study of MAD states exceeding the status quo by an order of magnitude in resolution. We use existing 3D simulations performed with the H-AMR code, up to a resolution of 5376 × 2304 × 2304 in a logarithmic spherical-polar grid. We find consistent time-averaged disc properties across all resolutions. However, higher resolutions reveal signs of inward angular momentum transport attributed to turbulent convection, particularly evident when mixing instabilities occur at the surfaces of flux tubes during flux eruptions. Additionally, we see wave-like features in the jet sheath, which become more prominent at higher resolutions, that may induce mixing between the jet and disc. At higher resolutions, we observe the sheath to be thinner, resulting in increased temperature, reduced magnetization, and greater variability. Those differences could affect the dissipation of energy, which would eventually result in distinct observable radiative emission from high-resolution simulations. With higher resolutions, we can delve into crucial questions about horizon-scale physics and its impact on the dynamics and emission properties of larger-scale jets.

Grey‐zone simulations of shallow‐to‐deep convection transition using dynamic subgrid‐scale turbulence models

AbstractWe examine the ability of two dynamic turbulence closure models to simulate the diurnal development of convection and the transition from dry to shallow cumuli and then to deep convection. The dynamic models are compared with the conventional Smagorinsky scheme at a range of cloud‐resolving and grey‐zone resolutions. The dynamic schemes include the Lagrangian‐averaged, scale‐dependent dynamic Smagorinsky model and a Lagrangian‐averaged, dynamic mixed model. The conventional Smagorinsky model fails to reproduce the shallow convection stage beyond the large‐eddy simulation regime, continuously building up the convective available potential energy that eventually leads to an unrealistic deep convection phase. The dynamic Smagorinsky model significantly improves the representation of shallow and deep convection; however, it exhibits issues similar to the conventional scheme at coarser resolutions. In contrast, the dynamic mixed model closely follows the large‐eddy simulation results across the range of sub‐kilometre simulations. This is achieved by the combined effect of an adaptive length scale and the inclusion of the Leonard terms, which can produce counter‐gradient fluxes through the backscatter of energy from the subgrid to the resolved scales and enable appropriate non‐local contributions. A further sensitivity test on the inclusion of the Leonard terms on all hydrometeor fluxes reveals the strong interaction between turbulent transport and microphysics and the possible need for further optimisation of the dynamic mixed model coefficients together with the microphysical representation.

Cyclogenesis: Simulating Hurricanes and Tornadoes

Cyclones are large-scale phenomena that result from complex heat and water transfer processes in the atmosphere, as well as from the interaction of multiple hydrometeors , i.e., water and ice particles. When cyclones make landfall, they are considered natural disasters and spawn dread and awe alike. We propose a physically-based approach to describe the 3D development of cyclones in a visually convincing and physically plausible manner. Our approach allows us to capture large-scale heat and water continuity, turbulent microphysical dynamics of hydrometeors, and mesoscale cyclonic processes within the planetary boundary layer. Modeling these processes enables us to simulate multiple hurricane and tornado phenomena. We evaluate our simulations quantitatively by comparing to real data from storm soundings and observations of hurricane landfall from climatology research. Additionally, qualitative comparisons to previous methods are performed to validate the different parts of our scheme. In summary, our model simulates cyclogenesis in a comprehensive way that allows us to interactively render animations of some of the most complex weather events.

Unveiling Turbulent Flow Dynamics in Blind-Tee Pipelines: Enhancing Fluid Mixing in Subsea Pipeline Systems

Blind tees, as important junctions, are widely used in offshore oil and gas transportation systems to improve mixing flow conditions and measurement accuracies in curved pipes. Despite the significance of blind tees, their unsteady flow characteristics and mixing mechanisms in turbulent flow regimes are not clearly established. Therefore, in this study, Unsteady Reynolds-Averaged Navier–Stokes (URANS) simulations, coupled with Explicit Algebraic Reynolds Stress Model (EARSM), are employed to explore the complex turbulent flow characteristics within blind-tee pipes. Firstly, the statistical flow features are investigated based on the time-averaged results, and the swirl dissipation analysis reveals an intense dissipative process occurring within blind tees, surpassing conventional elbows in swirling intensity. Then, the instantaneous flow characteristics are investigated through time and frequency domain analysis, uncovering the oscillatory patterns and elucidating the mechanisms behind unsteady secondary flow motions. In a 2D-length blind tee, a nondimensional dominant frequency of oscillation (Stbt = 0.0361) is identified, highlighting the significant correlation between dominant frequencies inside and downstream of the plugged section, which emphasizes the critical role of the plugged structure in these unsteady motions. Finally, a power spectra analysis is conducted to explore the influence of blind-tee structures, indicating that the blind-tee length of lbt = 2D enhances the flow-mixing conditions by amplifying the oscillation intensities of secondary flow motions.

Chaotic edge regimes in magnetohydrodynamic channel flow: An alternative path towards the tipping point

The effect of an imposed magnetic field on the flow of an electrically conducting fluid in a channel geometry is investigated numerically using high-performance temporal simulations. For the strongest spanwise magnetic fields considered, the turbulent state appears metastable, which makes the determination of the associated tipping point arduous. As an alternative, edge states, i.e., unstable states located on the state space boundary between the laminar and the turbulent basin of attraction, are investigated in detail. Their continuation smoothly leads to the tipping point where they are expected to collide with the turbulent dynamics. As the magnetic field intensity is raised, edge states become, on average, more energetic and more unstable, while their fluctuations become more chaotic, less predictable, and less symmetric. Nevertheless, their continuation allows one to accurately determine the value of the tipping point beyond which the laminar state becomes the only attractor. Published by the American Physical Society 2024

Enhancing flood wave modelling of reservoir failure: a comparative study of structure-from-motion based 2D and 3D methodologies

Predicting flood wave propagation from reservoir failures is critical to practical flood hazard assessment and risk management. Flood waves are sensitive to topography, channel geometry, structures, and natural features along floodplain paths. Thus, the accuracy of flood wave modelling depends on how precisely those features are represented. This study introduces an enhancing approach to flood wave modelling by accurately representing three-dimensional objects in floodplains using the structure-from-motion (SfM). This method uses an unmanned aerial vehicle to capture topographic complexities and account for ground objects that impact flood propagation. Using the three-dimensional volume of fluid numerical approach significantly improves an enhanced representation of turbulent flow dynamics and computational efficiency, especially in handling large topography datasets. Reproductions from this enhanced three-dimensional approach were validated against recent reservoir failure observations and contrasted with traditional two-dimensional models. The results revealed that the suggested three-dimensional methodology achieved a significant 84.4% reproducibility when juxtaposed with actual inundation traces. It was 35.5%p more accurate than the two-dimensional diffusion wave equation (DWE) and 17.1%p more than the shallow water equation (SWE) methods in predicting flood waves. This suggests that the reproducibility of the DWE and SWE decreases compared to the three-dimensional approach when considering more complex floodplains. These results demonstrate that three-dimensional flood wave analysis with the SfM methodology is optimal for effectively minimising topographic and flood wave reproduction errors across extensive areas. This dual reduction in errors significantly enhances the reliability of flood hazard assessments and improves risk management by providing more precise and realistic predictions of flood waves.

Droplet dynamics in homogeneous isotropic turbulence with the immersed boundary-lattice Boltzmann method.

We develop a numerical method for simulating the dynamics of a droplet immersed in a generic time-dependent velocity gradient field. This approach is grounded on the hybrid coupling between the lattice Boltzmann (LB) method, employed for the flow simulation, and the immersed boundary (IB) method, utilized to couple the droplet with the surrounding fluid. We show how to enrich the numerical scheme with a mesh regularization technique, allowing droplets to sustain large deformations. The resulting methodology is adapted to simulate the dynamics of droplets in homogeneous and isotropic turbulence, with the characteristic size of the droplet being smaller than the characteristic Kolmogorov scale of the outer turbulent flow. We report statistical results for droplet deformation and orientation collected from an ensemble of turbulent trajectories, as well as comparisons with theoretical models in the limit of small deformation.

Direct observation of atmospheric turbulence with a video-rate wide-field wavefront sensor

Turbulence is a complex and chaotic state of fluid motion. Atmospheric turbulence within the Earth’s atmosphere poses fundamental challenges for applications such as remote sensing, free-space optical communications and astronomical observation due to its rapid evolution across temporal and spatial scales. Conventional methods for studying atmospheric turbulence face hurdles in capturing the wide-field distribution of turbulence due to its transparency and anisoplanatism. Here we develop a light-field-based plug-and-play wide-field wavefront sensor (WWS), facilitating the direct observation of atmospheric turbulence over 1,100 arcsec at 30 Hz. The experimental measurements agreed with the von Kármán turbulence model, further verified using a differential image motion monitor. Attached to an 80 cm telescope, our WWS enables clear turbulence profiling of three layers below an altitude of 750 m and high-resolution aberration-corrected imaging without additional deformable mirrors. The WWS also enables prediction of the evolution of turbulence dynamics within 33 ms using a convolutional recurrent neural network with wide-field measurements, leading to more accurate pre-compensation of turbulence-induced errors during free-space optical communication. Wide-field sensing of dynamic turbulence wavefronts provides new opportunities for studying the evolution of turbulence in the broad field of atmospheric optics.