arXiv subjects

Kunihiko Taira

Publications and source records attributed to Kunihiko Taira.

At least 19 recordsLinked to original sources

arXiv2026

Vertical vortex gust encounters of a delta wing

The present study analyzes encounters of a vertical vortex with a tailless NACA 0012 delta wing with a sweep angle of 60 degrees at an angle of attack of 10 degrees and Reynolds number 1000 using direct numerical simulations. Motivated by the need to fly in complex settings such as urban canyons, mountainous areas, wildfires, or vehicle swarms, we focus on the influence of a vertical vortex gust on the delta wing, complementing previous efforts that predominantly studied spanwise and streamwise vortex encounters. The vertical orientation can impose strong transient loads on all six degrees of freedom, and particular attention is devoted to connecting these loads to the flow response. By varying the gust's lateral position, size, and strength, we find a fundamental process that characterizes vertical vortex gust encounters. The gust consistently imprints a low-pressure core on the wing surface. The evolving core creates an adverse pressure gradient that distorts the baseline skin-friction pattern and induces separation that lifts the boundary layers. These lifted boundary layers are elongated and twisted by the gust's strain into lobed vortical structures, which are shown by force element analysis to make a critical contribution to the lift. As the gust's lateral position is varied from root to tip, the low-pressure core and the induced flow separation are increasingly localized around the leading edge closest to the gust, modifying the lobe evolution and leading to complex dependence of the force and moment response on gust position compared to the largely monotonic dependence on gust size and strength.

physics.flu-dyn↗

arXiv2026

Weak Dominant Balance for Robust Identification of Dynamically Consistent Fluid Flow Structure

Extracting interpretable, localized physical mechanisms from complex spatiotemporal data is a foundational challenge across physics, biology, and engineering, but has remained out of reach on real measurements. The central obstacle is obtaining high-quality gradients of data via numerical differentiation, which amplifies noise, diverges for high-order equations, and falters on irregular geometries, limiting the scope of existing approaches to clean simulations of low-order systems. Here, we present weak dominant balance, a derivative-free framework that projects governing equations into a weak (integral) formulation, offloading differentiation onto smooth analytical test functions and leaving the data untouched. The method sustains accurate regime identification under severe noise where existing approaches categorically fail, delivers the first data-driven decomposition of a third-order partial differential equation applied to turbulent duct flow, and produces matching decompositions across direct numerical simulation and particle-image velocimetry measurements of a wavy channel flow, uncovering a previously uncharacterized dynamical regime. Weak dominant balance brings mechanism-level analysis out of simulation and onto measured data, and opens complex physical systems to direct, equation-grounded interpretation.

cs.CE↗

arXiv2026

Forcing-informed resolvent analysis: Identification of input-output relations in self-sustained flows

We present a forcing-informed (FI) resolvent analysis framework to identify input-output relations for statistically stationary self-sustained unsteady flows. The central idea of this method is to inform the resolvent operator about the spatiotemporal structures of the nonlinear terms that act as exogenous forcing with respect to the mean flow. To construct the FI resolvent operator, we estimate the basis vectors for the input subspace spanned by forcing snapshots and, similarly, for the output subspace, from simulation data. The extracted FI response and forcing modes are expressed through the estimated bases of the output and input subspaces, respectively, and the singular values of the FI resolvent operator correspond to the actual output amplitudes. These properties ensure that the extracted modes are consistent with the actual self-sustained flow fields. Additionally, the forcing snapshots can be used to construct the linear operator, enabling a fully data-driven FI resolvent analysis. The proposed framework is validated using the Stuart-Landau oscillator and demonstrated for a two-dimensional cylinder wake and a three-dimensional transitional boundary layer. We successfully identify the gains and the corresponding pairs of forcing and response modes, even at frequencies where the nonlinear amplification mechanism is crucial. Furthermore, leveraging the balance between the time-averaged energy amplification/attenuation by the linear operator and nonlinear forcing, we introduce a nonlinear energy transfer map that identifies the spatial domains where the extracted forcing mode injects or removes fluctuation energy, thereby providing key physical insight into the self-sustaining mechanisms.

physics.flu-dyn↗

arXiv2026

Data-driven oscillator model for multi-frequency turbulent flows

The complex dynamics of high-dimensional oscillatory flows can be simplified using phase-reduction analysis, providing a deeper understanding of the flow response to external perturbations. Although phase-based modeling and analysis have been utilized in recent studies on oscillatory fluid flows, their usages are still limited to single-frequency flows due to difficulties in addressing chaotic characteristics induced by multiple frequencies of turbulent flows. In order to overcome this limitation, we propose a data-driven framework that models the dynamics of multi-frequency turbulent flows based on a set of oscillators. The representative oscillators are extracted from the flow field data by training specially designed autoencoders. The oscillator dynamics are modeled through a machine-learning technique using neural networks to accurately predict the multi-frequency oscillatory behavior of turbulent flows. We verify the oscillator-based model of the multi-frequency turbulent flow by applying the proposed data-driven method to the three-dimensional supersonic turbulent flow over a cavity. We show that the extracted oscillators represent the dominant large-scale flow features and reflect the physical characteristics of the turbulent cavity flow. The data-driven oscillator dynamics model accurately forecasts the oscillatory behavior of the turbulent cavity flow for a long period. The proposed data-driven method for reduced-order modeling of turbulent flows with oscillators will enable deeper investigations of perturbation dynamics and control of turbulent flows.

physics.flu-dyn↗

arXiv2026

Vortical similarities across laminar and turbulent extreme gust encounters

This study uncovers a striking similarity between massively separated laminar and turbulent flows that develop over a square wing during extreme vortex gust encounters. The evolving large-scale, vortical core structures responsible for significant transient lift variations exhibit remarkable similarity across Re = 600 and 10,000. The formation of these structures is attributed to a substantial gust-induced vorticity flux produced at the wing surface, resulting in shared large-scale topological features between the low- and high-Reynolds-number flows. Although fine-scale vortical structures quickly emerge in the Re = 10,000 case, the large-scale structures identified by scale decomposition of the turbulent flow resemble those observed at Re = 600. These findings suggest that large-scale vortical features present in laminar extreme aerodynamic flows provide key insights into their higher Reynolds number counterparts, potentially reducing the complexity of flow modeling and control for extreme aerodynamics.

physics.flu-dyn↗

arXiv2025

Extreme vortex gust encounters by a square wing

Extreme gust encounters by finite wings with disturbance velocity exceeding their cruise speed remain largely unexplored, while particularly relevant to miniature-scale aircraft. This study considers extreme aerodynamic flows around a square wing and the large, unsteady forces that result from gust encounters. We analyse the evolution of three-dimensional, large-scale vortical structures and their complex interactions with the wing by performing direct numerical simulations at a chord-based Reynolds number of 600. We find that a strong incoming positive gust vortex induces a prominent leading-edge vortex (LEV) on the upper surface of the wing, accompanied by tip vortices (TiVs) strengthened through the interaction. Conversely, a strong negative gust vortex induces an LEV on the lower surface of the wing and causes a reversal in TiV orientation. In both extreme vortex gust encounters, the wing experiences significant lift fluctuations. Furthermore, we identify two opposing effects of the TiVs on the large lift fluctuations. First, the enhanced or reversed TiVs contribute to significant lift surges or drops by generating large low-pressure cores near the wing. Second, the TiVs play a part in attenuating lift fluctuations through enhanced downwash or upwash, formation of an arch vortex, and distortion of vortical structure around the wing corners. The second effect outweighs the first, resulting in smaller transient lift changes on the finite wing compared to the 2D wing. We also show that flying above a positive gust vortex or flying below a negative one can mitigate lift fluctuations during encounters. The current findings provide potential guidance on how TiV dynamics and wing positions could be leveraged to alleviate large transient lift fluctuations experienced by finite wings in severe gust conditions.

physics.flu-dyn↗

arXiv2025

Extreme Aerodynamics: A Data-Driven Perspective

While experiencing atmospheric turbulence on a commercial flight can be uncomfortable, it rarely compromises the stability of the aircraft. The situation is quite different for small air vehicles that operate in urban canyons, around mountainous terrains, and in the wakes of marine vessels, where they could encounter highly unsteady atmospheric conditions with relatively strong gusts. The spatiotemporal scales of such disturbances can be larger than the characteristic aerodynamic scales of the small vehicles, making the relative effect of disturbance significantly stronger than what a large commercial aircraft would experience. The gust ratio can exceed 1 in these extreme flight environments, making stable flight difficult, if not currently impossible. We refer to the study of aerodynamics for gust ratios over 1, extreme aerodynamics, and identify major challenges that require breakthroughs, particularly with data-driven approaches. Extreme aerodynamics present unique opportunities for innovative analysis techniques to study rich flow physics problems with strong nonlinearity, transient dynamics, and low-dimensional modeling over a large parameter space. Some of the approaches discussed herein should apply to a wider range of fluid dynamics problems with similar challenges.

physics.flu-dyn↗

arXiv2025

Using Optimal Transport Aligned Latent Embeddings for Separated Flow Analysis

Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise comparisons but can fail to distinguish distributional changes in flow fields. To address this limitation, we employ optimal transport (OT) theory, which is a mathematical framework built on probability and measure theory. By aligning Euclidean distances between flow fields in a latent space learned by an autoencoder with the corresponding OT geodesics, we seek to learn low-dimensional representations of flow fields that are interpretable from the perspective of unbalanced OT. As a demonstration, we utilize this OT-based analysis on controlled, separated flows past a NACA 0012 airfoil with a chord-based Reynolds number of 23,000 and a freestream Mach number of 0.3 for two angles of attack of $6^\circ$ and $9^\circ$. For each angle of attack, we identify a two-dimensional embedding that succinctly captures the different effective regimes of flow responses and control performance, characterized by the degree of suppression of the separation bubble and secondary effects from laminarization and trailing-edge separation. The interpretation of the latent representation was found to be consistent across the two angles of attack, suggesting that the OT-based latent encoding was capable of extracting physical relationships that are common across the different suites of cases. This study demonstrates the potential utility of optimal transport in the analysis and interpretation of complex flow fields.

physics.flu-dyn↗

arXiv2025

On the effect of airfoil geometry on extreme vortex-gust encounters

Historically, investigations on gust encounters have been limited to thin airfoils. In this work, we examine vortex-gust encounters by a family of airfoils at a chord-based Reynolds number Re_c=100, which includes variations in the gust ratio, initial gust position, gust radius, angle of attack, airfoil thickness, and airfoil camber. We examine differences in the flow fields, lift-element distributions, and aerodynamic responses across several airfoil-gust interactions. We observe a large deviation of the flow fields and aerodynamic responses with respect to the baseline flows for increasing gust ratios and gust sizes. The initial position of the vortex gust influences the magnitude of the velocity gradients observed near the leading edge, effectively heightening or mitigating the amplitude of the lift response. Moreover, the lift fluctuation increases with the angle of attack until it flattens around $10^\circ$, reminiscent of an unsteady stall-like regime. Furthermore, we report a decrease in the amplitude of the gust-induced lift fluctuations for thicker airfoils, which we attribute to a decrease in the vorticity production levels from the leading edge. The exploration of a sensitive subset of the parameter space uncovers relevant trends, shedding light on regions that have received limited attention in past studies, with special focus on the influence of airfoil geometry.

physics.flu-dyn↗

arXiv2025

Machine learning in fluid dynamics: A critical assessment

The fluid dynamics community has increasingly adopted machine learning to analyze, model, predict, and control a wide range of flows. These methods offer powerful computational capabilities for regression, compression, and optimization. In some cases, machine learning has even outperformed traditional approaches. However, many fluid mechanics problems remain beyond the reach of current machine learning techniques. As the field moves from its current state toward a more mature paradigm, this article offers a critical assessment of the key challenges that must be addressed. Tackling these technical issues will not only deepen our understanding of flow physics but also expand the applicability of machine learning beyond fundamental research. We also highlight the importance of community-maintained datasets and open-source code repositories to accelerate progress in this area. Furthermore, the future success of machine learning in fluid dynamics will depend on effective training -- not only for the next generation of researchers but also for established fluid mechanicians adapting to this evolving landscape. Data-driven fluid dynamics is in its critical transitional state over the next few years to shape its future. This perspective article aims to spark discussions and encourage collaborative efforts to advance the integration of machine learning in fluid dynamics.

physics.flu-dyn↗

arXiv2025

Phase autoencoder for rapid data-driven synchronization of rhythmic spatiotemporal patterns

We present a machine-learning method for data-driven synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems. Based on the phase autoencoder [Yawata {\it et al.}, Chaos {\bf 34}, 063111 (2024)], we map high-dimensional field variables of the reaction-diffusion system to low-dimensional latent variables characterizing the asymptotic phase and amplitudes of the field variables. This yields a reduced phase description of the limit cycle underlying the rhythmic spatiotemporal dynamics in a data-driven manner. We propose a method to drive the system along the tangential direction of the limit cycle, enabling phase control without inducing amplitude deviations. With examples of 1D oscillating spots and 2D spiral waves in the FitzHugh-Nagumo reaction-diffusion system, we show that the method achieves rapid synchronization in both reference-based and coupling-based settings. These results demonstrate the potential of data-driven phase description based on the phase autoencoder for synchronization of high-dimensional spatiotemporal dynamics.

nlin.AO↗

arXiv2025

Extracting dominant dynamics about unsteady base flows

A wide range of techniques exist for extracting the dominant flow dynamics and features about steady, or periodic base flows. However, there have been limited efforts in extracting the dominant dynamics about unsteady, aperiodic base flow. These flows appear in many applications such as when there is a sudden change in the flow rate through a pipe, when an airfoil experiences stall, or when a vortex forms. For these unsteady flows, it is valuable to know not only the dynamics of the base flow but also the features that form around this base flow. Here, we discuss the current state of research on extracting important flow structures and their dynamics in such cases with time-varying base flows. In particular, we consider data-driven decompositions, operator-based methods, causality analysis, and some other approaches. We also offer an outlook and call attention to key areas that require future efforts.

physics.flu-dyn↗

arXiv2025

Phase-based analysis and control of supersonic turbulent cavity flows

We present a phase-based framework for reducing the pressure fluctuations within a spanwise-periodic supersonic turbulent cavity flow with an incoming free-stream Mach number of 1.4 and a depth-based Reynolds number of 10,000. Open cavity flows exhibit large fluctuations due to the feedback between the shear layer instabilities and the acoustic field. The dominant flow physics includes the formation, convection, and impingement of large-scale spanwise-oriented vortical structures. We formulate a flow control strategy to effectively modify the vortex convection frequency, thereby disrupting the feedback loop and suppressing pressure fluctuations within the cavity. We implement a phase-reduction approach to identify the flow response about the time-varying convective process by defining a phase variable using dynamic mode decomposition. Three-dimensional impulse perturbations are introduced from the cavity leading edge to characterize phase response in terms of advancement or delay of convection. We perform open-loop flow control through unsteady blowing using actuation frequencies slightly different from the vortex convection frequency to disrupt the feedback loop. After designing a phase-sensitivity-based actuation waveform optimized for quick flow modification, we investigate the speed of fluctuation reduction and compare it to a sinusoidal waveform. At a spanwise actuation wavenumber of $β=2π$, both perform similarly, achieving a 46% reduction of pressure fluctuations within five convective times. At $β=π$, the phase-sensitivity-based actuation performs better by achieving a 40% reduction compared to the 30% with a sinusoidal waveform within six convective times. This study shows the potential of phase-based analysis for timing-based flow control of unsteady turbulent flows.

physics.flu-dyn↗

arXiv2025

Leveraging three-dimensionality for navigation in bluff-body wakes

Biological flyers and swimmers navigate in unsteady wake flows using limited sensory abilities and actuation energies. Understanding how vortical structures can be leveraged for energy-efficient navigation in unsteady flows is beneficial in developing autonomous navigation for small-scale aerial and marine vehicles. Such vehicles are typically operated with constrained onboard actuation and sensing capabilities, making energy-efficient trajectory planning critically important. This study finds that trajectory planners can leverage three-dimensionality appearing in a complex unsteady wake for efficient navigation using limited flowfield information. This is revealed with comprehensive investigations by finite-horizon model-predictive control for trajectory planning of a swimmer behind a cylinder wake at Re=300. The navigation performance of three-dimensional (3D) cases is compared to scenarios in a two-dimensional (2D) wake. The underactuated swimmer is able to reach the target by leveraging the background flow when the prediction horizon exceeds one-tenth of the wake-shedding period, demonstrating that navigation is feasible with limited information about the flowfield. Further, we identify that the swimmer can leverage the secondary transverse vortical structures to reach the target faster than is achievable navigating in a 2D wake.

physics.flu-dyn↗

arXiv2025

Biglobal resolvent analysis of separated flow over a NACA0012 airfoil

The effects of Reynolds number across $Re=1000$, $2500$, $5000$, and $10000$ on separated flow over a two-dimensional NACA0012 airfoil at an angle of attack of $α=14^\circ$ are investigated through the biglobal resolvent analysis. We identify modal structures and energy amplifications over a range of frequency, spanwise wavenumber, and discount parameter, providing insights across various timescales. Using temporal discounting, we find that the shear layer dynamics dominates over short time horizons, while the wake dynamics becomes the primary amplification mechanism over long time horizons. Spanwise effects also appear over long time horizon, sustained by low frequencies. At a fixed timescale, we investigate the influence of Reynolds number on response and forcing mode structures, as well as the energy gain over different frequencies. Across all Reynolds numbers, the response modes shift from wake-dominated structures at low frequencies to shear layer-dominated structures at higher frequencies. The frequency at which the dominant mechanism changes is independent of the Reynolds number. The response mode structures show similarities across different Reynolds numbers, with local streamwise wavelengths only depending on frequency. Comparisons at a different angle of attack ($α=9^\circ$) show that the transition from wake to shear layer dynamics with increasing frequency only occurs if the unsteady flow is three-dimensional. We also study the dominant frequencies associated with wake and shear layer dynamics across the angles of attack and Reynolds numbers, and present the characteristic scaling for each mechanism.

physics.flu-dyn↗

arXiv2025

Optimally time-dependent modes of vortex gust-airfoil interactions

We find the optimally time-dependent (OTD) orthogonal modes about a time-varying flow generated by a strong gust vortex impacting a NACA 0012 airfoil. This OTD analysis reveals the amplification characteristics of perturbations about the unsteady base flow and their amplified spatiotemporal structures that evolve over time. We consider four time-varying laminar base flows in which a vortex with a strength corresponding to the gust ratio $G$ of $\{-1,-0.5,0.5,1\}$ impinges on the leading edge of the airfoil at an angle of attack of $12^\circ$. In these cases, the impingement of the strong gust vortex causes massive separation and the generation of large-scale vortices around the airfoil within two convective time units. The highly unsteady nature of these vortex-airfoil interactions necessitates an advanced analytical technique capable of capturing the transient perturbation dynamics. For each of the considered gust ratios, the OTD analysis identifies the most amplified region to perturbations, the location of which changes as the wake evolves differently. For interactions between a moderate positive vortex gust ($G=0.5$) and the airfoil, the area where perturbations are amplified transitions from the leading-edge vortex sheet to the forming leading-edge vortex. Later, this most amplified structure becomes supported in the airfoil wake directly behind the trailing edge. In contrast, a strong vortex gust ($G=\pm 1$) encountered by the airfoil shows the most amplified OTD mode to appear around the core of the shed vortices. This study provides an analysis technique and fundamental insights into the broader family of unsteady aerodynamic problems.

physics.flu-dyn↗

arXiv2024

Hierarchical equivariant graph neural networks for forecasting collective motion in vortex clusters and microswimmers

Data-driven modeling of collective dynamics is a challenging problem because emergent phenomena in multi-agent systems are often shaped by long-range interactions among individuals. For example, in bird flocks and fish schools, long-range vision and flow coupling drive individual behaviors across the collective. Such collective motion can be modeled using graph neural networks (GNNs), but GNNs struggle when graphs become large and often fail to capture long-range interactions. Here, we construct hierarchical and equivariant GNNs, and show that these GNNs accurately predict local and global behavior in systems with collective motion. As representative examples, we apply this approach to simulations of clusters of point vortices and populations of microswimmers. For the point vortices, we define a local graph of vortices within a cluster and a global graph of interactions between clusters. For the microswimmers, we define a local graph around each microswimmer and a global graph that groups long-range interactions. We then combine this hierarchy of graphs with an approach that enforces equivariance to rotations and translations. This combination results in a significant improvement over a fully-connected GNN. For point vortices, our method conserves the Hamiltonian over long times, and, for microswimmers, our method predicts the transition from aggregation to swirling.

physics.flu-dyn↗

arXiv2024

Influence of three-dimensionality on wake synchronization of oscillatory cylinder

We investigate the effect of three-dimensionality on the synchronization characteristics of the wake behind an oscillating circular cylinder at Re = 300. Cylinder oscillations in rotation, transverse translation, and streamwise translation are considered. We utilize phase-reduction analysis, which quantifies the phase-sensitivity function of periodic flows, to examine the synchronization properties. Here, we present an ensemble-based framework for phase-reduction analysis to handle three-dimensional wakes that are not perfectly time-periodic. Based on the phase-sensitivity functions, synchronizability to three types of cylinder oscillations is evaluated. In spite of similar trends, we find that phase-sensitivity functions involving three-dimensional wakes are lower in magnitude compared to those of two-dimensional wakes, which leads to narrower conditions for synchronization to weak cylinder oscillations. We unveil that the difference between the phase-sensitivity functions of two- and three-dimensional flows is strongly correlated to the amplitude variation of the three-dimensional flow by the cylinder motions. This finding reveals that the cylinder motion modifies the three-dimensionality of the wake as well as the phase of vortex shedding, which leads to reduced phase modulation. The synchronization conditions of three-dimensional wakes, predicted by phase-reduction analysis, agree with the identification by parametric studies using direct numerical simulations for forced oscillations with small amplitudes. This study presents the potential capability of phase-reduction to study synchronization characteristics of complex flows.

physics.flu-dyn↗