arXiv subjects

H. Jane Bae

Publications and source records attributed to H. Jane Bae.

At least 19 recordsLinked to original sources

arXiv2026

Coherent-structure dynamics in wall turbulence from state-space trajectories

We identify dynamical processes in the near-wall region of turbulent wall-bounded flow by representing coherent-structure energy as trajectories in a low-dimensional state space and analyzing recurring trajectory patterns using network motifs. Direct numerical simulations (DNS) are performed for three configurations: a minimal flow unit (MFU) at $Re_τ\approx 180$ to isolate the self-sustaining process (SSP), a full-scale channel at the same Reynolds number to study interactions between near-wall structures, and an MFU at $Re_τ\approx 2200$ to investigate near-wall/outer-layer coupling. Proper orthogonal decomposition (POD) is used to identify modes corresponding to streaks, rolls, and meandering structures of the SSP, and the flow is projected onto these modes to track their energy over time. Motif analysis then identifies statistically significant dynamical pathways in the resulting state-space trajectories. Several motifs are common to all three configurations, indicating robust near-wall dynamics across different background flows. While motifs associated with the classical SSP are recovered, equally prominent motifs with no direct SSP analogue are also identified, demonstrating that preferred near-wall dynamics extend beyond the canonical regeneration cycle. Conditioning the $Re_τ\approx 180$ MFU on outer-layer energy further shows that quiescent outer-layer states produce dynamics resembling those of the low-Reynolds-number full channel, whereas energetic outer-layer states promote high-energy bursting events. These results demonstrate that near-wall turbulence evolves along preferred dynamical pathways whose prevalence is modified, but not eliminated, by outer-layer activity.

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

Data-driven Sensor Placement for Predictive Applications: A Correlation-Assisted Attribution Framework (CAAF)

Optimal sensor placement (OSP) is critical for efficient, accurate monitoring, control, and inference in complex physical systems. We propose a machine-learning-based feature attribution (FA) framework to identify OSP for target predictions. FA quantifies input contributions to a model output; however, it struggles with highly correlated input data often encountered in practical applications for OSP. To address this, we propose a Correlation-Assisted Attribution Framework (CAAF), which introduces a clustering step on the candidate sensor locations before performing FA to reduce redundancy and enhance generalizability. We first illustrate the core principles of the proposed framework through a series of validation cases, then demonstrate its effectiveness in realistic dynamical systems such as structural health monitoring, airfoil lift prediction, and wall-normal velocity estimation for turbulent channel flow. The results show that the CAAF outperforms alternative approaches that typically struggle due to the presence of nonlinear dynamics, chaotic behavior, and multi-scale interactions, and enables the effective application of FA for identifying OSP in real-world environments.

cs.CE↗

arXiv2026

Effect of subgrid-scale anisotropy on wall-modeled large-eddy simulation of turbulent flow with smooth-body separation

We examine the role of anisotropic subgrid-scale (SGS) stress in wall-modeled large-eddy simulation (WMLES) of flow over a spanwise-uniform Gaussian-shaped bump, with emphasis on predicting flow separation. The simulations show that eddy-viscosity-based SGS models often yield non-monotonic predictions of the mean separation bubble size on the leeward side under grid refinement, whereas models incorporating anisotropic SGS stress produce more consistent results. To identify where SGS anisotropy is most critical, we introduce anisotropic SGS stress in selected regions of the domain. The results reveal that the windward side, where a strong favorable pressure gradient (FPG) occurs, is crucial in determining downstream separation. Analysis of the Reynolds stress transport equation shows that fluctuations of anisotropic SGS stress modify SGS dissipation and diffusion in this region, thereby altering the Reynolds stress and the onset of separation. Examination of the mean streamwise momentum equation indicates that at coarse resolutions, the mean SGS shear stress dominates, and the differences between the eddy-viscosity-based and anisotropic models remain minor. With grid refinement, resolved Reynolds stresses increasingly govern the near-wall momentum transport, and the influence of SGS stress fluctuations grows as they determine the SGS dissipation and diffusion of Reynolds stresses. Component-wise analysis of the SGS stress tensor further shows that the improvement arises mainly from including significant normal stress contributions. An a priori study using filtered direct numerical simulation of turbulent Couette-Poiseuille flow confirms that wall-bounded turbulence under FPG is highly anisotropic and that anisotropic SGS models provide a more realistic SGS stress representation than eddy-viscosity-based models.

physics.flu-dyn↗

arXiv2026

Beyond first-order accuracy in continuous-forcing immersed boundary methods, and their well-conditioned projection-based solution

We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a singular source term in the governing equations. Our method leverages a smoothed indicator (Heaviside) function, following ideas from multiphase flow and immersed layers formulations, to recast the IB solution as a composite of distinct interior and exterior fields. We demonstrate that, when cast through this composite-solution lens, prior continuous-forcing IB methods can be seen as neglecting terms in the governing and constraint equations that restrict the solution to first-order accuracy. We incorporate these terms to systematically improve accuracy without the need for heuristic corrections. In canonical Poisson problems, we empirically demonstrate second-order convergence, and in incompressible Navier-Stokes simulations the method achieves slightly sub-second-order performance. While our present study focuses on these cases, the framework suggests a path towards second-order accuracy or higher, with further extensions. This perspective reframes accuracy limitations typically attributed to IB schemes. Although continuous-forcing IB methods are often reported to be only first-order accurate, we show that neither smoothing nor interface interpolation inherently restricts attainable order. Moreover, we naturally incorporate this higher-order formulation into a projection-based solution process. The resulting algorithm simultaneously mitigates the spurious surface stresses produced by ill-conditioned linear systems and reduces sensitivity to geometric resolution, addressing both conditioning and accuracy concerns within a unified approach.

math.NA↗

arXiv2026

Weakly coupled fluid-structure interaction between wall-bounded turbulent flows and defect-embedded phononic subsurfaces

We investigate the interaction between wall-bounded turbulence and defect-embedded phononic subsurface (D-Psub) using a weakly coupled fluid--structure framework, in which the flow and structure are advanced sequentially without sub-iterations. The D-Psub subsurface is modeled as a dynamic wall with a resonance introduced via a localized structural defect, driven by spatially averaged wall-pressure fluctuations from a turbulent channel flow. This configuration enables a controlled study of how a narrow-band structural response interacts with the broadband forcing of near-wall turbulence. Despite broadband turbulent forcing, the D-Psub exhibits a narrow-band response that modifies near-wall dynamics, with representative cases showing suppression of velocity fluctuations, increased coherence of streamwise streaks, and a measurable reduction in turbulent drag. Crucially, the coupled system displays behavior that cannot be replicated by prescribed wall motion: the dominant oscillation frequency shifts away from the designed resonance due to fluid--structure interaction. Additionally, the phase between panels is shown to be governed by the convection of turbulent structures. These results reveal a mechanism by which phononic subsurfaces filter and reorganize turbulent energy through frequency-selective coupling, distinct from conventional compliant or actively forced walls. The findings provide a physical basis for designing passive resonant surfaces that exploit turbulence-structure coupling for flow control.

physics.flu-dyn↗

arXiv2025

Consistency requirement of data-driven subgrid-scale modeling in large-eddy simulation

Data-driven subgrid-scale (SGS) modeling in the large-eddy simulations (LES) suffers from the inconsistency between the \textit{a priori} tests and the a posteriori tests, which make training accurate SGS models a difficult task. We study the difference in filtered high-fidelity data and LES to identify the numerical deviation between the two cases, which is a combined impact of commutation error, numerical errors, and error coupling. The impact of the numerical deviation is examined through two SGS model formulations: the eddy-viscosity and the complex nonlinear models. By incorporating numerical deviations into model training, we enhance consistency, stabilize simulations, and improve predictions of energy spectra in a posteriori tests. Our findings highlight that data-driven methods introduce significant nonlinearity and equation coupling, exacerbating inconsistencies compared to non-data-driven approaches. Finally, while the impact of the numerical deviation can be generalized, achieving accurate model predictions necessitates a physically grounded model form and an optimal filter width.

physics.flu-dyn↗

arXiv2025

Physics-informed Neural-operator Predictive Control for Drag Reduction in Turbulent Flows

Assessing turbulence control effects for wall friction numerically is a significant challenge since it requires expensive simulations of turbulent fluid dynamics. We instead propose an efficient deep reinforcement learning (RL) framework for modeling and control of turbulent flows. It is model-based RL for predictive control (PC), where both the policy and the observer models for turbulence control are learned jointly using Physics Informed Neural Operators (PINO), which are discretization invariant and can capture fine scales in turbulent flows accurately. Our PINO-PC outperforms prior model-free reinforcement learning methods in various challenging scenarios where the flows are of high Reynolds numbers and unseen, i.e., not provided during model training. We find that PINO-PC achieves a drag reduction of 39.0\% under a bulk-velocity Reynolds number of 15,000, outperforming previous fluid control methods by more than 32\%.

cs.LG↗

arXiv2025

Transient growth and nonlinear breakdown of wavelet-based resolvent modes in turbulent channel flow

We study the effectiveness of the time-localised principal resolvent forcing mode at actuating the near wall cycle of turbulence. The mode is restricted to a wavelet pulse and computed from an SVD of the windowed wavelet-based resolvent operator so that it produces the largest amplification via the linearised Navier-Stokes equations. We then inject this time-localised mode into the turbulent minimal flow unit at different intensities, and measure the instantaneous deviation of the system's response from the optimal resolvent response mode. This is possible under the new formulation, which enables the modes to represent transient trajectories. For the most energetic spatial wave numbers in the minimal flow unit -- constant in the streamwise direction and once-periodic in the spanwise direction -- the forcing mode takes the shape of streamwise rolls and produces a response mode in the form of streamwise streaks that transiently grow and decay. For initial times and close to the wall, the DNS response matches the principal response mode well, but due to nonlinearities, the response across all forcing intensities decays prematurely, and a higher forcing intensity leads to faster energy decay. The principal forcing mode still leads to significant energy amplification and is more effective than a randomly-generated forcing structure and the second suboptimal resolvent forcing mode at amplifying the near-wall streaks. We compute the nonlinear energy transfer to secondary modes and observe that the breakdown of the actuated mode proceeds similarly across all forcing intensities: in the near-wall region, the induced streak forks into a structure twice periodic in the spanwise direction; in the outer region, the streak breaks up into a structure that is once periodic in the streamwise direction. In both regions, spanwise gradients account for the dominant share of nonlinear energy transfer.

physics.flu-dyn↗

arXiv2024

Wavelet-based resolvent analysis of non-stationary flows

This work introduces a formulation of resolvent analysis that uses wavelet transforms rather than Fourier transforms in time. Under this formulation, resolvent analysis may extend to turbulent flows with non-stationary mean states; the optimal resolvent modes are augmented with a temporal dimension and are able to encode the time-transient trajectories that are most amplified by the linearised Navier-Stokes equations. We first show that the wavelet- and Fourier-based resolvent analyses give equivalent results for statistically-stationary flow by applying them to turbulent channel flow. We then use wavelet-based resolvent analysis to study the transient growth mechanism in the near-wall region of turbulent channel flow by windowing the resolvent operator in time and frequency. The computed principal resolvent response mode, i.e. the velocity field optimally amplified by the linearised dynamics of the flow, exhibits the Orr mechanism, supporting the claim that this mechanism is key to linear transient energy growth. We also apply this method to non-stationary parallel shear flows such as an oscillating boundary layer, and three-dimensional channel flow in which a sudden spanwise pressure gradient perturbs a fully-developed turbulent channel flow. In both cases, wavelet-based resolvent analysis yields modes that are sensitive to the changing mean profile of the flow. For the oscillating boundary layer, wavelet-based resolvent analysis produces oscillating principal forcing and response modes that peak at times and wall-normal locations associated with high turbulent activity. For the three-dimensional turbulent channel flow, the resolvent modes gradually realign themselves with the mean flow as it deviates.

physics.flu-dyn↗

arXiv2024

Sparse space-time resolvent analysis for statistically-stationary and time-varying flows

Resolvent analysis provides a framework to predict coherent spatio-temporal structures of largest linear energy amplification, through a singular value decomposition (SVD) of the resolvent operator, obtained by linearizing the Navier-Stokes equations about a known turbulent mean velocity profile. Resolvent analysis utilizes a Fourier decomposition in time, which limits its application to statistically-stationary or time-periodic flows. This work develops a variant of resolvent analysis applicable to time-evolving flows, and proposes a variant that identifies spatio-temporally sparse structures, applicable to either stationary or time-varying systems. Spatio-temporal resolvent analysis is formulated through the incorporation of the temporal dimension via a discrete time-differentiation operator. Sparsity (localisation) is achieved through the addition of an l1-norm penalisation term to the optimisation associated with the SVD. This modified problem can be formulated as a nonlinear eigenproblem, and solved via an inverse power method. We first showcase the implementation of the sparse analysis on statistically-stationary turbulent channel flow, and demonstrate that the sparse variant can identify aspects of the physics not directly evident from standard resolvent analysis. This is followed by applying the sparse space-time formulation on systems that are time-varying: a time-periodic turbulent Stokes boundary layer, and then a turbulent channel flow with a sudden imposition of a lateral pressure gradient, with the original streamwise pressure gradient unchanged. We present results demonstrating how the sparsity-promoting variant can either change the quantitative structure of the leading space-time modes to increase their sparsity, or identify entirely different linear amplification mechanisms compared to non-sparse resolvent analysis.

physics.flu-dyn↗

arXiv2024

Wall Modeling of Turbulent Flows with Varying Pressure Gradients Using Multi-Agent Reinforcement Learning

We propose a framework for developing wall models for large-eddy simulation that is able to capture pressure-gradient effects using multi-agent reinforcement learning. Within this framework, the distributed reinforcement learning agents receive off-wall environmental states including pressure gradient and turbulence strain rate, ensuring adaptability to a wide range of flows characterized by pressure-gradient effects and separations. Based on these states, the agents determine an action to adjust the wall eddy viscosity, and consequently the wall-shear stress. The model training is in situ with wall-modeled large-eddy simulation grid resolutions and does not rely on the instantaneous velocity fields from high-fidelity simulations. Throughout the training, the agents compute rewards from the relative error in the estimated wall-shear stress, which allows the agents to refine an optimal control policy that minimizes prediction errors. Employing this framework, wall models are trained for two distinct subgrid-scale models using low-Reynolds-number flow over periodic hills. These models are validated through simulations of flows over periodic hills at higher Reynolds numbers and flow over the Boeing Gaussian bump. The developed wall models successfully capture the acceleration and deceleration of wall-bounded turbulent flows under pressure gradients and outperform the equilibrium wall model in predicting skin friction.

physics.flu-dyn↗

arXiv2024

Sensitivity analysis of wall-modeled large-eddy simulation for separated turbulent flow

In this study, we conduct a parametric analysis to evaluate the sensitivities of wall-modeled large-eddy simulation (LES) with respect to subgrid-scale (SGS) models, mesh resolution, wall boundary conditions and mesh anisotropy. While such investigations have been conducted for attached/flat-plate flow configurations, systematic studies specifically targeting turbulent flows with separation are notably sparse. To bridge this gap, our study focuses on the flow over a two-dimensional Gaussian-shaped bump at a moderately high Reynolds number, which involves smooth-body separation of a turbulent boundary layer under pressure-gradient and surface-curvature effects. In the simulations, the no-slip condition at the wall is replaced by three different forms of boundary condition based on the thin boundary layer equations and the mean wall-shear stress from high-fidelity numerical simulation to avoid the additional complexity of modeling the wall-shear stress. Various statistics, including the mean separation bubble size, mean velocity profile, and dissipation from SGS model, are compared and analyzed. The results reveal that capturing the separation bubble strongly depends on the choice of SGS model. While simulations approach grid convergence with resolutions nearing those of wall-resolved LES meshes, above this limit, the LES predictions exhibit intricate sensitivities to mesh resolution. Furthermore, both wall boundary conditions and the anisotropy of mesh cells exert discernible impacts on the turbulent flow predictions, yet the magnitudes of these impacts vary based on the specific SGS model chosen for the simulation.

physics.flu-dyn↗

arXiv2024

Are the dynamics of wall turbulence in minimal channels and larger domain channels equivalent? A graph-theoretic approach

This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at $Re_τ\approx 180$, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately $2.83$ times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately $2.21$ times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately $2.17$ slower in the MFU than the FC.

physics.flu-dyn↗

arXiv2024

Linear and nonlinear Granger causality analysis of turbulent duct flows

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

physics.flu-dyn↗

arXiv2023

Transient growth of wavelet-based resolvent modes in the buffer layer of wall-bounded turbulence

In this work, we study the transient growth of the principal resolvent modes in the minimal flow unit using a reformulation of resolvent analysis in a time-localized wavelet basis. We target the most energetic spatial wavenumbers for the minimal flow unit and obtain modes that are constant in the streamwise direction and once-periodic in the spanwise direction. The forcing modes are in the shape of streamwise rolls, though pulse-like in time, and the response modes are in the form of transiently growing streaks. We inject the principal transient forcing mode at different intensities into a simulation of the minimal flow unit and compare the resulting nonlinear response to the linear one. The peak energy amplification scales quadratically with the intensity of the injected mode, and this peak occurs roughly at the same time for all forcing intensities. However, the larger energy amplification intensifies the magnitude of the nonlinear terms, which play an important role in damping the energy growth and accelerating energy decay of the principal resolvent mode. We also observe that the damping effect of the nonlinearities is less prominent close to the wall. Finally, we find that the principal resolvent forcing mode is more effective than other structures at amplifying the streak energy in the turbulent minimal-flow unit. In addition to lending support to the claim that linear mechanisms are important to near-wall turbulence, this work identifies time scales for the nonlinear breakdown of linearly-generated streaks.

physics.flu-dyn↗

arXiv2023

Towards real-time reconstruction of velocity fluctuations in turbulent channel flow

We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing linear estimators using flow statistics from an initial training period and evaluating their performance during a subsequent testing period with data obtained from direct numerical simulation. We address cases where (i) no, (ii) limited, and (iii) full-field training data are available using estimators based on (i) resolvent modes, (ii) resolvent-based estimation, and (iii) spectral proper orthogonal decomposition modes. During training, we introduce blockwise inversion to accurately and efficiently compute the resolvent operator in an interpretable manner. During testing, we enable efficient streaming reconstructions by using a temporal sliding discrete Fourier transform to recursively update Fourier coefficients using incoming measurements. We use this framework to reconstruct with minimal time delay the turbulent velocity fluctuations in a minimal channel at ${\rm Re}_τ\approx 186$ from sparse planar measurements. We evaluate reconstruction accuracy in the context of the extent of data required and thereby identify potential use cases for each estimator. The reconstructions capture large portions of the dynamics from relatively few measurement planes when the linear estimators are computed with sufficient fidelity. We also evaluate the efficiency of our reconstructions and show that the present framework has the potential to help enable real-time reconstructions of turbulent velocity fluctuations in an analogous experimental setting.

physics.flu-dyn↗

arXiv2023

Log-law recovery through reinforcement-learning wall model for large-eddy simulation

This paper focuses on the use of reinforcement learning (RL) as a machine-learning (ML) modeling tool for near-wall turbulence. RL has demonstrated its effectiveness in solving high-dimensional problems, especially in domains such as games. Despite its potential, RL is still not widely used for turbulence modeling and is primarily used for flow control and optimization purposes. A new RL wall model (WM) called VYBA23 is developed in this work, which uses agents dispersed in the flow near the wall. The model is trained on a single Reynolds number ($Re_τ= 10^4$) and does not rely on high-fidelity data, as the back-propagation process is based on a reward rather than output error. The states of the RLWM, which are the representation of the environment by the agents, are normalized to remove dependence on the Reynolds number. The model is tested and compared to another RLWM (BK22) and to an equilibrium wall model, in a half-channel flow at eleven different Reynolds numbers ($Re_τ\in [180;10^{10}]$). The effects of varying agents' parameters such as actions range, time-step, and spacing are also studied. The results are promising, showing little effect on the average flow field but some effect on wall-shear stress fluctuations and velocity fluctuations. This work offers positive prospects for developing RLWMs that can recover physical laws, and for extending this type of ML models to more complex flows in the future.

physics.flu-dyn↗