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Xiang I. A. Yang

Publications and source records attributed to Xiang I. A. Yang.

At least 19 recordsLinked to original sources
arXiv2026

Effects of the Coriolis force on the coherent structures in conventionally neutral atmospheric boundary layers

It is well known that the Coriolis force due to Earth's rotation can induce wind veer in the mean flow velocity of an atmospheric boundary layer (ABL), but much less is known about its effects on turbulent coherent structures. In this work, large-eddy simulation (LES) is employed to investigate the effects of the Coriolis force on the characteristics of turbulent coherent structures in the conventionally neutral atmospheric boundary layers (CNBL). Variation of the Coriolis force is realized by changing latitude or geostrophic wind speed. We found that the Coriolis force causes distinct deflection of coherent velocity structures to the geostrophic wind direction, which is not aligned with the direction of either the mean wind or the mean shear. When a relative structure deflection angle is plotted against a relative local wind veer angle, a universal relationship between them can be established regardless of latitude or geostrophic wind speed. Moreover, we also studied the effect of the Coriolis force on the inclination of large-scale turbulent structures. It is found that the inclination angle in the surface layer varies under different conditions, which is probably due to the deflection of turbulent structures caused by the Coriolis force.

physics.ao-ph↗
arXiv2026

A formal log(Re)-cost framework for the engineering turbulence problem

In fluid engineering, the turbulence problem is the longstanding challenge of obtaining accurate predictions of engineering quantities at affordable computational cost. Viewed through computational complexity, a practical algorithm requires cost growth no worse than $O(N)$, where $N$ denotes problem size. For turbulent flows, the problem size may be approximated by the number of dynamically relevant scales and hence by the Reynolds number $Re$. We propose a multi-fidelity, physics-constrained, data-driven framework designed to meet this criterion under stated assumptions. We augment the Spalart--Allmaras model through field inversion and machine learning using a constrained formulation that preserves the law of the wall. The model is trained at a low Reynolds number, where high-fidelity data are affordable, and deployed at higher Reynolds numbers. For a mean-flow-aligned grid in a wall-bounded flow, fixed spanwise resolution, and steady-solver cost linear in grid-point count, the low-fidelity RANS prediction scales as $O(\log(Re))$. The high-fidelity calculation and learning stage each contribute $O(Re^0)$ relative to the target Reynolds number, giving an overall formal cost of $O(\log(Re))$. In plane channel flow, a model trained at $Re_τ=1000$ corrects the wake-layer error of the baseline model and retains the improvement at $Re_τ=5200$. In the periodic hill, a model trained at $Re_b=5600$ is tested at $Re_b=10595$, $19000$, and $37000$. The constrained formulation preserves separation and recovery behavior as Reynolds number increases, yields the lowest root-mean-square error across all tests, and exhibits nearly Reynolds-number-independent error, indicating robust extrapolation.

physics.flu-dyn↗
arXiv2026

Least-Action-Guided Diffusion for Physical Extrapolation

Reliable extrapolation remains a central challenge for generative models in computational physics, because models trained over finite ranges of time, parameters, or geometries may produce physically inconsistent predictions outside the training distribution. We introduce a least-action-principle-guided diffusion, LAPG, a framework that promotes physical consistency during inference rather than relying solely on constraints imposed during training. The method combines a conditional score-based diffusion model with an action-derived physical guidance score. In the first stage, the learned score model generates an in-distribution proposal; in the second, an action-based variational prior refines this proposal toward the target out-of-distribution condition. This formulation turns the principle of least action into a differentiable inference-time correction mechanism and provides an alternative to pointwise residual penalties that often require empirical loss balancing. We evaluate LAPG on representative ordinary- and partial-differential-equation systems, including free fall, conservative and dissipative spring-mass dynamics, interacting point vortices, and potential flow over parameterized airfoils. In temporal, parameter, and geometric extrapolation tests, LAPG reduces phase drift, preserves dissipative decay, captures vortex motion, and improves the lift response of airfoil flows compared with training-time physics-informed baselines.

cs.LG↗
arXiv2026

Turbulence-like 5/3 spectral scaling in contextual representations of language as a complex system

Natural language is a complex system that exhibits robust statistical regularities. Here, we represent text as a trajectory in a high-dimensional embedding space generated by transformer-based language models, and quantify scale-dependent fluctuations along the token sequence using an embedding-step signal. Across multiple languages and corpora, the resulting power spectrum exhibits a robust power law with an exponent close to $5/3$ over an extended frequency range. This scaling is observed consistently in contextual embeddings from both human-written and AI-generated text, but is absent in static word embeddings and is disrupted by randomization of token order. These results show that the observed scaling reflects multiscale, context-dependent organization rather than lexical statistics alone. By analogy with the Kolmogorov spectrum in turbulence, our findings suggest that semantic information is integrated in a scale-free, self-similar manner across linguistic scales, and provide a quantitative, model-agnostic benchmark for studying complex structure in language representations.

cs.CL↗
arXiv2026

Integral analysis based diagnostics of turbulence model errors in skin friction

Error diagnostics for turbulence models have traditionally focused on engineering quantities of interest, such as the skin-friction coefficient, $C_f$, most often by comparing the predicted $C_f$ against reference data. In wall-bounded turbulent boundary layers, however, $C_f$ results from several physical mechanisms -- viscous effects, turbulence, pressure gradients, and mean-flow development -- whose relative importance depends on the flow conditions. Modeling errors in these mechanisms vary across turbulence closures, and identifying them offers valuable physical insight for model evaluation and improvement. We propose a diagnostics framework that systematically isolates and quantifies such errors using the angular momentum integral (AMI) formulation. The method is applied to five transport-type Reynolds-averaged Navier-Stokes (RANS) models in two test cases: a canonical zero-pressure-gradient flat-plate boundary layer and flow over a three-dimensional hill. For the flat-plate case, comparison with direct numerical simulation (DNS) data shows that all models reproduce $C_f$ reasonably well, but often through strong error cancellation, particularly between the turbulent torque and mean-flux contributions; individual terms can deviate by more than 20% of $C_f$. For the hill case, where wall-resolved large-eddy simulation (WRLES) is used as the reference, errors are significantly larger. The dominant erroneous contribution differs by model and may exceed several times the local $C_f$, depending on streamwise position. In separated-flow regions, the error cancellation that was observed in the flat-plate case largely disappears for the hill case, and the leading source of error shifts between mechanisms. These results highlight the value of mechanism-resolved diagnostics and provide guidance for targeted turbulence-model improvements.

physics.flu-dyn↗
arXiv2025

A generalisable data-augmented turbulence model with progressive and interpretable corrections for incompressible wall-bounded flows

The integration of interpretability and generalisability in data-driven turbulence modelling remains a fundamental challenge for computational fluid dynamics applications. This study yields a generalisable advancement of the $k$-$ω$ Shear Stress Transport (SST) model through a progressive data-augmented framework, combining Bayesian optimisation with physics-guided corrections to improve the predictions of anisotropy-induced secondary flows and flow separation simultaneously. Two interpretable modifications are systematically embedded: 1) a non-linear Reynolds stress anisotropy correction to enhance secondary flow predictions, and 2) an activation-based separation correction in the $ω$-equation, regulated by an optimised power-law function to locally adjust turbulent viscosity under adverse pressure gradients. The model is trained using a multi-case computational fluid dynamics-driven a posteriori approach, incorporating periodic hills, duct flow, and channel flow to balance correction efficacy with baseline consistency. Validation across multiple unseen cases -- spanning flat-plate boundary layers, high-Reynolds-number periodic hills, and flow over diverse obstacle configurations -- demonstrates enhanced accuracy in velocity profiles, recirculation zones, streamwise vorticity, and skin friction distributions while retaining the robustness of the original $k$-$ω$ SST in attached flows. Sparsity-enforced regression ensures reduced parametric complexity, preserving computational efficiency and physical transparency. Results underscore the framework's ability to generalise across geometries and Reynolds numbers without destabilising corrections, offering a validated framework toward deployable, data-augmented turbulence models for numerical simulations.

physics.flu-dyn↗
arXiv2025

Large Language Model Driven Development of Turbulence Models

Artificial intelligence (AI) has achieved human-level performance in specialized tasks such as Go, image recognition, and protein folding, raising the prospect of an AI singularity-where machines not only match but surpass human reasoning. Here, we demonstrate a step toward this vision in the context of turbulence modeling. By treating a large language model (LLM), DeepSeek-R1, as an equal partner, we establish a closed-loop, iterative workflow in which the LLM proposes, refines, and reasons about near-wall turbulence models under adverse pressure gradients (APGs), system rotation, and surface roughness. Through multiple rounds of interaction involving long-chain reasoning and a priori and a posteriori evaluations, the LLM generates models that not only rediscover established strategies but also synthesize new ones that outperform baseline wall models. Specifically, it recommends incorporating a material derivative to capture history effects in APG flows, modifying the law of the wall to account for system rotation, and developing rough-wall models informed by surface statistics. In contrast to conventional data-driven turbulence modeling-often characterized by human-designed, black-box architectures-the models developed here are physically interpretable and grounded in clear reasoning.

physics.flu-dyn↗
arXiv2024

Wall-modeled large-eddy simulation of turbulent smooth body separation using the OpenFOAM flow solver

This work investigates the current wall-modeled large-eddy simulation (WMLES) capabilities of the open-source computational fluid dynamics solver OpenFOAM, which is used widely in academia and industry. This is achieved by a simulation campaign that covers both attached and smooth body separation cases. The campaign includes simulations using four different wall models and aims to investigate the sensitivity of the results to changes in numerics, mesh resolution, and subgrid-scale modeling. The results demonstrate that two main factors largely determine OpenFOAM-based WMLES performance. These are the discretization of the convective term and wall modeling. For the former, the best performance in the attached case is achieved with low-dissipation numerics, however, for the smooth body separation case, more dissipative numerics give the best performance. For the latter, we find that both equilibrium and non-equilibrium wall models perform well in the attached case but that the non-equilibrium models significantly improve the prediction of smooth body separation. Still, the non-equilibrium wall model results do not show a uniform improvement over equilibrium models. This is explained by an inconsistent accounting of non-equilibrium physics in these models, i.e., including the pressure gradient term without also including the convective term. This highlights the potential for future performance improvements by using non-equilibrium wall models that consistently account for both the convective and pressure gradient terms.

physics.flu-dyn↗
arXiv2024

Rough surfaces in under-explored surface morphology space and their implications on roughness modelling

We report direct numerical simulation (DNS) results of the rough-wall channel, focusing on roughness with high $k_{rms}/k_a$ statistics but small to negative $Sk$ statistics, and we study the implications of this new dataset on rough-wall modelling. Here, $k_{rms}$ is the root-mean-square, $k_a$ is the first order moment of roughness height, and $Sk$ is the skewness. The effects of packing density, skewness and arrangement of roughness elements on mean streamwise velocity, equivalent roughness height ($z_0$) and Reynolds and dispersive stresses have been studied. We demonstrate that two-point correlation lengths of roughness height statistics play an important role in characterizing rough surfaces with identical moments of roughness height but different arrangements of roughness elements. Analysis of the present as well as historical data suggests that the task of rough-wall modelling is to identify geometric parameters that distinguish the rough surfaces within the calibration dataset. We demonstrate a novel feature selection procedure to determine these parameters. Further, since there is not a finite set of roughness statistics that distinguish between all rough surfaces, we argue that obtaining a universal rough-wall model for making equivalent sand-grain roughness ($k_s$) predictions would be challenging, and that each rough-wall model would have its applicable range. This motivates the development of group-based rough-wall models. The applicability of multi-variate polynomial regression and feedforward neural networks for building such group-based rough-wall models using the selected features has been shown.

physics.flu-dyn↗
arXiv2023

Extension of the law of the wall exploiting weak similarity of velocity fluctuations in turbulent channels

This paper explores the similarity of the streamwise velocity fluctuations in a channel. In the analysis, we employ a one-dimensional scalar variant of the proper orthogonal decomposition (POD). This approach naturally motivates the introduction of two different levels of similarity which we will refer to as strong and weak similarity. Strong similarity requires that the two-point correlation, and thus, all POD modes, show Reynolds number similarity, while weak similarity only requires that the first few POD modes show similarity. As POD concerns information at more than one location, these similarities are more general than various similarities found in the literature concerning single-point flow statistics. We examine flows at $Re_τ=$180, 540, 1000, and 5200. Strong similarity is observed in the viscous layer and the wake region, and weak similarity is found in both the viscous wall region and the outer part of the logarithmic layer. The presence of weak similarity suggests the existence of an extension to the law of the wall (LoW). We propose such an extension based on the results from the one-dimensional POD analysis. The usefulness of the LoW extension is then assessed by comparing flow reconstructions according to the conventional equilibrium LoW and the extended LoW. We show that the extended LoW provides accurate flow reconstructions in the wall layer, capturing fine-scale motions that are entirely missed by the equilibrium LoW.

physics.flu-dyn↗
arXiv2023

Incorporating basic calibrations in existing machine-learned turbulence modeling

This work aims to incorporate basic calibrations of Reynolds-averaged Navier-Stokes (RANS) models as part of machine learning (ML) frameworks. The ML frameworks considered are tensor-basis neural network (TBNN), physics-informed machine learning (PIML), and field inversion & machine learning (FIML) in J. Fluid Mech., 2016, 807, 155-166, Phys. Rev. Fluids, 2017, 2(3), 034603 and J. Comp. Phys., 2016, 305, 758-774, and the baseline RANS models are the one-equation Spalart-Allmaras model, the two-equation $k$-$ω$ model, and the seven-equation Reynolds stress transport models. ML frameworks are trained against plane channel flow and shear-layer flow data. We compare the ML frameworks and study whether the machine-learned augmentations are detrimental outside the training set. The findings are summarized as follows. The augmentations due to TBNN are detrimental. PIML leads to augmentations that are beneficial inside the training dataset but detrimental outside it. These results are not affected by the baseline RANS model. FIML's augmentations to the two eddy viscosity models, where an inner-layer treatment already exists, are largely neutral. Its augmentation to the seven-equation model, where an inner-layer treatment does not exist, improves the mean flow prediction in a channel. Furthermore, these FIML augmentations are mostly non-detrimental outside the training dataset. In addition to reporting these results, the paper offers physical explanations of the results. Last, we note that the conclusions drawn here are confined to the ML frameworks and the flows considered in this study. More detailed comparative studies and validation & verification studies are needed to account for developments in recent years.

physics.flu-dyn↗
arXiv2023

Large-eddy simulation of separated flows on unconventionally coarse grids

We examine and benchmark the emerging idea of applying the large-eddy simulation (LES) formalism to unconventionally coarse grids where RANS would be considered more appropriate at first glance. We distinguish this idea from very-large-eddy-simulation (VLES) and detached-eddy-simulation (DES), which require switching between RANS and LES formalism. LES on RANS grid is appealing because first, it requires minimal changes to a production code; second, it is more cost-effective than LES; third, it converges to LES; and most importantly, it accurately predicts flows with separation. This work quantifies the benefit of LES on RANS-like grids as compared to RANS on the same grids. Three canonical cases are considered: periodic hill, backward-facing step, and jet in cross flow. We conduct direct numerical simulation (DNS), proper LES on LES grids, LES on RANS-quality grids, and RANS. We show that while the LES solutions on the RANS-quality grids are not grid converged, they are twice as accurate as the RANS on the same grids.

physics.flu-dyn↗
arXiv2023

Survey of machine learning wall models for large eddy simulation

This survey investigates wall modeling in large eddy simulations (LES) using data-driven machine learning (ML) techniques. To this end, we implement three ML wall models in an open-source code and compare their performances with the equilibrium wall model in LES of half-channel flow at eleven friction Reynolds numbers between $180$ and $10^{10}$. The three models have ''seen'' flows at only a few Reynolds numbers. We test if these ML wall models can extrapolate to unseen Reynolds numbers. Among the three models, two are supervised ML models, and one is a reinforcement learning ML model. The two supervised ML models are trained against direct numerical simulation (DNS) data, whereas the reinforcement learning ML model is trained in the context of a wall-modeled LES with no access to high-fidelity data. The two supervised ML models capture the law of the wall at both seen and unseen Reynolds numbers--although one model requires re-training and predicts a smaller von Kármán constant. The reinforcement learning model captures the law of the wall reasonably well but has errors at both low ($Re_τ<10^3$) and high Reynolds numbers ($Re_τ>10^6$). In addition to documenting the results, we try to ''understand'' why the ML models behave the way they behave. Analysis shows that the errors of the supervised ML model is a result of the network design and the errors in the reinforcement learning model arise due to the present choice of the ''states'' and the mismatch between the neutral line and the line separating the action map. In all, we see promises in data-driven machine learning models.

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↗
arXiv2021

LES wall modeling for heat transfer at high speeds

A practical application of universal wall scalings is near-wall turbulence modeling. In this paper, we exploit temperature's semi-local scaling [Patel, Boersma, and Pecnik, {Scalar statistics in variable property turbulent channel flows}, Phys. Rev. Fluids, 2017, 2(8), 084604] and derive an eddy conductivity closure for wall-modeled large-eddy simulation of high-speed flows. We show that while the semi-local scaling does not collapse high-speed direct numerical simulation (DNS) data, the resulting eddy conductivity and the wall model work fairly well. The paper attempts to answer the following outstanding question: why the semi-local scaling fails but the resulting eddy conductivity works well. We conduct DNSs of Couette flows at Mach numbers from $M=1.4$ to 6. We add a source term in the energy equation to get a cold, a close-to-adiabatic wall, and a hot wall. Detailed analysis of the flows' energy budgets shows that aerodynamic heating is the answer to our question: aerodynamic heating is not accounted for in Patel et al.'s semi-local scaling but is modeled in the equilibrium wall model. We incorporate aerodynamic heating in semi-local scaling and show that the new scaling successfully collapses the high-speed DNS data. We also show that incorporating aerodynamic heating or not, the semi-local scaling gives rise to the exact same eddy conductivity, thereby answering the outstanding question.

physics.flu-dyn↗
arXiv2021

Grid-point and time-step requirements for direct numerical simulation and large-eddy simulation

We revisit the grid-point requirement estimates in Choi and Moin [Phys. Fluid, 24, 011702 (2012)] and establish more general grid-point requirements for direct numerical simulations (DNS) and large-eddy simulations (LES) of a spatially developing turbulent boundary layer. We show that, by allowing the local grid spacing to scale with the local Kolmogorov length scale, the grid-point requirement for DNS of a spatially developing turbulent boundary layer is $N\sim Re_{L_x}^{2.05}$ rather than $N\sim Re_{L_x}^{2.64}$ as suggested by Choi and Moin, where $N$ is the number of grid points and $L_x$ is the length of the plate. In addition to the grid-point requirement, we estimate the time-step requirement for DNS and LES. We show that, for a code that treats the convective term explicitly, the time steps required to get converged statistics are $N_t\sim Re_{L_x}/Re_{x_0}^{6/7}$ for wall-modeled LES and $N_t\sim Re_{L_x}/Re_{x_0}^{1/7}$ for wall-resolved LES and DNS (with different prefactors), where $Re_{x_0}$ is the inlet Reynolds number. The grid-point and time-step requirement estimates allow us to estimate the overall cost of DNS and LES. According to present estimates, the costs of DNS, wall-resolved LES and wall-modeled LES scale as $Re_{L_x}^{2.91}$, $Re_{L_x}^{2.72}$, and $Re_{L_x}^{1.14}$.

physics.flu-dyn↗
arXiv2020

On skin friction in wall-bounded turbulence

In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specially, with the theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region $[h_0, h_1]$. The formulas are validated using the direct numerical simulation data of turbulent channel and boundary layer flows, and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than $2\%$. We believe that the present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near wall statistics are very difficult to measure accurately.

physics.flu-dyn↗
arXiv2017

Direct numerical simulations of turbulent channel flow under transcritical conditions

Turbulent flows under transcritical conditions are present in regenerative cooling systems of rocker engines and extraction processes in chemical engineering. The turbulent flows and the corresponding heat transfer phenomena in these complex processes are still not well understood experimentally and numerically. The objective of this work is to investigate the turbulent flows under transcritical conditions using DNS of turbulent channel flows. A fully compressible solver is used in conjunction with a Peng-Robinson real-fluid equation of state to describe the transcritical flows. A channel flow with two isothermal walls is simulated with one heated and one cooled boundary layers. The grid resolution adopted in this study is slightly finer than that required for DNS of incompressible channel flows. The simulations are conducted using both fully (FC) and quasi-conservative (QC) schemes to assess their performance for transcritical wall-bounded flows. The instantaneous flows and the statistics are analyzed and compared with the canonical theories. It is found that results from both FC and QC schemes qualitatively agree well with noticeable difference near the top heated wall, where spurious oscillations in velocity can be observed. Using the DNS data, we then examine the usefulness of Townsend attached eddy hypothesis in the context of flows at transcritical conditions. It is shown that the streamwise energy spectrum exhibits the inverse wavenumber scaling and that the streamwise velocity structure function follows a logarithmic scaling, thus providing support to the attached eddy model at transcritical conditions.

physics.flu-dyn↗