Three-dimensional Turbulence Research Articles

Characterisation of turbulence at sites with coexisting waves and currents: An analysis by empirical mode decomposition

This paper presents a novel side information assisted Empirical Mode Decomposition (EMD) method for separating wave orbital velocity from a combined wave-tidal current velocity data, measured by three different Acoustic Doppler Current Profilers (ADCPs) deployed in the Pentland Firth, Orkney Waters, UK. The effectiveness of this technique is confirmed through two methods: (1) the spectra of the wave-removed velocity align with the Kolmogorov −5/3 power law, and (2) the extracted wave orbital velocities were used to derive significant wave heights, which were validated against wave heights measured by the same ADCPs and through numerical modelling carried out with a coupled wave-current tool (TOMAWAC-TELEMAC 3D).The decomposed data was further used to calculate three-dimensional turbulence intensities (TI) for combined wave-current, wave-only, and current-only conditions, across different flow speeds and wave heights. The results demonstrate the robustness of the decomposition method in various scenarios and quantify the individual TI contributions from waves, currents, and their combined effects. This work provides valuable insights into the dynamics of areas where waves and currents coexist.

Coherent turbulent flow structure under plunging breaker on movable grain bed simulated by 3D DEM-MPS method

ABSTRACT Breaking waves transport momentum, gas, and sediment vertically. Recent particle image velocimetry (PIV) measurements have elucidated the coherent vortex and turbulence structures under breaking waves. However, clarifying three-dimensional fluid motion under breaking waves with PIV remains challenging. Although particle methods have performed wave-breaking simulations, they have never been validated through velocity distributions for breaking waves above movable sediment beds. This study simulated the sediment transport process under plunging waves using a 3D Lagrangian fluid-particle mixture model. The investigation focuses on the first wave plunging for a fundamental investigation. Our simulation shows the instantaneous velocity distributions at different wave phases, which agree with the PIV measurement. A physically-based turbulence extraction method is introduced: a numerical filter based on the coherence between the water elevation and horizontal velocity. Visualized three-dimensional vortex and turbulence structures are consistent with previous studies. The transport equation of the kinetic turbulence energy investigates the turbulence budget near the bed surface and emphasizes the negative contribution of the fluid-particle interaction. Our findings show that a contribution of the pressure gradient to offshore sediment transport. The pressure gradient is difficult to correlate to the water surface gradient and is derived from the large vortex induced by the plunging wave.

Effect of volute structure on the performance of double suction centrifugal pump

Abstract This study aims to investigate the impact of the double volute structure on the internal flow dynamics and hydraulic performance of a double-suction pump. To achieve this, a double-suction centrifugal pump was selected as the research subject, and three-dimensional turbulence numerical simulations were conducted under various working conditions using the Reynolds average method (RANS) and RNG k-ε turbulence model. The results of the simulation are compared with the experimental data, which demonstrates the validity of the numerical simulation. This study analyzes the impact of the splitter on the flow field within the volute and impeller, as well as its effect on the radial force of the impeller. The results indicate that the water flow has a significant impact on the head of the splitter, resulting in a noticeable high-pressure zone on the pressure side of the blade in close proximity to the starting end of the splitter; Under off-design conditions, a significant recirculation zone exists between the end of the splitter and the pump outlet, and it increases as the deviation from the designed condition increases; In the case of a small flow rate, the flow inhomogeneity near the starting end of the splitter is serious, and there are large zones of low speed on the outside of the splitter; The double volute structure can make the inlet velocity of the volute more evenly distributed along the circumferential direction, and can be effectively utilized to reduce the radial force exerted on the impeller, thereby improving its performance.

GPU-enabled extreme-scale turbulence simulations: Fourier pseudo-spectral algorithms at the exascale using OpenMP offloading

Fourier pseudo-spectral methods for nonlinear partial differential equations are of wide interest in many areas of advanced computational science, including direct numerical simulation of three-dimensional (3-D) turbulence governed by the Navier-Stokes equations in fluid dynamics. This paper presents a new capability for simulating turbulence at a new record resolution up to 35 trillion grid points, on the world's first exascale computer, Frontier, comprising AMD MI250x GPUs with HPE's Slingshot interconnect and operated by the US Department of Energy's Oak Ridge Leadership Computing Facility (OLCF). Key programming strategies designed to take maximum advantage of the machine architecture involve performing almost all computations on the GPU which has the same memory capacity as the CPU, performing all-to-all communication among sets of parallel processes directly on the GPU, and targeting GPUs efficiently using OpenMP offloading for intensive number-crunching including 1-D Fast Fourier Transforms (FFT) performed using AMD ROCm library calls. With 99% of computing power on Frontier being on the GPU, leaving the CPU idle leads to a net performance gain via avoiding the overhead of data movement between host and device except when needed for some I/O purposes. Memory footprint including the size of communication buffers for MPI_ALLTOALL is managed carefully to maximize the largest problem size possible for a given node count.Detailed performance data including separate contributions from different categories of operations to the elapsed wall time per step are reported for five grid resolutions, from 20483 on a single node to 327683 on 4096 or 8192 nodes out of 9408 on the system. Both 1D and 2D domain decompositions which divide a 3D periodic domain into slabs and pencils respectively are implemented. The present code suite (labeled by the acronym GESTS, GPUs for Extreme Scale Turbulence Simulations) achieves a figure of merit (in grid points per second) exceeding goals set in the Center for Accelerated Application Readiness (CAAR) program for Frontier. The performance attained is highly favorable in both weak scaling and strong scaling, with notable departures only for 20483 where communication is entirely intra-node, and for 327683, where a challenge due to small message sizes does arise. Communication performance is addressed further using a lightweight test code that performs all-to-all communication in a manner matching the full turbulence simulation code. Performance at large problem sizes is affected by both small message size due to high node counts as well as dragonfly network topology features on the machine, but is consistent with official expectations of sustained performance on Frontier. Overall, although not perfect, the scalability achieved at the extreme problem size of 327683 (and up to 8192 nodes — which corresponds to hardware rated at just under 1 exaflop/sec of theoretical peak computational performance) is arguably better than the scalability observed using prior state-of-the-art algorithms on Frontier's predecessor machine (Summit) at OLCF. New science results for the study of intermittency in turbulence enabled by this code and its extensions are to be reported separately in the near future.

Benchmark of computational hydraulics models for open-channel flow with lateral cavities

Computational models in hydro-environmental engineering are diverse in their background formulation and span from two-dimensional depth-averaged shallow water models, to complex fully three-dimensional turbulence models resolving large-eddy simulation with surface capturing techniques, and to Lagrangian particle-based methods. This paper presents a first-of-its-kind comparison of six different computational hydraulics fluid dynamics models, namely Iber+, HO-SWM, GBVC, OpenFOAM (RANS), Hydro3D (LES) and DualSPHysics (SPH), in the prediction of mean velocities and free-surface dynamics in two benchmarks involving open-channel flows with symmetric lateral cavities. Results show that shallow-water models capture relatively well the main large-scale coherent structures of the in-cavity flow, with wider shear layers compared to three-dimensional models, and higher velocities in the main channel. Three-dimensional RANS, LES and SPH yield improved predictions of mean velocities compared with experimental data. Computational cost has been quantified for all models with a logarithmic growth when increasing model complexity. The transverse standing wave is captured by most models, with the shallow-water ones matching the theoretical value, while the three-dimensional models overestimate it slightly.

Effect of three-dimensionality of turbulence on the along-wind loads of square cross-sectional structures

The existing theories for along-wind loads on slender structures, based on the “strip assumption” overlook the three-dimensionality of turbulence. However, numerous experimental phenomena contradicting the “strip assumption” highlight the need to consider the effects of three-dimensional turbulence (3D effect). This study develops an analysis model that considers the three-dimensionality of turbulence and derives a function containing the section-shape-dependent characteristic parameters to represent the 3D effect. A method for identifying the parameters through a wind tunnel test is proposed to solve this function. The parameters for the square cross section are then identified in two different turbulence fields, revealing that the identification parameters of both cases are nearly identical. This similarity indicates that the parameters are independent of the turbulence validating the proposed theories. Finally, the 3D effect on square cross-sectional structures with different aspect ratios under various turbulence integral scales is analyzed. The results showed that as the ratio of the turbulence integral scale to the windward width of the structures increases, the 3D effect reduces, but the rate of reduction slows down. In addition, increasing the aspect ratios of structures further mitigates the 3D effect, enhancing the accuracy of the “strip assumption.” These results can be a reference for evaluating the accuracy of the “strip assumption” theory for square cross-sectional high-rise buildings in atmospheric boundary layer turbulence. The proposed method can be applied to investigate the 3D effect on along-wind loads of slender structures with various cross-sectional shapes.

Large eddy simulation analysis of a model reactive tracer through spatial filtering

Large eddy simulations (LES) provide a methodology for both analyzing and simulating multi-scale flows when the smallest scales of motion cannot be resolved. Within environmental flows there exist numerous biogeochemical processes involving tracers undergoing reactions. In this study, we perform an a posteriori LES analysis on a direct numerical simulation of an idealized model reactive tracer subjected to three-dimensional turbulence induced by a Rayleigh–Taylor instability. The governing equations, including an advection–diffusion–reaction equation for the reactive tracer, are filtered, and the resulting sub-filter-scale terms are expressed in terms of interactions between scales. The procedure is demonstrated for a generalized degree N polynomial reaction function. Various spectral filters are applied to the data and compared. The preferential choice is to use the widest filter possible with a smoothed cutoff. The sub-filter-scale reaction term that results from filtering the reaction function is considered for each of the filter choices. When using a particularly harsh filter, local balances are found for the resolved scale and cross-scale components of the sub-filter-scale reaction term. The same result is shown for the vertical sub-filter-scale flux for both a reactive and a passive tracer. The components of the sub-filter-scale reaction and vertical flux terms involving interactions at the sub-filter-scale do not show any evidence of local balances and are distributed around the fine turbulent structures in the flow. This suggests that parameterizations for the sub-filter-scale terms would benefit from considering event specific dynamics.

Generative diffusion models for synthetic trajectories of heavy and light particles in turbulence

Heavy and light particles are commonly found in many natural phenomena and industrial processes, such as suspensions of bubbles, dust, and droplets in incompressible turbulent flows. Based on a recent machine learning approach using a diffusion model that successfully generated single tracer trajectories in three-dimensional turbulence and passed most statistical benchmarks across time scales, we extend this model to include heavy and light particles. Given the particle type – tracer, light, or heavy – the model can generate synthetic, realistic trajectories with correct fat-tail distributions for acceleration, anomalous power laws, and scale dependent local slope properties. This work paves the way for future exploration of the use of diffusion models to produce high-quality synthetic datasets for different flow configurations, potentially allowing interpolation between different setups and adaptation to new conditions.

Three-dimensional plasmoid-mediated reconnection and turbulence in Hall magnetohydrodynamics

Three-dimensional plasmoid-mediated reconnection and turbulence in Hall magnetohydrodynamics

Lifting relations for a generalized total-energy double-distribution-function kinetic model and their impact on compressible turbulence simulation

Recently, Qi et al. (2022) and Guo et al. (2023) proposed two alternative designs of an efficient mesoscopic method using the total-energy double-distribution-function (DDF) formulation, hereafter referred to as the Qi model and the Guo model. The two models share the same advantage of using only 40 discrete particle velocities to fully reproduce the Navier–Stokes-Fourier (NSF) system. However, the Guo model is based on a more rigorous kinetic consideration, while the Qi model relies on a more general design of the source term to allow for adjustable bulk-to-shear viscosity ratio. In this paper, we derive lifting relations for the Qi model based on two alternative approaches, namely, the Hermite expansion and the Chapman–Enskog expansion, which can be used to construct the boundary and initial conditions for the mesoscopic method. For three-dimensional compressible turbulence simulations, including compressible decaying homogeneous isotropic turbulence and Taylor–Green vortex flows, the derived two sets of lifting relations are applied to the initialization distribution function to study their impacts. Interestingly, for the Qi model, the two sets of lifting relations yield the same results without numerical artifacts, whereas for the Guo model, an appropriate lifting relation must be specified to avoid numerical artifacts resulting from the flow initialization (Qi et al., 2023).

Chirality, anisotropic viscosity and elastic anisotropy in three-dimensional active nematic turbulence

Various active materials exhibit strong spatio-temporal variability of their orientational order known as active turbulence, characterised by irregular and chaotic motion of topological defects, including colloidal suspensions, biofilaments, and bacterial colonies.In particular in three dimensions, it has not yet been explored how active turbulence responds to changes in material parameters and chirality.Here, we present a numerical study of three-dimensional (3D) active nematic turbulence, examining the influence of main material constants: (i) the flow-alignment viscosity, (ii) the magnitude and anisotropy of elastic deformation modes (elastic constants), and (iii) the chirality. Specifically, this main parameter space covers contractile or extensile, flow-aligning or flow tumbling, chiral or achiral elastically anisotropic active nematic fluids. The results are presented using time- and space-averaged fields of defect density and mean square velocity. The results also discuss defect density and mean square velocity as possible effective order parameters in chiral active nematics, distinguishing two chiral nematic states—active nematic blue phase and chiral active turbulence. This research contributes to the understanding of active turbulence, providing a numerical main phase space parameter sweep to help guide future experimental design and use of active materials.

Freely Decaying Saffman Turbulence Experimentally Generated by Magnetic Stirrers.

We investigate experimentally the decay of three-dimensional hydrodynamic turbulence, initially generated by the erratic motions of centimeter-size magnetic stirrers in a closed container. Such zero-mean-flow homogeneous isotropic turbulence is well suited to test Saffman's model and Batchelor's model of freely decaying turbulence. Here, we report a consistent set of experimental measurements (temporal decay of the turbulent kinetic energy, of the energy dissipation rate, and growth of the integral scale) strongly supporting the Saffman model. We also measure the conservation of the Saffman invariant at early times of the decay and show that the energy spectrum scales as k^{2} at large scales and keeps its self-similar shape during the decay. This Letter thus presents the first experimental evidence of the validity of the connection between the Saffman invariant and the k^{2}-energy spectrum of the large scales. The final decay regime closely corresponds to Saffman's model when the container size is sufficiently large.

Impact of Fan Position and Speed Adjustments in Glass Greenhouse Environments

In the context of the contemporary development of precision agriculture, glass greenhouses, as an important infrastructure for enhancing crop production efficiency and quality, have become a frontier area of agricultural science and technology innovation for the internal microenvironmental regulation, especially the optimization of airflow dynamics and temperature distribution. In this paper, the study is based on the three-dimensional turbulence model equations of Reynolds number and Darcy-Forkheimer law, and modeled the cases without and with crops, simulated their different wind velocity and temperature, generated the corresponding simulation diagrams and analyzed them, and the results show that changing the Wind velocity to 3m/s or changing the fan position to 1m is a better condition than that with Wind velocity of 2m/s and fan position of 1.3m. In this study, it was found that both variables, Wind velocity and fan position, could affect the growth of crops in glasshouse, excluding most of the factors.

Study on the influence of intermediate airshafts on the aerodynamic effect of urban rapid rail transit

This study explores how intermediate airshafts affect the aerodynamics of urban rapid transit trains in tunnels. It employs a three-dimensional turbulence model to simulate train-tunnel interactions, specifically examining airshafts’ impact on transient pressure variations along surfaces. The model’s accuracy and reliability are confirmed by comparing results with full-scale experimental data. The results show that airshafts effectively mitigate peak tunnel wall pressures, with the lowest peak overpressure observed at the airshaft location. With the airshaft-reflected expansion wave arriving ahead of the train, the pressure between the train front and tunnel wall decreases compared to scenarios without airshafts. Similar transient pressure changes at the tunnel entrance and rear half suggest the emergence of a “secondary compression wave” due to the train’s transit.

Turbulence generation in transonic shock diffraction

In this Letter, we have quantified the zones of turbulence in transonic shock diffraction across a 90° step corner using Lamb vector analysis. We have analyzed the nature of the three-dimensional turbulence structures using invariants of the velocity gradient tensor. From our results, we conclude that the vortex-induced shock, the lambda shock on the shear layer, and the Kelvin–Helmholtz instability forming on the shear layer are the main contributors in turbulence generation. In our study, we have shown that two-dimensional simulations can resolve the gasdynamic behavior accurately, though three-dimensional simulations are required to understand turbulent structures.

Triad interactions investigated by dual wave component injection

The study of the exchange of momentum and energy between wave components of the turbulent velocity field, the so-called triad interactions, offers a unique way of visualizing and describing turbulence. Most often, this study has been carried out by direct numerical simulations or by power spectral measurements. Due to the complexity of the problem and the great range of velocity scales in high Reynolds number developed turbulence, direct measurements of the interaction between the individual wave components have been rare. In the present work, we present measurements and related computations of triad interactions between controlled wave components injected into an approximately laminar and uniform flow from an open wind tunnel by vortex shedding from two rods suspended into the flow. This results in two-dimensional interactions of three-dimensional turbulence, which makes the analysis of the triadic interactions considerably less complex to analyze than in a fully developed three-dimensional flow. With the information obtained from the computations, we are able to isolate the individual triad interactions contributing to the generated frequency components as the flow develops downstream as well as understanding, mapping out and predicting the strengths of these interactions. The analysis also provides the time constants governing the development of higher order frequency components. We are thus able to see the pattern of frequency combinations, the strengths of the individual mode combinations and the time sequence in which they occur. Any of the higher order combinations is not just the result of a single term in the Navier–Stokes Equation, but a combination of various previous combinations occurring with different strengths and in a varied pattern of generation. The combination of these experiments and computations thus provide unique insight into the inner workings of turbulence and shows how the nonlinear term in the Navier–Stokes equation on average forces the energy towards higher frequencies, which is the reason for the so-called energy cascade.

Deep tomography for the three-dimensional atmospheric turbulence wavefront aberration

Multiconjugate adaptive optics (MCAO) can overcome atmospheric anisoplanatism to achieve high-resolution imaging with a large field of view (FOV). Atmospheric tomography is the key technology for MCAO. The commonly used modal tomography approach reconstructs the three-dimensional atmospheric turbulence wavefront aberration based on the wavefront sensor (WFS) detection information from multiple guide star (GS) directions. However, the atmospheric tomography problem is severely ill-posed. The incomplete GS coverage in the FOV coupled with the WFS detection error significantly affects the reconstruction accuracy of the three-dimensional atmospheric turbulence wavefront aberration, leading to a nonuniform aberration detection precision over the whole FOV. We propose an efficient approach for achieving accurate atmospheric tomography to overcome the limitations of the traditional modal tomography approach. We employed a deep-learning-based approach to the tomographic reconstruction of the three-dimensional atmospheric turbulence wavefront aberration. We propose an atmospheric tomography residual network (AT-ResNet) that is specifically designed for this task, which can directly generate wavefronts of multiple turbulence layers based on the Shack-Hartmann (SH) WFS detection images from multiple GS directions. The AT-ResNet was trained under different turbulence intensity conditions to improve its generalization ability. We verified the performance of the proposed approach under different conditions and compared it with the traditional modal tomography approach. The well-trained AT-ResNet demonstrates a superior performance compared to the traditional modal tomography approach under different atmospheric turbulence intensities, various turbulence layer distributions, higher-order turbulence aberrations, detection noise, and reduced GSs conditions. The proposed approach effectively addresses the limitations of the modal tomography approach, leading to a notable improvement in the accuracy of atmospheric tomography. It achieves a highly uniform and high-precision wavefront reconstruction over the whole FOV. This study holds great significance for the development and application of the MCAO technology.

An Implicit Factorized Transformer with Applications to Fast Prediction of Three-dimensional Turbulence

Transformer has achieved remarkable results in various fields, including its application in modeling dynamic systems governed by partial differential equations. However, transformer still face challenges in achieving long-term stable predictions for three-dimensional turbulence. In this paper, we propose an implicit factorized transformer (IFactFormer) model, which enables stable training at greater depths through implicit iteration over factorized attention. IFactFormer is applied to large eddy simulation of three-dimensional homogeneous isotropic turbulence (HIT), and is shown to be more accurate than the FactFormer, Fourier neural operator (FNO), and dynamic Smagorinsky model (DSM) in the prediction of the velocity spectra, probability density functions of velocity increments and vorticity, temporal evolutions of velocity and vorticity root-mean-square value and isosurface of the normalized vorticity. IFactFormer can achieve long-term stable predictions of a series of turbulence statistics in HIT. Furthermore, IFactFormer showcases superior computational efficiency compared to the conventional DSM in large eddy simulation.

Multi-objective layout optimization for wind farms based on non-uniformly distributed turbulence and a new three-dimensional multiple wake model

Wind farm layout optimization (WFLO) can reduce the turbulence intensity on the wind turbines while maximizing power generation. To accurately compute turbulence intensity distribution in the wind farm, we utilize the innovative three-dimensional cosine-shaped turbulence intensity (3D-COTI) model. By integrating the three-dimensional cosine-shaped linear entrainment (3DCLE) wake model previously developed by the authors, we introduce a new multiple wind turbine wake model (3DCLE-M). This model considers the wake superposition effect, enabling precise calculation of power generation. Building upon the 3D-COTI and 3DCLE-M models, we propose a multi-objective WFLO approach to maximize power generation and minimize streamwise turbulence intensity in the wind-turbine-swept area. The results indicate that under maximized power generation, this approach significantly reduces turbulence intensity and its non-uniform distribution in the wind-turbine-swept area. In two ideal cases, the maximum turbulence intensity in all wind-turbine-swept areas of the optimized layout is 25 % and 3.8 % lower than that of the selected benchmark layout. By optimizing the layout of the Horns Rev offshore wind farm, a new layout can be obtained with increased total power output by 1.58 % and the reduced total duration of high-fatigue-load wind turbines under high turbulence intensity by 25 % compared to the benchmark.

Effects of plasma resistivity in FELTOR simulations of three-dimensional full-F gyro-fluid turbulence

A full-F, isothermal, electromagnetic, gyro-fluid model is used to simulate plasma turbulence in a COMPASS-sized, diverted tokamak. A parameter scan covering three orders of magnitude of plasma resistivity and two values for the ion to electron temperature ratio with otherwise fixed parameters is setup and analysed. Two transport regimes for high and low plasma resistivities are revealed. Beyond a critical resistivity the mass and energy confinement reduces with increasing resistivity. Further, for high plasma resistivity the direction of parallel acceleration is swapped compared to low resistivity.Three-dimensional visualisations using ray tracing techniques are displayed and discussed. The field-alignment of turbulent fluctuations in density and parallel current becomes evident. Relative density fluctuation amplitudes increase from below 1% in the core to 15% in the edge and up to 40% in the scrape-off layer.Finally, the integration of exact conservation laws over the closed field line region allows for an identification of numerical errors within the simulations. The electron force balance and energy conservation show relative errors on the order of 10−3 while the particle conservation and ion momentum balance show errors on the order of 10−2.All simulations are performed with a new version of the FELTOR code, which is fully parallelized on GPUs. Each simulation covers a couple of milliseconds of turbulence.