Three-dimensional Velocity Field Research Articles

Assessing the modulation of outer bank erosion by slump blocks: A case study from Marqu Meadow, China

The outer bank slump blocks play a fundamental role in modulating the rate of bank erosion, and consequently, have a profound influence on many geomorphic and ecologic processes in meandering streams, e.g., channel evolution and habitat creation. To date, no adequate research has been developed regarding how these blocks, partially strengthened by roots of herbaceous plants, impact the near-bank flow velocity, bank erosion, and migration of streambanks. This paper analyzes 246 slump blocks in a meandering stream on the Marqu Meadow, China. Aerial surveys were conducted once a year from 2018 to 2021 and the lateral migration rates (M) of streambanks are estimated by superimposing the current-year drone imagery onto its previous-year counterpart. When compared to the outer bank segments lacking slumps, our research findings indicate that the bank segments exhibiting slumps demonstrate a reduction of 57 % and 43 % in the maximum and average bank erosion rates, respectively. Overall, the wider blocks provide stronger bank protection; nevertheless, they may also introduce or enhance local scouring in their vicinity, thereby increasing the heterogeneity of bank erosion rates. To elucidate this complex influence mechanism, we simulate the three-dimensional flow velocity field of a ~100 m meandering bend containing three slump blocks using the MIKE-3 model. Furthermore, we compare one-year bank migration distance with and without the blocks by correlating the lateral migration distance of outer banks to the longitudinal gradient of near-bank velocity. The paper provides valuable insights into the complex interplay between flow dynamics and streambank behavior in real-world settings, thereby enhancing the effectiveness of future management and restoration practices.

A Three-Dimensional Velocity Field Related to a Generalized Third-Grade Fluid Model

In this work, we propose a new three-dimensional constitutive equation related to a third-grade fluid. This proposal is based on experimental work for which the viscosity term and the terms related to viscoelasticity may depend on the shear rate, in accordance with a power-law type model. The numerical implementation of this fluid model is rather demanding in terms of computational calculation and, in this sense, we use the Cosserat theory related to fluid dynamics, which makes the transition from the three-dimensional fluid model to a one-dimensional fluid model for a specific geometry under study which, in this case, is a straight tube with constant circular cross-section. Based on this approximation theory, the one-dimensional fluid model is solved by assuming an ordinary differential equation involving: an unsteady mean pressure gradient; an unsteady volume flow rate; the Womersley number; and the viscosity and viscoelasticity parameters. Consequently, for specific data, and using the Runge–Kutta method, we can obtain the solution for the unsteady volume flow rate and we can present simulations to the three-dimensional velocity field.

Fully determined three-dimensional velocity field in a divergence-free convection experiment with rigid boundary conditions

Fully determined three-dimensional velocity field in a divergence-free convection experiment with rigid boundary conditions

A reduced-order configuration approach for the real-time calculation of three-dimensional flow behavior in a pipe network

The real-time computation of a three-dimensional pipe network flow is crucial for both pipe design and operational maintenance. This study devises a novel reduced-order configuration approach that combines the advantages of the acceleration characteristics of the reduced-order model and the structural applicability of the configuration model. First, a configuration model is established by categorizing sub-pipes extracted from a pipe network into sets based on the sub-pipes' type. Subsequently, reduced-order configurations are realized by a reduced-order model established for each type of configuration, enabling real-time computation of individual sub-pipes. Thus, the concatenation of sub-pipes allows the computation of an entire pipe network. A complex boundary–deep learning–reduced-order configuration model and a complex boundary–deep learning–reduced-order configuration–multi-source data–reduced-order configuration model integrated with a local multi-physical–discrete empirical interpolation method and a multi-source data fusion model are devised. These models were employed for the real-time computation and prediction of a three-dimensional velocity field for 300 snapshots composed of one to four sub-pipes extrapolated from a dataset of 294 pipe network snapshots composed of one to three sub-pipes. The maximum relative errors for snapshots from the dataset were similar to the limit precision of the proper orthogonal decomposition, with more precise accuracy than the relevant studies, indicating the excellent performance of our reduced-order configuration approach.

Variational construction of tubular and toroidal streamsurfaces for flow visualization

Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical regions in three-dimensional flows. Here we propose a variational construction of these approximate streamsurfaces to remove the limitation of Fourier series representation of the first integral in earlier work. Specifically, we use finite-element methods to solve a partial differential equation that describes the best approximate first integral for a given velocity field. We use several examples to demonstrate the power of our approach for three-dimensional flows in domains with arbitrary geometries and boundary conditions. These include generalized axisymmetric flows in the domains of a sphere (spherical vortex), a cylinder (cylindrical vortex) and a hollow cylinder (Taylor–Couette flow) as benchmark studies for various computational domains, non-integrable periodic flows (ABC and Euler flows) and Rayleigh–Bénard convection flows. We also illustrate the use of the variational construction in extracting momentum barriers in Rayleigh–Bénard convection.

Three dimensional analysis of the exhalation flow in the proximity of the mouth

The human exhalation flow is characterized in this work from the three-dimensional velocimetry results obtained by using the stereo particle image velocimetry (SPIV) measurement technique on the flow emitted from a realistic airway model. For this purpose, the transient exhalation flow through the mouth of a person performing two different breaths corresponding to two metabolic rates, standing relaxed (SR) and walking active (WA), is emulated and studied. To reproduce the flow realistically, a detailed three-dimensional model obtained from computed tomography measurements on real subjects is used. To cope with the variability of the experimental data, a subsequent analysis of the results is performed using the TR-PIV (time resolved particle image velocimetry) technique. Exhalation produces a transient jet that becomes a puff when flow emission ends. Three-dimensional vector fields of the jet velocity are obtained in five equally spaced transverse planes up to a distance of ▪ from the mouth at equally spaced time instants ▪ which will be referred to as phases (φ), from the beginning to the end of exhalation. The time evolution during exhalation of the jet area of influence, the velocity field and the jet air entrainment have been characterized for each of the jet cross sections. The importance of the use of realistic airway models for the study of this type of flow and the influence of the metabolic rate on its development are also analyzed. The results obtained contribute to the characterization of the human exhalation as a pathway of the transmission of pathogens such as SARS-CoV-2 virus.

Three-dimensional turbulent velocity field and air entrainment of the 22 March 1944 Vesuvius eruption plume

Three-dimensional turbulent velocity field and air entrainment of the 22 March 1944 Vesuvius eruption plume

Three-dimensional Velocity Fields of the Solar Filament Eruptions Detected by CHASE

The eruption of solar filaments, also known as prominences appearing off limb, is a common phenomenon in the solar atmosphere. It ejects massive plasma and high-energy particles into interplanetary space, disturbing the solar-terrestrial environment. It is vital to obtain the three-dimensional velocity fields of erupting filaments for space-weather predictions. We derive the three-dimensional kinematics of an off-limb prominence and an on-disk filament, respectively, using the full-disk spectral and imaging data detected by the Chinese Hα Solar Explorer (CHASE). It is found that both the prominence and the filament experience a fast semicircle-shaped expansion at first. The prominence keeps propagating outward with an increasing velocity until escaping successfully, with the south leg of the prominence finally moving back to the Sun in a swirling manner. For the filament, the internal plasma falls back to the Sun in a counterclockwise rotation in the late ejection, matching the failed eruption without a coronal mass ejection. During the eruptions, both the prominence and the filament show material splitting along the line-of-sight direction, revealed by the bimodal Hα spectral profiles. For the prominence, the splitting begins at the top and gradually spreads to almost the whole prominence with a fast blueshift component and a slow redshift component. The material splitting in the filament is more fragmental. As shown by the present results, the CHASE full-disk spectroscopic observations make it possible to systematically study the three-dimensional kinematics of solar filament eruptions.

Meta-Lens Particle Image Velocimetry.

Fluid flow behavior is visualized through particle image velocimetry (PIV) for understanding and studying experimental fluid dynamics. However, traditional PIV methods require multiple cameras and conventional lens systems for image acquisition to resolve multi-dimensional velocity fields. In turn, it introduces complexity to the entire system. Meta-lenses are advanced flat optical devices composed of artificial nanoantenna arrays. It can manipulate the wavefront of light with the advantages of ultrathin, compact, and no spherical aberration. Meta-lenses offer novel functionalities and promise to replace traditional optical imaging systems. Here, a binocular meta-lens PIV technique is proposed, where a pair of GaN meta-lenses are fabricated on one substrate and integrated with a imagingsensor to form a compact binocular PIV system. The meta-lens weigh only 116mg, much lighter than commercial lenses. The3Dvelocity field can be obtained by the binocular disparity and particle image displacement information of fluid flow. The measurement error of vortex-ring diameter is ≈1.25% experimentally validates via a Reynolds-number (Re) 2000 vortex-ring. This work demonstrates a new development trend for the PIV technique for rejuvenating traditional flow diagnostic tools toward a more compact, easy-to-deploy technique. It enables further miniaturization and low-power systems for portable, field-use, and space-constrained PIV applications.

Three-Dimensional Velocity Field Interpolation Based on Attention Mechanism

The establishment of a three-dimensional velocity field is an essential step in seismic exploration, playing a crucial role in understanding complex underground geological structures. Accurate 3D velocity fields are significant for seismic imaging, observation system design, precise positioning of underground geological targets, structural interpretation, and reservoir prediction. Therefore, obtaining an accurate 3D velocity field is a focus and challenge in this field of study. To achieve intelligent interpolation of the 3D velocity field more accurately, we have built a network model based on the attention mechanism, JointA 3DUnet. Based on the traditional U-Net, we have added triple attention blocks and channel attention blocks to enhance dimension information interaction, while adapting to the different changes of geoscience data in horizontal and vertical directions. Moreover, the network also incorporates dilated convolution to enlarge the receptive field. During the training process, we introduced transfer learning to further enhance the network’s performance for interpolation tasks. At the same time, our method is a deep learning interpolation algorithm based on an unsupervised model. It does not require a training set and learns information solely from the input data, automatically interpolating the missing velocity data at the missing positions. We tested our method on both synthetic and real data. The results show that, compared with traditional intelligent interpolation methods, our approach can effectively interpolate the three-dimensional velocity field. The SNR increased to 36.22 dB, and the pointwise relative error decreased to 0.89%.

High-resolution microscale velocity field measurement using light field particle image-tracking velocimetry

Light field microparticle image velocimetry (LF-μPIV) can realize the three-dimensional (3D) microscale velocity field measurement, but the spatial resolution of the velocity field is low. Therefore, this study proposes a high-resolution LF particle image-tracking velocimetry (PIV–PTV) in combination with a cross-validation matching (CVM) algorithm. The proposed method performs motion compensation for the distribution of particle center position based on the low-resolution velocity field achieved by PIV and then conducts the CVM on tracer particles with the nearest neighbor method. The motion compensation reduces the particle displacement during the matching, while the CVM reduces the impact of missing particles on the matching accuracy. Thus, the proposed method enables precise tracking of individual particles at higher particle concentrations and improves the spatial resolution of the velocity field. Numerical simulations were conducted on the 3D displacement field reconstruction. The influence of interrogation window size, particle diameter, and concentration was analyzed. Experiments were conducted on the microscale 3D velocity field within the microchannel with right-angle bends. Results indicate that the proposed method provides the high-resolution measurement of the microscale 3D velocity field and improves the precision of the velocity field compared to the PTV at higher particle concentrations. It demonstrates that the proposed method outperforms PIV by 26% in resolution and PTV by 76% in precision at a higher particle concentration of 1.5 particles per microlens.

Supply mechanisms of the geostrophic mode in rotating turbulence: interactions with self, waves and eddies

Direct numerical simulations are performed in rotating turbulence for different regimes at various Rossby and inertial Reynolds numbers ( $\textit {Re}_I$ ). A new algorithm, adapted from stratified turbulence (Lam et al., J. Fluid Mech., vol. 923, 2021, A31) to rotating turbulence, permits to separate the three-dimensional velocity field into three parts: inertial waves (IWs), eddies and a geostrophic mode (GM). It uses the space–time properties of waves and their advection by the GM to filter the IWs from the rest of the motion. We obtain balance equations for the separate energies of waves, eddies and the GM. Their mutual interactions are evaluated and analysed via Sankey diagrams that provide a global picture of energy exchanges. When the flow is forced at large scale, it mainly feeds the wave part and the multiple interactions lead to energy dissipation in eddy and GM motion. We also show that, in addition to the wave/wave interaction that feeds the GM, corresponding to different mechanisms described in the literature, other non-documented interactions feed it, as the eddy/wave interaction or the eddy/eddy interaction at moderate $\textit {Re}_I$ . We propose a scale-by-scale analysis of the transfer to the GM: we show that transfers from wave or eddy occur at large scale, that they either inject or remove energy, and that this occurs with or without direct cascade depending on the kind of interaction, wave/wave, eddy/wave or eddy/eddy. The self-interaction of the GM is an inverse cascade for its horizontal component, shaping it into a very large-scale flow.

Steady flow at a breached levee

The present study uses a laboratory scale experimental model and an analytical model to study the steady flow at a breached levee. Flow past a zero height side weir is considered for the purpose. Water surface elevation and the three-dimensional velocity field are measured by a point gauge and an Acoustic Doppler Velocimeter (Vectrino), respectively. Experimental results include the velocity field, free surface elevation, turbulent kinetic energy and bed shear stress. Empirical relations to predict the minimum water depth and discharge at the breach are obtained. An analytical model to predict the approximate flow field at the breach is also developed. The model parameters are calibrated using the experimental results. The approximate flow conditions predicted by the analytical model can be used for field conditions. The 17th Street Canal breach is employed as a case study to demonstrate the performance of the analytical model.

The interfacial modes and modal causality in a dispersed bubbly turbulent flow

While data-driven analysis has demonstrated significant success in single-phase flow systems, its application to multi-phase flows has been relatively limited with fewer examples. In this study, we present a modal analysis and modal causality analysis of dispersed bubbly turbulent flow, with the aim of providing new insights into the interfacial gas–liquid interaction. Our study employs an in-house coupled level-set volume-of-fluid solver, which is combined with a modified fast Fourier transforms algorithm to perform interface-resolved direct numerical simulations in a turbulent channel flow with 96 bubbles occupying 5.4% volume. In the downward flow orientation, we observe that bubbles are mainly clustered in the channel center, producing pseudo-turbulence with isotropic characteristics. We apply the proper orthogonal decomposition method to the phase-resolved, three-dimensional velocity field, radius of the bubble as well as the surface tension force in order to extract the dominant modes. Notably, our results reveal the presence of two energetic modes in both the gas and liquid phases, as well as the interface, namely, the vortex-ring mode and the quadrupolar mode. We further investigate the causal relationship across the gas–liquid interface using the modal information transfer entropy. Our findings demonstrate a strong causality between the gas phase and the surface tension, whereas the causality between the liquid phase and surface tension is comparatively weak due to the multi-scale characteristics of the turbulent fields. Overall, our novel approach to investigating the interfacial gas–liquid interaction in dispersed bubbly turbulent flow provides valuable insights that enhance physical understanding and could lead to improved flow control and efficiency in a range of industrial processes. The identification of previously unidentified energetic modes using the POD method has the potential to advance research in this field, with potential implications for future design of control strategies in complex systems.

Super-resolution of three-dimensional temperature and velocity for building-resolving urban micrometeorology using physics-guided convolutional neural networks with image inpainting techniques

This study proposes a convolutional neural network (CNN) that enhances the resolution of instantaneous snapshots of three-dimensional air temperature and wind velocity fields around buildings in urban areas. The CNN not only increases the resolution of flow fields but also recovers the missing data associated with changes in resolution-dependent building shapes. The proposed CNN incorporates gated convolution, which is an image inpainting technique that infers missing pixels, to improve accuracy. The CNN performance has been verified via supervised learning utilizing building-resolving micrometeorological simulations around Tokyo Station in Japan. The CNN has successfully reconstructed the temperature and velocity fields around the high-resolution buildings, despite the missing data at lower altitudes due to the coarseness of the low-resolution buildings. This result implies that near-surface flows can be inferred from flows above buildings. This hypothesis has been assessed through numerical experiments in which all inputs below a certain height are set as missing values. This research suggests that airflows around buildings can be efficiently estimated by combining neural network inferences and low-resolution fluid simulations.

Numerical investigation of the three-dimensional paths of plastic polymers in the Gulf of Naples

The high-resolution Campania Regional Ocean Model (CROM), coupled with an online Lagrangian particle tracking algorithm, is used to investigate the horizontal and vertical behavior of different (in terms of size and density) plastic polymer types during February and August 2016 in the Gulf of Naples. The transport of passive particles is evaluated based on the three-dimensional Eulerian velocity fields provided by the ocean model. The virtual particles are released in several hot spot areas in the Gulf of Naples where most of the marine debris is supposed to come from. A sensitivity analysis on the vertical sinking for negatively buoyant particles is carried out. The sinking behavior is determined by the settling velocity, which depends on the physical properties of the individual litter item as well as on the hydrodynamical features of the marine environment. Different numerical experiments are carried out to evaluate the effect of marine dynamics on three-dimensional transport.

Effects of tributary floodplain on confluence hydrodynamics

Confluences are common components of river networks and are characterized by a highly complex flow structure. Two confluence geometries, without and with the floodplain in the tributary, were comparatively investigated to highlight the effects of floodplain on confluence hydrodynamics. The three-dimensional velocity field and the spatial distribution of turbulent kinetic energy and Reynolds shear stresses were analysed. In the second geometry, a tilted shear layer was observed, which was related to the flow expansion from the main channel into the tributary. Significant secondary motions are mainly related to the fluid upwelling in the lee of the floodplain step and streamline curvature. A wider flow separation zone was found, while the length of the separation zone was not affected by the floodplain flow. The results could be useful to understand the complex hydrodynamics of the large confluence between the Yangtze River and the Poyang Lake, characterized from a floodplain under high flow conditions.

A deep neural network architecture for reliable 3D position and size determination for Lagrangian particle tracking using a single camera

Microfluidic flows feature typically fully three-dimensional velocity fields. However, often the optical access for measurements is limited. Astigmatism or defocus particle tracking velocimetry is a technique that enables the 3D position determination of individual particles by the analysis of astigmatic/defocused particle images. The classification and position determination of particles is a task well suited to deep neural networks (DNNs). In this work, two DNNs are used to extract the class and in-plane position (object detection) as well as the depth position (regression). The performance of both DNNs is assessed by the position uncertainties as well as the precision of the size classes and the amount of recalled particles. The DNNs are evaluated on a synthetic dataset and establish a new benchmark of DNNs in defocus tracking applications. The recall is higher than compared to classic methods and the in-plane errors are always subpixel accurate. The relative uncertainty in the depth position is below 1% for all examined particle seeding concentrations. Additionally, the performance on experimental images, using four different particle sizes, ranging from 1.14 to 5.03 is analyzed. The particle images are systematically rearranged to produce comprehensive datasets of varying particle seeding concentrations. The distinction between particles of similar size is more challenging but the DNNs still show very good results. A precision above 96% is reached with a high recall above 95%. The error in the depth position remains below 1% and the in-plane errors are subpixel accurate with respect to the labels. The work shows that first, DNNs can be trained with artificially rearranged data sets based on individual experimental images and are therefore easily adaptable to various experimental setups and applicable by non-experts. Second, the DNNs can be successfully adapted to determine additional variables as in this case the size of the suspended particles.

High-resolution reconstruction algorithm for the three-dimensional velocity field produced by atomization of two impinging jets based on deep learning

The velocity fields measured by experiments or determined through simulations are essential in advancing our understanding of the complex atomization process of impinging jets. However, existing methods are expensive and time-consuming. In this study, we apply deep learning to the estimation of the three-dimensional velocity fields produced by the atomization of two impinging jets. Two deep learning models are developed, namely, a liquid volume fraction (LVF) estimation model based on the Swin Transformer architecture and a three-dimensional velocity field estimation model based on four-dimensional convolution (4D-Conv). The dataset for training the models is generated by direct numerical simulations (DNS). To train the LVF model, we utilize two gray images generated by a pinhole camera model, mimicking the acquisition of experimental images. We then introduce a mask generated by binocular vision techniques into the LVF model. The LVF fields estimated with the mask are in better agreement with the reference DNS data. We further utilize the estimated LVF fields to train the 4D-Conv-based model. The mean absolute percentage error compared with the results of a full-flow test is found to be less than 5%. The results indicate that the proposed approach has the potential to accurately reconstruct volume velocity data from two-dimensional images.

Experimental and numerical investigation of a density-driven instability during a horizontal miscible displacement

We performed an experimental and numerical investigation of a convective buoyancy-driven instability that arises during the injection of a denser miscible fluid into a less dense one in a rectilinear geometry. We visualized the instability using a shadowgraph technique, and we obtained quantitative information using micro-Particle Image Velocimetry. Numerical simulations provided further insights into the three-dimensional (3D) velocity field. We have shown that the instability only occurs above a certain Péclet number, Pe, depending on the Rayleigh, Ra, and Schmidt, Sc, numbers. We suggest scalings of the critical time, TC, and dimensionless wavelength, λ/h, of the instability, both of which increase with increasing Pe and Ra. Finally, we investigated the interactions of the instability vortices with each other and the geometry boundaries.