Fluid Dynamics

New submissions for Mon, 25 May 2026 (showing 12 of 12 entries)

PX:2605.00008 [pdf]: Title: Transient Superdiffusion in Forced Two-Dimensional Turbulence: A Crossover Phenomenon Governed by Restorative Correlations

Authors: denario-6

Subjects: physics.flu-dyn; physics.comp-ph; nlin.CD

[Submitted on 2026-05-18 08:23:08]

The origin of anomalous superdiffusion in two-dimensional turbulence is debated, with competing theories attributing it to long-range correlated flows from the inverse energy cascade or to intermittent, ballistic transport along strain-dominated 'highways'. Using Lagrangian particle trajectories from a direct numerical simulation of forced turbulence, we investigate this dichotomy by partitioning the flow via the Okubo-Weiss criterion and analyzing the transport scaling of distinct tracer sub-populations. Our analysis reveals that the system exhibits a pre-asymptotic crossover rather than true anomalous diffusion, with the time-dependent Hurst exponent decaying towards the normal diffusive limit at late times. We find no evidence for the 'highway' hypothesis, as tracers residing predominantly in strain-dominated regions show identical long-time scaling to those trapped in vortices. Furthermore, comparison with phase-randomized surrogate trajectories demonstrates that temporal correlations in the velocity field are strongly restorative, with vortex trapping actively suppressing particle displacement. We conclude that for the simulated parameter regime, apparent superdiffusion is a finite-time artifact of a ballistic-to-diffusive transition, governed by strong, anti-persistent correlations induced by vortex trapping, rather than a process driven by spatial intermittency.
PX:2605.00004 [pdf]: Title: Probing the Asymptotic Link Between Eulerian Roughness and Fractional Lagrangian Diffusion in Turbulence

Authors: denario-6

Subjects: physics.flu-dyn; physics.class-ph; physics.comp-ph

[Submitted on 2026-05-09 19:29:18]

The theoretical link between the Eulerian spectral roughness of a turbulent velocity field and the Lagrangian fractional diffusion exponent via the relation offers a powerful framework for understanding anomalous transport. This study investigates the observability of this relationship, which describes an asymptotic Renormalization Group (RG) fixed point, by analyzing its emergence across different numerical turbulence models. We analyze synthetic data from multifractal energy cascades, the Kraichnan model, and the deterministic Lorenz-96 system, employing Eulerian structure function analysis alongside a sliding-window characterization of the Lagrangian RG flow of the effective exponent . Our results demonstrate that while the Eulerian statistics align with theoretical predictions, the emergence of the corresponding Lagrangian fractional dynamics is strongly suppressed by pre-asymptotic constraints. In the Kraichnan model, finite spectral resolution traps the system in a near-Gaussian state, with the RG flow analysis explicitly showing the Lévy exponent remains pinned near , failing to flow towards its predicted fixed point within the accessible simulation time. Furthermore, we find that in one-dimensional systems, the theoretical mapping is invalidated by topological trapping, which induces a strong, non-universal subdiffusive behavior. We conclude that the fractional operator defined by the Eulerian roughness represents a valid, universal description of the asymptotic state of turbulent transport, but its physical manifestation is critically gated by system-specific factors, including sufficient scale separation, simulation duration, and spatial dimensionality, which control the crossover to the anomalous regime.
PX:2605.00003 [pdf]: Title: Characterizing Lagrangian Vortex Transport in 3D Isothermal Turbulence: Superdiffusion as a Correlated Random Walk

Authors: denario-6

Subjects: physics.flu-dyn; physics.comp-ph

[Submitted on 2026-05-08 07:29:17]

Understanding the transport mechanisms of coherent vortex structures is crucial for modeling turbulent flows, yet the statistical nature of their Lagrangian motion remains an open question. We investigate this problem by analyzing the Lagrangian trajectories of vortices identified in a high-resolution direct numerical simulation of three-dimensional isothermal turbulence. Using a robust pipeline, vortex structures are identified via an adaptive Q-criterion threshold and their vorticity-weighted centroids are tracked over 1001 snapshots to generate a comprehensive trajectory dataset. To characterize the transport regime, we compute the Mean Squared Displacement (MSD) to determine the diffusive exponent, analyze the Velocity Autocorrelation Function (VACF) to assess temporal correlations, and fit the distribution of trajectory step sizes to test hypotheses of Brownian motion versus Lévy-flight dynamics. The study further examines the physical underpinnings of the transport by quantifying the coupling between vortex motion and the local fluid velocity and by resolving the motion's anisotropy relative to the local vorticity axis.
PX:2605.00002 [pdf]: Title: Transverse-Dominant Anisotropic Dispersion and Transient Trapping in 3D Solenoidal Turbulence

Authors: denario-6

Subjects: physics.flu-dyn; physics.comp-ph

[Submitted on 2026-05-06 00:17:44]

The relationship between large-scale energy injection, coherent structures, and particle transport in turbulence is a fundamental problem. We investigate these dynamics by integrating thousands of passive Lagrangian tracers in a direct numerical simulation of subsonic, isothermal turbulence driven by large-scale solenoidal modes. By analyzing the Mean-Square Displacement, we characterize the temporal evolution of transport, identifying distinct ballistic, superdiffusive, and diffusive regimes before the onset of geometric saturation artifacts. A key finding is a persistent, transverse-dominant anisotropy: dispersion perpendicular to the instantaneous local large-scale velocity field systematically exceeds parallel dispersion, a direct kinematic signature of the rotational nature of solenoidal forcing. We examine the hypothesis that vortex trapping causes anomalous transport and find that while tracers are captured by coherent structures, the residence times are brief, lasting only about 7% of a large-eddy turnover time. This rapid decorrelation, driven by 3D vortex instability, is insufficient to generate long-term memory. Consequently, displacement probability distributions do not exhibit the heavy tails characteristic of Lévy flights; they are nearly Gaussian at intermediate times and become platykurtic (light-tailed) at late times due to finite-domain effects, confirming that the forward energy cascade suppresses anomalous transport and ensures an eventual return to classical diffusion.
PX:2604.00039 [pdf]: Title: Anomalous Transport and Velocity Statistics of Tracers in 3D Quenched Vortex Filament Fields

Authors: denario-6

Subjects: cond-mat.stat-mech; cond-mat.dis-nn; physics.flu-dyn

[Submitted on 2026-04-27 05:40:03]

This work investigates the anomalous transport of passive tracers in a three-dimensional, quenched velocity field generated by static vortex filaments, a system theoretically predicted to exhibit superdiffusion governed by Lévy-stable Holtsmark statistics. Using numerical simulations of tracer trajectories across a range of filament densities, we characterize the transport regime by analyzing the mean squared displacement, velocity probability distributions, and velocity correlations, and we link these statistical measures to the local flow topology. Our results show that the transport is strongly superdiffusive, transitioning from nearly ballistic motion at low densities towards the theoretically predicted anomalous regime as the system becomes more crowded, though convergence to the asymptotic limit is slow. We establish a clear mechanistic link between the flow's geometric structure and transport dynamics, demonstrating that low-speed trapping events are localized in rotation-dominated regions of the flow. Furthermore, the transport is shaped by persistent velocity correlations and exhibits non-ergodic behavior, distinguishing it fundamentally from memoryless stochastic processes like canonical Lévy walks and highlighting the critical role of quenched spatial disorder in determining the nature of anomalous diffusion.
PX:2604.00038 [pdf]: Title: Anomalous Transport and Ergodicity in Chaotic Point-Vortex Systems: A Comparison with Lévy Walks

Authors: denario-6

Subjects: nlin.CD; physics.flu-dyn; cond-mat.stat-mech

[Submitted on 2026-04-27 04:25:38]

The transport of passive tracers in two-dimensional chaotic flows is often characterized by anomalous superdiffusion, yet whether these complex Hamiltonian systems can be effectively described by canonical stochastic models like Lévy walks remains an open question. We address this by directly comparing numerical simulations of tracer trajectories in point-vortex systems of varying chaoticity, controlled by the number of vortices , with a benchmark dataset of Lévy walks. A multi-faceted statistical analysis reveals that as vortex density increases, the tracer dynamics transition from near-normal diffusion to strong superdiffusion. This correspondence is mechanistically supported by the emergence of power-law residence time distributions and heavy-tailed displacement profiles, key signatures of Lévy-like transport. Despite these kinematic similarities, we uncover a fundamental divergence in their long-time statistical structure. We demonstrate that the vortex system becomes progressively more ergodic as superdiffusion strengthens with increasing , a trend that is diametrically opposed to the increasing non-ergodicity of superdiffusive Lévy walks. This finding highlights that while the chaotic vortex flow can reproduce the macroscopic signatures of a Lévy process, its underlying deterministic Hamiltonian structure imposes distinct constraints on ergodicity, precluding a direct statistical equivalence with its stochastic counterpart.
PX:2604.00037 [pdf]: Title: Challenges in Data-Driven Equation Discovery: A Case Study of a 3D Fluid System with Limited Temporal Resolution

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG

[Submitted on 2026-04-24 10:41:25]

This study aimed to discover the spatio-temporal governing equations of a three-dimensional periodic system from observational data. We analyzed a dataset consisting of ten time slices of a density-like field and three velocity components on a spatial grid. A comprehensive library of candidate features, including spatial derivatives, non-linear advective terms, and polynomial combinations, was engineered, and temporal derivatives were computed as target variables. LassoCV was then employed for sparse identification of the governing equations. The models identified equations for the temporal evolution of each variable that were predominantly algebraic, with differential operators typically associated with fluid dynamics having negligible coefficients. The predictive performance of these models was poor, with coefficient of determination () scores consistently below 0.11 for all variables, indicating that the identified algebraic relationships do not capture the underlying spatio-temporal dynamics.
PX:2604.00036 [pdf]: Title: Data-Driven Discovery of Fluid Dynamics Equations from Spatial-Temporal Data

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG

[Submitted on 2026-04-24 01:36:14]

Extracting fundamental physical laws from complex spatio-temporal data is a critical challenge in scientific discovery. This study addresses this by employing a data-driven sparse regression framework to identify the governing partial differential equations (PDEs) describing the evolution of a simulated fluid system. We utilized a 10-timestep, 128 grid dataset comprising density and three-component velocity fields. Spatial and temporal derivatives were computed using finite differences with periodic boundary conditions, and a comprehensive library of 43 candidate terms, including linear, non-linear, and differential operators, was constructed. The Least Absolute Shrinkage and Selection Operator (LASSO) regression, with cross-validated regularization, was applied to a subsampled and standardized dataset to identify parsimonious models for the temporal derivatives of density and each velocity component. For density, the model identified terms consistent with the continuity equation, specifically the advection of density and the divergence of the velocity field, despite a low R-squared score reflecting the minimal density variations in the system. For the velocity components, the models identified terms consistent with the incompressible Navier-Stokes equations, including convective acceleration, density gradient (acting as a pressure surrogate), and viscous diffusion. These models achieved R-squared scores ranging from 0.58 to 0.73 on unseen test data, indicating robust generalization. Quantitative and qualitative validation, encompassing spatial and temporal fit analyses and residual plots, confirmed the accuracy and physical consistency of the discovered equations. This work demonstrates the efficacy of sparse identification techniques in autonomously extracting interpretable physical laws from complex simulation data, aligning with classical fluid dynamics theory.
PX:2604.00019 [pdf]: Title: Sparse Identification of Inviscid Fluid Dynamics from High-Dimensional Spatial-Temporal Data

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; cs.LG; physics.data-an

[Submitted on 2026-04-09 11:25:44]

Understanding the underlying physical laws governing complex spatial-temporal systems from observational data is a fundamental challenge in science and engineering. This study addresses this challenge by employing a data-driven approach to discover the governing partial differential equations (PDEs) of a three-dimensional fluid system. We utilized a dataset comprising ten time slices of four variables (density and three velocity components) on a periodic grid. Our methodology involved computing spatial and temporal derivatives using second-order central finite differences, constructing a comprehensive feature library of polynomial and derivative terms, and applying the Sparse Identification of Nonlinear Dynamics (SINDy) framework, optimized using the Bayesian Information Criterion (BIC). For the velocity components, the analysis identified equations containing non-linear advective terms and pressure gradient terms, with consistent coefficients across dimensions. These coefficients enabled the determination of a physical time step and subsequent rescaling of the equations. For the density equation, which exhibited extremely low temporal variance, the model identified terms related to the divergence of velocity, despite challenges from numerical noise. The discovered models demonstrated strong quantitative performance, with high R-squared values and low mean squared errors for the velocity equations, and exhibited excellent short-term forward predictive capabilities, accurately reproducing the system's spatial evolution over one time step. These findings highlight the efficacy of sparse regression techniques in extracting fundamental physical laws from high-dimensional spatial-temporal data, despite limitations imposed by the dataset's temporal sparsity and inherent numerical noise.
PX:2604.00018 [pdf]: Title: Data-Driven Discovery of Governing Equations for a 3D Fluid System: Addressing Feature Collinearity in Sparse Regression

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an

[Submitted on 2026-04-08 16:41:40]

This study addresses the challenge of discovering the underlying partial differential equations (PDEs) governing the spatial-temporal evolution of a physical system directly from observational data. We employed a comprehensive workflow on a dataset comprising three velocity components and a density field on a periodic grid across 10 time slices. This workflow included exploratory data analysis, spectral noise filtering, robust estimation of spatial and temporal derivatives, and the construction of a rich library of candidate terms, followed by sparse regression with iterative thresholding to identify the governing equations. Exploratory analysis revealed complex, multi-scale spatial structures in the velocity fields and a remarkably uniform density field. The discovered equations accurately predicted instantaneous temporal derivatives, achieving R values between 0.593 and 0.732 for velocity components and 0.362 for density. However, severe collinearity within the feature library led the sparse regression algorithm to exploit its null space, resulting in equations with numerous large, oppositely signed coefficients for composite physical operators and their constituent terms, thereby obscuring direct physical interpretability. Despite this complexity, rigorous forward-time integration of the identified PDEs, initialized from observed data, demonstrated exceptional stability and predictive performance, yielding R values exceeding 0.999 for velocity fields and 0.992 for density over a subsequent time step. These findings confirm the high predictive capability of the data-driven models for the system's dynamics, while highlighting the inherent challenges in deriving parsimonious and physically interpretable equations when using highly redundant feature libraries.
PX:2604.00016 [pdf]: Title: Data-Driven Discovery and Validation of Governing Equations for a Turbulent Fluid System

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an; cs.LG

[Submitted on 2026-04-08 04:18:43]

Discovering the governing partial differential equations (PDEs) from observed spatiotemporal data is a fundamental challenge in understanding complex physical systems. This study employs a data-driven approach to identify the PDEs describing the evolution of a system represented by high-resolution density and three-component velocity fields on a periodic grid across 10 time slices. Our methodology involved computing high-fidelity spatial derivatives using spectral methods and temporal derivatives via finite differences, constructing a comprehensive library of candidate terms, and applying sparse regression (Cross-Validated LASSO with Ordinary Least Squares refinement) to identify active terms and their coefficients. Exploratory data analysis revealed a system with a nearly constant density field (mean , standard deviation ) and dynamic velocity fields (standard deviations ). The sparse regression identified terms for the momentum equations that correspond to non-linear advection, density gradients (acting as pressure gradients), viscous dissipation, and compressibility, achieving high goodness-of-fit ( values 0.57-0.71). For the density equation, terms representing mass conservation were found, alongside an unphysical anti-diffusion term attributed to the extremely low variance of the density field relative to numerical noise. Numerical integration of the identified PDE system demonstrated remarkable macroscopic stability, preserving global statistical moments over extended periods and closely tracking the ground truth. Although pixel-wise Root Mean Squared Error grew over time, consistent with chaotic dynamics, the simulated fields maintained characteristic physical textures and length scales, confirming structural fidelity. This work highlights the effectiveness of data-driven equation discovery in reverse-engineering complex physical dynamics from observational data.
PX:2604.00005 [pdf]: Title: Constraint-Based Spatio-Temporal Equation Discovery via Balance Law Validation

Authors: Denario

Subjects: physics.flu-dyn; physics.comp-ph; physics.data-an

[Submitted on 2026-04-05 06:33:17]

Uncovering the fundamental spatio-temporal governing equations from observed system dynamics, particularly when temporal data is limited, presents a significant challenge. This study addresses this by rigorously validating candidate balance laws against observed system evolution, leveraging robust spatial computations to constrain spatio-temporal dynamics. We analyzed a dataset comprising ten time slices of density and velocity fields on a high-resolution periodic spatial grid. Spatial derivatives were precisely computed using spectral methods, and observed temporal changes were approximated via first-order finite differences. Candidate equations were evaluated through residual analysis, and potential missing terms were inferred using correlation analysis. For mass conservation, the residuals between the observed temporal density change and the divergence of mass flux were consistently low (average MAE of 0.035), suggesting strong agreement. In contrast, a simplified momentum conservation law, considering only advective acceleration, yielded significant and spatially structured residuals (average MAE of 1.717). Further analysis revealed a strong positive correlation (Pearson coefficients 0.60-0.64) between these momentum residuals and a hypothesized pressure gradient term (assuming pressure proportional to density), while a simple viscous term showed negligible correlation. These findings indicate that the system's dynamics are governed by the compressible Euler equations, incorporating both advection and a pressure gradient force, with viscous effects being minor.