Flow Statistics Research Articles (Page 1)

We explore the fundamental flow structure of temporally evolving inclined gravity currents with direct numerical simulations. A velocity maximum naturally divides the current into inner and outer shear layers, which are weakly coupled by momentum and buoyancy exchanges on time scales that are much longer than the typical time scale characterising either layer. The outer layer evolves to a self-similar state and can be described by theory developed for a current on a free-slip slope (Van Reeuwijk et al. 2019, J. Fluid Mech., vol. 873, pp. 786–815) when expressed in terms of outer-layer properties. The inner layer evolves to a quasi-steady state and is essentially unstratified for shallow slopes, with flow statistics that are virtually indistinguishable from fully developed open channel flow. We present the classic buoyancy–drag force balance proposed by Ellison & Turner (1959, J. Fluid Mech., vol. 6, pp. 423–448) for each layer, and find that buoyancy forces in the outer layer balance entrainment drag, while buoyancy forces in the inner layer balance wall friction drag. Using scaling laws within each layer and a matching condition at the velocity maximum, the entire flow system can be solved as a function of the slope angle, in good agreement with the simulation data. We further derive an entrainment law from the solution, which exhibits relatively high accuracy across a wide range of Richardson numbers, and provides new insights into the long runout of oceanographic gravity currents on mild slopes.

Abstract Frequency analysis is crucial in low flow statistics, helping estimate the probability of water availability during low flow seasons and droughts. Low flow frequency analysis typically assumes stationarity, which has been challenged by climate change and variability. Therefore, non-stationary frequency analysis is essential when trends and non-stationarity exist in low streamflow data. This study developed a methodology that includes trend, change point, non-stationarity detection, and stationary and non-stationary low flow frequency analysis for annual minimum streamflow series of 7-day (Q7), 14-day (Q14), 30-day (Q30) and 90-day (Q90) periods, applied to selected river basins in Victoria, Australia. Significant decreasing trends were detected in several basins, with the strongest trends observed in the East Gippsland Basin, where the trend slopes were − 1.02, − 0.989, − 1.035 and − 1.534 for Q7, Q14, Q30, and Q90, respectively. Similarly, significant change points were found with year 2002 being the most common change point year, followed by year 1996, 2000 and 2001. Non-stationary frequency analysis proved superior in capturing the changing characteristics of low flow series. Moreover, the non-stationary models that included physical covariates outperformed those with only time covariates, highlighting the benefit of using covariates related to the physical mechanisms of low flow events. This study emphasizes the importance of non-stationary frequency analysis to prevent misleading conclusions in low flow-based water management, thereby enhancing the reliability and effectiveness of water management strategies.

ABSTRACT Geographical flows describe the movements and connections of materials, energy, and information among locations and are commonly represented by origin-destination (OD) flows (flows for short). The spatial heterogeneity of such flows is characterized by their inhomogeneous distributions and offers a novel perspective for revealing the global spatial pattern of relevant geographical phenomena. In practice, comparing the spatial heterogeneity of different flow datasets is essential for gaining deeper insights into their global spatial patterns. This requires reliable quantification of the spatial heterogeneity of flows, a challenge that has been largely overlooked in previous studies. To address this gap, we first define the spatial heterogeneity of flows as the degree of deviation from complete spatial randomness (CSR). Based on this definition, we propose a benchmark spatial heterogeneity metric for flows called the normalized level of flow heterogeneity (NLFH*). Additionally, we propose nine nearest-neighbor (NN) distance-based statistics for flows by extending relevant methods for points. Simulation experiments and case studies involving tropical cyclone tracks and taxi OD data demonstrate that statistic NLFH*, along with two NN distance-based statistics of flows (FA-w and FH-xw), outperforms other statistics in quantifying the spatial heterogeneity of flows. Among them, FA-w and FH-xw are recommended for practical use due to their powerful performance and computational efficiency.

A stochastic data-driven reduced-order model applicable to a wide range of turbulent natural and engineering flows is presented. Combining ideas from Koopman theory and spectral model order reduction, the stochastic low-dimensional inflated convolutional Koopman model accurately forecasts short-time transient dynamics while preserving long-term statistical properties. A discrete Koopman operator is used to evolve convolutional coordinates that govern the temporal dynamics of spectral orthogonal modes, which, in turn, represent the energetically most salient large-scale coherent flow structures. Turbulence closure is achieved in two steps: first, by inflating the convolutional coordinates to incorporate nonlinear interactions between different scales, and second, by modelling the residual error as a stochastic source. An empirical dewhitening filter informed by the data is used to maintain the second-order flow statistics. The model uncertainty is quantified through either Monte–Carlo simulation or by directly propagating the model covariance matrix. The model is demonstrated on the Ginzburg–Landau equations, large-eddy simulation data of a turbulent jet, and particle image velocimetry data of the flow over an open cavity. In all cases, the model is predictive over time horizons indicated by a detailed error analysis and integrates stably over arbitrary time horizons, generating realistic surrogate data.

Influence of geometric parameters of façade protruding ribs on turbulent flow statistics in street canyons: A large-eddy simulation study

We focus on the intermittent bistable stall dynamics of an airfoil under varying angle of attack. We propose a one-dimensional Langevin equationwhere the stochastic forcing depends on the state of the system-high-lift attached flow or low-lift detached flow-and where the deterministic potential depends continuously on the angle of attack. The model, identified based on the flow statistics and dynamics, reproduces the S-shaped lift curve, as well as the flow dynamics. It also predicts the nature of the bifurcations that the flow undergoes as the angle of attack varies.

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

Well-resolved large-eddy simulations (LES) of supersonic turbulent pipe flow at centerline Mach numbers of 1.6 and 1.8 and moderate friction Reynolds numbers of 1000 and 2200 are performed. The present LES of the supersonic pipe flow at friction Reynolds number 2200 is the first in the literature for which no direct numerical simulation (DNS) data are available. The statistics of the lower Reynolds number pipe flow agree quite well with those of the existing DNS by Modesti and Pirozzoli, “Direct numerical simulation of supersonic pipe flow at moderate Reynolds number,” Int. J. Heat Fluid Flow 76, 100–112 (2019), at similar Mach and Reynolds numbers. A distinct low wavenumber k−1 region in the streamwise velocity spectra, appearing due to the presence of large-scale motions (LSM) and very large-scale motions (VLSM), is observed along with a distinct logarithmic region in mean velocity. Other well-known high Reynolds number features such as a bimodal behavior of the premultiplied spectra of streamwise velocity fluctuations and a second outer peak in the Reynolds stresses are seen, which are compared with those found in incompressible pipe flows. A logarithmic variation of azimuthal velocity variance is also observed in a region away from the wall, as predicted by Townsend's attached eddy hypothesis [Townsend, The Structure of Turbulent Shear Flow, 2nd ed. (Cambridge University Press, 1976)].

Accurate dynamic flow statistics for trackless vehicles are critical for efficiently scheduling trackless transportation systems in underground mining. However, traditional discrete time-point methods suffer from “time membership discontinuity” due to RFID timestamp sparsity. This study proposes a fuzzy five-region membership (FZFM) model to address this issue by subdividing time intervals into five characteristic regions and constructing a composite Gaussian–quadratic membership function. The model dynamically assigns weights to adjacent segments based on temporal distances, ensuring smooth transitions between time intervals while preserving flow conservation. When validated on a 29-day RFID dataset from a large coal mine, FZFM eliminated conservation bias, reduced the boundary mutation index by 11.1% compared with traditional absolute segmentation, and maintained high computational efficiency, proving suitable for real-time systems. The method effectively mitigates abrupt flow jumps at segment boundaries, providing continuous and robust flow distributions for intelligent scheduling algorithms in complex underground logistics systems.

The influence of realistic optic flow and ecological self-motion statistics on optic flow tuning in deep neural networks

Abstract High-resolution simulations of turbulent flow over complex terrain provide accurate wind energy resource assessments and inform turbine design requirements. Large-eddy simulations (LESs) can capture the fine-scale features of turbulent flow; however, they are difficult to configure and prohibitively computationally expensive for use outside of the research community. Hence, a compound generative adversarial network (GAN) was developed to leverage the skill of an LES and produce a high-resolution (30 m) flow field with plausible fine-scale turbulence features and characteristics when conditioned on a coarse, computationally cheap mesoscale grid. Training data included flow and temperature fields from an LES in the vicinity of Mount Hood in the Pacific Northwest with high-resolution topographical information. The trained compound GAN generates high-resolution simulations over a sizable domain (90 km × 180 km) in seconds using a single general-purpose graphical processing unit as compared to the large high-performance computing resources needed to produce a similar LES. GAN-generated winds from the test dataset compared well with the LES in terms of energy spectra, flow statistics, and visual inspection. Finally, our models were applied in a region of complex terrain significantly different from the training region. Statistical analysis of GAN output and LES in this independent secondary testing region established that our models were able to leverage the skill of the LES in complex terrain for independent cases and regions. This result demonstrates that a deep learning approach to downscaling has the potential to greatly reduce cost and increase the availability of valuable high-resolution data products. Significance Statement This work demonstrates that the machine-learning technique, enhanced super-resolution generative adversarial networks can downscale from the mesoscale (order of a kilometer) to the microscale (order of tens of meters) with a good match to the turbulence metrics. Trained on data from large-eddy simulations, the method even shows success in an independent secondary testing region that was not part of the training data. This technique has the potential to provide high-resolution turbulence data conditioned on mesoscale model simulations with very little computational time.

We report on Lagrangian flow statistics from experimental measurements of homogeneous isotropic turbulence. The investigated flow is driven by 12 impellers inside an icosahedral volume. Seven impeller rotation rates are considered resulting in seven Reynolds numbers with 205≤Reλ≤602. We perform high-speed imaging using three cameras to record a total of 8.2×106 frames, and using high resolution three dimensional (3D) particle tracking velocimetry position, velocity, and acceleration of particle tracks are obtained in the vicinity of the center of the device. From these tracks, we obtain the Eulerian and Lagrangian flow statistics, mainly based on second-order structure functions and autocorrelation functions. The universal constants C0* (for the Lagrangian second order structure function), Cε (for the energy injection rate), and a0 (for the acceleration fluctuations) are determined, as well as all the relevant Lagrangian and Eulerian flow time scales. Analytical relations between these constants and time scales are experimentally verified.

Cybersecurity is a growing area of research due to the constantly emerging new types of cyberthreats. Tools and techniques exist to keep systems secure against certain known types of cyberattacks, but are insufficient for others that have recently appeared. Therefore, research is needed to design new strategies to deal with new types of cyberattacks as they arise. Existing tools that harness artificial intelligence techniques mainly use artificial neural networks designed from scratch. In this paper, we present a novel approach for cyberattack detection using an encoder–decoder pre-trained Large Language Model (T5), fine-tuned to adapt its classification scheme for the detection of cyberattacks. Our system is anomaly-based and takes statistics of already finished network flows as input. This work makes significant contributions by introducing a novel methodology for adapting its original task from natural language processing to cybersecurity, achieved by transforming numerical network flow features into a unique abstract artificial language for the model input. We validated the robustness of our detection system across three datasets using undersampling. Our model achieved consistently high performance across all evaluated datasets. Specifically, for the CIC-IDS-2017 dataset, we obtained an accuracy, precision, recall, and F-score of more than 99.94%. For CSE-CIC-IDS-2018, these metrics exceeded 99.84%, and for BCCC-CIC-IDS-2017, they were all above 99.90%. These results collectively demonstrate superior performance for cyberattack detection, while maintaining highly competitive false-positive rates and false-negative rates. This efficacy is achieved by relying exclusively on real-world network flow statistics, without the need for synthetic data generation.

In the process of urbanization, traffic flow statistics are of great significance to traffic management. Existing traffic flow statistics solutions suffer from incomplete functionality and lack effective solutions for core issues. The closed-set object detection algorithms they employ can only perform detections based on fixed categories, which leads to limited recognition scope and weak model generalization ability.Moreover, the tracking algorithms used are unstable and have low computational efficiency. To address these challenges, this paper proposes a traffic flow statistical method based on YBOVDT(YOLO-World and BOT-SORT-Open Vocabulary Detection and Tracking)and SAM2.Specifically, in the method, this paper proposes a “Traffic Flow Data Processing and Analysis” module, aiming to optimize and supplement the five core functions required for traffic flow statistics tasks, thereby making the functions of the entire solution more comprehensive.In addition, this paper combines the latest open set object detection and tracking algorithms to enhance the recognition ability and tracking stability of traffic objects. In this study, a custom dataset was used to train existing traffic flow statistics models.The experimental results showed that the YOLO-World model achieved a precision of 76.99% and an mAP50 of 70.08%. A comparative analysis with YOLO-v3,YOLO-v5, YOLO-v6,and YOLO-v8 algorithms indicated that, while balancing spatial and temporal resource consumption and accuracy, the proposed algorithm offers higher recognition accuracy and environmental adaptability. The experimental results further validated that this method demonstrates significant improvements in handling traffic flow statistics tasks in complex traffic environments.

Museums often face operational challenges such as managing high visitor volume, language barriers, and outdated ticketing systems. Our project introduces an intelligent ticketing platform powered by a multilingual chatbot, designed to streamline the visitor experience. Users can interact in their preferred language, book tickets for entry and shows, and receive real-time updates—all through a smart conversational interface. The system integrates secure payment gateways and generates gate passes digitally, minimizing manual effort and queue times. By providing an analytics dashboard, museum administrators gain valuable insights into visitor flow, revenue trends, and booking statistics, enabling informed decision-making. The platform supports a mobile application for on-the-go access, promoting convenience and modern digital engagement. Through this innovation, we aim to enhance cultural accessibility, optimize operations, and foster a more connected, user-friendly museum environment.

Zonal classifications, such as those based on biomes and ecozones, are commonly used to contextualize short-term dynamics and long-term environmental change. One challenge in hydrology is the lack of zonal classifications that explicitly incorporate flow statistics. To date, few studies have evaluated whether non-hydrological zonal classifications can serve as proxies for flow dynamics across large, heterogenous regions. Taking Canada as an example, the focus was on 2531 hydrometric stations for which select streamflow signatures were computed. Those signatures, coupled with catchment characteristics, were used to distinguish flow regimes based on their degree of temporal variability—categorizing them as erratic or persistent—and their main water sources—either shallow subsurface flow or groundwater. Results show that catchments with higher cropland and urban cover and higher percentages of clay soils were associated with erratic regimes fed by shallow subsurface flow. Conversely, catchments with higher forest and semi-permanent water features were associated with persistent regimes. The high degree of intra-region and inter-region hydrologic heterogeneity was typically not well captured by non-hydrological zonal classifications. Caution is therefore warranted when using existing non-hydrological zonal classifications for regional water policy planning, as they may lead to a mischaracterization of spatial differences in streamflow patterns.

This paper proposes an architecture design of intelligent electric power business hall based on 5G + edge computing technology, which includes three layers: business layer, platform layer and network layer, and realizes intelligent service, management and operation and maintenance of electric power business hall. This paper proposes a heterogeneous node deployment algorithm based on regional density, which divides the network regionally by raster and heterogeneous node communication range, and determines the optimal location of heterogeneous nodes by regional density, realizing the reasonable allocation and utilization of network resources. This paper also proposes an edge scheduling algorithm based on game theory, which enables each edge device to choose the optimal data processing task according to its own utility function through a non-cooperative game model, realizing the optimization of the efficacy and accuracy of data processing. The experimental results show that the intelligent monitoring system of the electric power business hall performs well in the aspects of passenger flow statistics, service evaluation and security warning, and at the same time has good system performance, providing powerful technical support for the operation and management of the business hall. This research not only realizes advanced intelligent monitoring functions, but also provides new perspectives on the application of 5G and edge computing in the field of security monitoring theoretically. At the practical level, the results of this research help to improve the security and efficiency of business office environments.

Abstract Taylor's hypothesis is traditionally invoked to infer the spatial behavior of flow statistics when its measurements are limited to time series on fixed positions. Here, we evaluate the hypothesis for the estimation of second‐order structure functions in the upper troposphere and lower stratosphere, using 4 years of horizontal wind measurements from the Middle Atmosphere Alomar Radar System, in Northern Norway. Global and local advection velocities are used for the time‐to‐space conversion. We compare with those estimated using wind climatologies from aircraft observations, finding a good agreement for separations between approximately 10 and 1,000 km at 10.5 km altitude. This result enables us to test the 2D turbulence model of a combined energy and enstrophy subrange. It is shown that the spectral energy flux has minima at fixed heights. In contrast, the spectral enstrophy flux steadily decreases with altitude. Both features are consistent with previous modeling and observational studies.

Superhydrophobic surfaces introduce partial slip at the surface submerged in water, reducing viscous drag. While the drag reduction of superhydrophobic surfaces is well understood in laminar flow, the complexity of turbulent flows requires further investigation to understand how these highly dynamic flows interact with surface superhydrophobicity. Additionally, the efficacy of a superhydrophobic surface is highly dependent on retaining the plastron, the air layer that generates the partial slip required for viscous drag reduction. This paper presents an experimental investigation of the effects of superhydrophobic surface treatment on the wake of a sphere, with the plastron maintained throughout the experiments using an active air supply. The first- and second-order flow statistics are compared between spheres with and without surface treatment, as are the wake characteristics. Proper orthogonal decomposition is performed on the velocity fluctuations in the near wake to compare the turbulent structures and the effect of superhydrophobicity thereon. The addition of superhydrophobic surface treatment is shown to have a substantial effect on the mean flow in the wake of the sphere as well as the structure of the turbulent fluctuations. The behavior of the flow in the wake of the superhydrophobic sphere is consistent with the fluctuating plastron observed in previous studies.

Enhancing SDN Traffic Analysis Through Machine Learning on Preprocessed Controller Flow Statistics and Packet Analysis Data