arXiv subjects

P. K. Yeung

Publications and source records attributed to P. K. Yeung.

18 recordsLinked to original sources

arXiv2026

Numerical study of Lagrangian velocity structure functions using acceleration statistics and a spatial-temporal perspective

A fundamental relation in Lagrangian Kolmogorov theory is concerned with inertial range scaling of the second-order velocity structure function over intermediate time lags at sufficiently high Reynolds numbers. Significant theoretical support for asymptotic constancy of the scaling constant ($C_0$) is known, but limitations in the range of time scales accessible in direct numerical simulation make unambiguous testing of the scaling challenging. In this paper, direct numerical simulations of forced isotropic turbulence at Taylor-scale Reynolds numbers between 140 and 1300 are used to improve understanding in this subject. Uncertainties arising from modest simulation time spans in the high Reynolds number data are addressed by expressing the velocity structure function in terms of the acceleration autocorrelation, which suggests that $C_0$ may be sensitive to effects of Lagrangian intermittency but does not rule out asymptotic constancy at Reynolds numbers beyond those that may be feasible in simulations in the foreseeable future. The Lagrangian velocity increment is examined further from a spatial-temporal perspective, as a combination of convective (spatial) and local (temporal) contributions, which are subject to a strong but incomplete mutual cancellation dependent on Reynolds number and time lag. The convective contribution is strongly influenced by the particle displacement, which is driven by large-scale dynamics and can thus grow into inertial range dimensions in space within just a few Kolmogorov time scales, without fully satisfying classical Lagrangian inertial-range requirements. An overall conclusion in this work is that both the limited range of time scales (narrower than that for length scales) and the effects of particle displacements have significant roles in the observed behavior of the second-order Lagrangian velocity structure function.

physics.flu-dyn↗

arXiv2025

Intelligent Sampling of Extreme-Scale Turbulence Datasets for Accurate and Efficient Spatiotemporal Model Training

With the end of Moore's law and Dennard scaling, efficient training increasingly requires rethinking data volume. Can we train better models with significantly less data via intelligent subsampling? To explore this, we develop SICKLE, a sparse intelligent curation framework for efficient learning, featuring a novel maximum entropy (MaxEnt) sampling approach, scalable training, and energy benchmarking. We compare MaxEnt with random and phase-space sampling on large direct numerical simulation (DNS) datasets of turbulence. Evaluating SICKLE at scale on Frontier, we show that subsampling as a preprocessing step can, in many cases, improve model accuracy and substantially lower energy consumption, with observed reductions of up to 38x.

cs.LG↗

arXiv2025

Analysis of inertial-range intermittency in forward and inverse cascade regions in isotropic turbulence

In order to test the hypothesis that inverse cascade regions in turbulent flows might exhibit more Gaussian noise-like and less intermittent small-scale statistics compared to the overall statistics, in this work we measure degrees of small-scale intermittency separately in regions of forward and inverse cascade. The local energy cascade rate $(Φ_\ell)$ at length scale $(\ell)$ is defined using the scale-integrated Kolmogorov-Hill (KH) equation. To characterize intermittency, we analyze the probability density functions (PDFs) of longitudinal and transverse velocity increments at scale $\ell$, conditioned on positive and negative $Φ_\ell$ (local forward and inverse cascades). Our findings reveal that transverse velocity increments display approximately the same degree of non-Gaussianity and intermittency, in both forward or inverse cascade regions. The only noticeable difference is observed for longitudinal velocity increments that display strong negative skewness in regions of forward cascade compared to small positive skewness in regions of inverse cascade. We repeat the analysis for filtered velocity gradient tensor elements at scale $\ell$ and obtain similar results, except that the skewness of its longitudinal elements is slightly negative even in regions of inverse cascade. The analysis is based on isotropic turbulence data ($Re_λ\sim 1{,}250$) available from the public Johns Hopkins Turbulence Databases, JHTDB v2.0. This refactored system is based on the Zarr storage format, while data access is based on the ``virtual sensor'' approach, enabled by a Python backend package (Giverny) that replaces the legacy SQL storage and SOAP Web Services-based approaches. Information about the new system as well as sample Python notebooks are described and illustrated. (Matlab, C, and Fortran access methods are also provided).

physics.flu-dyn↗

arXiv2024

Forward and inverse energy cascade and fluctuation relation in fluid turbulence adhere to Kolmogorov's refined similarity hypothesis

We study fluctuations of the local energy cascade rate $Φ_\ell$ in turbulent flows at scales ($\ell$) in the inertial range. According to the Kolmogorov refined similarity hypothesis (KRSH), relevant statistical properties of $Φ_\ell$ should depend on $ε_\ell$, the viscous dissipation rate locally averaged over a sphere of size $\ell$, rather than on the global average dissipation. However, the validity of KRSH applied to $Φ_\ell$ has not yet been tested from data. Conditional averages such as $\langle Φ_\ell|ε_{\ell}\rangle$ as well as of higher-order moments are measured from Direct Numerical Simulations data, and results clearly adhere to the predictions from KRSH. Remarkably, the same is true when considering forward ($Φ_\ell>0$) and inverse ($Φ_\ell<0$) cascade events separately. Measured ratios of forward and inverse cascade probability densities further show that a fluctuation relation adhering to the KRSH can be observed, raising the hope that important features of turbulence may be described using concepts from non-equilibrium thermodynamics.

physics.flu-dyn↗

arXiv2021

Small-scale isotropy and ramp-cliff structures in scalar turbulence

Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to $8192^3$ at high Péclet numbers to understand this anomaly as the scalar diffusivity, $D$, diminishes, or as the Schmidt number, $Sc = ν/D$, increases; here $ν$ is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and $Sc$ varies from 1 to 512. A simple model for the ramp-cliff structures is shown to characterize the scalar derivative statistics extremely well. It accurately captures how the small-scale isotropy is restored in the large-$Sc$ limit, and additionally suggests a slight correction to the Batchelor length scale as the relevant smallest scale in the scalar field.

physics.flu-dyn↗

arXiv2021

Turbulence is an ineffective mixer when Schmidt numbers are large

We solve the advection-diffusion equation for a stochastically stationary passive scalar $θ$, in conjunction with forced 3D Navier-Stokes equations, using direct numerical simulations in periodic domains of various sizes, the largest being $8192^3$. The Taylor-scale Reynolds number varies in the range $140-650$ and the Schmidt number $Sc \equiv ν/D$ in the range $1-512$, where $ν$ is the kinematic viscosity of the fluid and $D$ is the molecular diffusivity of $θ$. Our results show that turbulence becomes an ineffective mixer when $Sc$ is large. First, the mean scalar dissipation rate $\langle χ\rangle = 2D \langle |\nabla θ|^2\rangle$, when suitably non-dimensionalized, decreases as $1/\log Sc$. Second, 1D cuts through the scalar field indicate increasing density of sharp fronts on larger scales, oscillating with large excursions leading to reduced mixing, and additionally suggesting weakening of scalar variance flux across the scales. The scaling exponents of the scalar structure functions in the inertial-convective range appear to saturate with respect to the moment order and the saturation exponent approaches unity as $Sc$ increases, qualitatively consistent with 1D cuts of the scalar.

physics.flu-dyn↗

arXiv2021

Oscillations Modulating Power Law Exponents in Isotropic Turbulence: Comparison of Experiments with Simulations

Inertial-range features of turbulence are investigated using data from experimental measurements of grid turbulence and direct numerical simulations of isotropic turbulence simulated in a periodic box, both at the Taylor-scale Reynolds number $R_λ\sim 1000$. In particular, oscillations modulating the power-law scaling in the inertial range are examined for structure functions up to sixth order moments. The oscillations in exponent ratios decrease with increasing sample size in simulations though, in experiments, they survive at a low value of $4$ parts in $1000$ even after massive averaging. The two data sets are consistent in their intermittent character but differ in small but observable respects. Neither the scaling exponents themselves nor all the viscous effects are consistently reproduced by existing models of intermittency.

physics.flu-dyn↗

arXiv2020

A highly scalable particle tracking algorithm using partitioned global address space (PGAS) programming for extreme-scale turbulence simulations

A new parallel algorithm utilizing partitioned global address space (PGAS) programming model to achieve high scalability is reported for particle tracking in direct numerical simulations of turbulent flow. The work is motivated by the desire to obtain Lagrangian information necessary for the study of turbulent dispersion at the largest problem sizes feasible on current and next-generation multi-petaflop supercomputers. A large population of fluid particles is distributed among parallel processes dynamically, based on instantaneous particle positions such that all of the interpolation information needed for each particle is available either locally on its host process or neighboring processes holding adjacent sub-domains of the velocity field. With cubic splines as the preferred interpolation method, the new algorithm is designed to minimize the need for communication, by transferring between adjacent processes only those spline coefficients determined to be necessary for specific particles. This transfer is implemented very efficiently as a one-sided communication, using Co-Array Fortran (CAF) features which facilitate small data movements between different local partitions of a large global array. Detailed benchmarks are obtained on the Cray petascale supercomputer Blue Waters at the University of Illinois, Urbana-Champaign. For operations on the particles in a $8192^3$ simulation ($0.55$ trillion grid points) on $262,144$ Cray XE6 cores, the new algorithm is found to be orders of magnitude faster relative to a prior algorithm in which each particle is tracked by the same parallel process at all times. Improving support of PGAS models on major compilers suggests that this algorithm will be of wider applicability on most upcoming supercomputers.

physics.comp-ph↗

arXiv2020

Scaling exponents saturate in three-dimensional isotropic turbulence

From a database of direct numerical simulations of homogeneous and isotropic turbulence, generated in periodic boxes of various sizes, we extract the spherically symmetric part of moments of velocity increments and first verify the following (somewhat contested) results: the $4/5$-ths law holds in an intermediate range of scales and that the second order exponent over the same range of scales is {\it{anomalous}}, departing from the self-similar value of $2/3$ and approaching a constant of $0.72$ at high Reynolds numbers. We compare with some typical theories the dependence of longitudinal exponents as well as their derivatives with respect to the moment order $n$, and estimate the most probable value of the Hölder exponent. We demonstrate that the transverse scaling exponents saturate for large $n$, and trace this trend to the presence of large localized jumps in the signal. The saturation value of about $2$ at the highest Reynolds number suggests, when interpreted in the spirit of fractals, the presence of vortex sheets rather than more complex singularities. In general, the scaling concept in hydrodynamic turbulence appears to be more complex than even the multifractal description.

physics.flu-dyn↗

arXiv2019

Fractal iso-level sets in high-Reynolds-number scalar turbulence

We study the fractal scaling of iso-levels sets of a passive scalar mixed by three-dimensional homogeneous and isotropic turbulence at high Reynolds numbers. The Schmidt number is unity. A fractal box-counting dimension $D_F$ can be obtained for iso-levels below about $3$ standard deviations of the scalar fluctuation on either side of its mean value. The dimension varies systematically with the iso-level, with a maximum of about $8/3$ for the iso-level at the mean; this maximum dimension also follows as an upper bound from the geometric measure theory. We interpret this result to mean that mixing in turbulence is always incomplete. A unique box-counting dimension for all iso-levels results when we consider the spatial support of the steep cliffs of the scalar conditioned on local strain; that unique dimension is about $4/3$.

physics.flu-dyn↗

arXiv2019

Circulation in high Reynolds number isotropic turbulence is a bifractal

The turbulence problem at the level of scaling exponents is hard in part because of the multifractal scaling of small scales, which demands that each moment order be treated and understood independently. This conclusion derives from studies of velocity structure functions, energy dissipation, enstrophy density (that is, square of vorticity), etc. However, it is likely that there exist other physically pertinent quantities with uncomplicated structure in the inertial range, potentially resulting in huge simplifications in the turbulence theory. We show that velocity circulation around closed loops is such a quantity. By using a large databases of isotropic turbulence, generated from numerical simulations of the Navier-Stokes equations over a wide range of Reynolds numbers, we show that circulation exhibits a bifractal behavior at the highest Reynolds number considered: space filling for moments up to order $3$ and a mono-fractal with an unchanging dimension of about $2.5$ for higher orders; this change in character roughly at the third-order moment is reminiscent of a "phase transition". We explore the possibility that circulation becomes effectively space filling at much higher Reynolds numbers even though it may technically be regarded as a bifractal. We confirm that the circulation properties depend on only the area of the loop, not its shape; and, for a figure-$8$ loop, the relevant area is the scalar sum of the two segments of the loop.

physics.flu-dyn↗

arXiv2019

Extreme velocity gradients in turbulent flows

Fully turbulent flows are characterized by intermittent formation of very localized and intense velocity gradients. These gradients can be orders of magnitude larger than their typical value and lead to many unique properties of turbulence. Using direct numerical simulations of the Navier-Stokes equations with unprecedented small-scale resolution, we characterize such extreme events over a significant range of turbulence intensities, parameterized by the Taylor-scale Reynolds number ($R_λ$). Remarkably, we find the strongest velocity gradients to empirically scale as $τ_K^{-1} R_λ^β$, with $β\approx 0.775 \pm 0.025$, where $τ_K$ is the Kolmogorov time scale (with its inverse, $τ_K^{-1}$, being the {r.m.s.} of velocity gradient fluctuations). Additionally, we observe velocity increments across very small distances $r \le η$, where $η$ is the Kolmogorov length scale, to be as large as the {r.m.s.} of the velocity fluctuations. Both observations suggest that the smallest length scale in the flow behaves as $ηR_λ^{-α}$, with $α= β- \frac{1}{2}$, which is at odds with predictions from existing phenomenological theories. We find that extreme gradients are arranged in vortex tubes, such that strain conditioned on vorticity grows on average slower than vorticity, approximately as a power law with an exponent $γ< 1$, which weakly increases with $R_λ$. Using scaling arguments, we get $β=(2-γ)^{-1}$, which suggests that $β$ would also slowly increase with $R_λ$. We conjecture that approaching the limit of infinite $R_λ$, the flow is overall smooth, with intense velocity gradients over scale $ ηR_λ^{-1/2}$, corresponding to $β= 1$.

physics.flu-dyn↗

arXiv2018

Cancellation exponents in isotropic turbulence and magnetohydrodynamic turbulence

Small scale characteristics of turbulence such as velocity gradients and vorticity fluctuate rapidly in magnitude and oscillate in sign. Much work exists on the characterization of magnitude variations, but far less on sign oscillations. While averages performed on large scales tend to zero because of the oscillatory character, those performed on increasingly smaller scales will vary with the averaging scale in some characteristic way. This characteristic variation at high Reynolds numbers is captured by the so-called cancellation exponent, which measures how local averages tend to cancel out as the averaging scale increases, in space or time. Past experimental work suggests that the exponents in turbulence depend on whether one considers quantities in full three-dimensional space or uses their one- or two-dimensional cuts. We compute cancellation exponents of vorticity and longitudinal as well as transverse velocity gradients in isotropic turbulence at Taylor-scale Reynolds number up to 1300 on $8192^3$ grids. The 2D cuts yield the same exponents as those for full 3D, while the 1D cuts yield smaller numbers, suggesting that the results in higher dimensions are more reliable. We make the case that the presence of vortical filaments in isotropic turbulence leads to this conclusion. This effect is particularly conspicuous in magnetohydrodynamic turbulence, where an increased degree of spatial coherence develops along the imposed magnetic field.

physics.flu-dyn↗

arXiv2016

Refined similarity hypothesis using 3D local averages

The refined similarity hypotheses of Kolmogorov, regarded as an important ingredient of intermittent turbulence, has been tested in the past using one-dimensional data and plausible surrogates of energy dissipation. We employ data from direct numerical simulations, at the microscale Reynolds number $R_λ\sim 650$, on a periodic box of $4096^3$ grid points to test the hypotheses using 3D averages. In particular, we study the small-scale properties of the stochastic variable $V = Δu(r)/(r ε_r)^{1/3}$, where $Δu(r)$ is the longitudinal velocity increment and $ε_r$ is the dissipation rate averaged over a three-dimensional volume of linear size $r$. We show that $V$ is universal in the inertial subrange. In the dissipation range, the statistics of $V$ are shown to depend solely on a local Reynolds number.

physics.flu-dyn↗

arXiv2008

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets, from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range $R_λ\in [120:740]$. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, revealing a universal statistics, and calling for a unified theoretical description. Parisi-Frisch Multifractal theory, suitable extended to the dissipative scales and to the Lagrangian domain, is found to capture intermittency of velocity statistics over the whole three decades of temporal scales here investigated.

nlin.CD↗

arXiv2005

A Conditionally Cubic-Gaussian Stochastic Lagrangian Model for Acceleration in Isotropic Turbulence

The modelling of fluid particle accelerations in homogeneous, isotropic turbulence in terms of second-order stochastic models for the Lagrangian velocity is considered. The basis for the Reynolds model (A. M. Reynolds, \textit{Phys. Rev. Lett.} $\mathbf{91}(8)$, 084503 (2003)) is reviewed and examined by reference to DNS data. In particular, we show DNS data that support stochastic modelling of the logarithm of pseudo-dissipation as an Ornstein-Uhlenbeck process (Pope and Chen 1990) and reveal non-Gaussianity of the conditional acceleration PDF. The DNS data are used to construct a simple stochastic model that is exactly consistent with Gaussian velocity and conditionally cubic-Gaussian acceleration statistics. This model captures the effects of intermittency of dissipation on acceleration and the conditional dependence of acceleration on pseudo-dissipation (which differs from that predicted by the refined Kolmogorov (1962) hypotheses). Non-Gaussianity of the conditional acceleration PDF is accounted for in terms of model nonlinearity. The diffusion coefficient for the new model is chosen based on DNS data for conditional two-time velocity statistics. The resulting model predictions for conditional and unconditional velocity statistics and timescales are shown to be in good agreement with DNS data.

cond-mat.soft↗

arXiv2003

Schmidt number dependence of derivative moments for quasistatic straining motion

Bounds on high-order derivative moments of a passive scalar are obtained for large values of the Schmidt number, $Sc$. The procedure is based on the approach pioneered by Batchelor for the viscous-convective range. The upper bounds for derivative moments of order $n$ are shown to grow as $Sc^{n/2}$ for very large Schmidt numbers. The results are consistent with direct numerical simulations of a passive scalar, whose $Sc$ varies between 1/4 and 64, mixed by homogeneous isotropic turbulence. Although the analysis does not provide proper bounds for normalized moments, the combination of analysis and numerical data suggests that they decay with $Sc$, at least for odd orders. This paper has been withdrawn by the authors due to copyright. It appears in Journal of Fluid Mechanics (2003). http://jfm-www.damtp.cam.ac.uk/

nlin.CD↗

arXiv2002

Derivative moments in turbulent shear flows

We propose a generalized perspective on the behavior of high-order derivative moments in turbulent shear flows by taking account of the roles of small-scale intermittency and mean shear, in addition to the Reynolds number. Two asymptotic regimes are discussed with respect to shear effects. By these means, some existing disagreements on the Reynolds number dependence of derivative moments can be explained. That odd-order moments of transverse velocity derivatives tend not vanish as expected from elementary scaling considerations does not necessarily imply that small-scale anisotropy persists at all Reynolds numbers.

nlin.CD↗