arXiv subjects

Stephen M. de Bruyn Kops

Publications and source records attributed to Stephen M. de Bruyn Kops.

13 recordsLinked to original sources

arXiv2026

Impact of alignments between fluctuating and mean density gradients on the scale-dependent energetics of stably stratified turbulence

Non-trivial alignments between vorticity and the strain-rate tensor play an important role in the evolution of velocity gradients and the energy cascade in isotropic turbulence. Here we explore how alignments between the fluctuating and mean density gradients impact the mechanisms governing the turbulent kinetic energy (TKE) and available potential energy (APE) across scales in stably stratified turbulence. This is motivated by analytical results that demonstrate a connection between them, and is conducted using direct numerical simulations (DNS) of statistically stationary, stably stratified turbulence for $Pr = 1, 7, 50$ in the strongly stratified regime. After demonstrating how the gradient field alignments depend on scale and $Pr$, we show that the alignments are intimately connected to the reversal of the buoyancy flux at small-scales, and that regions of strong alignment and misalignment correspond to regions where the horizontal TKE inter-scale flux becomes weak. The same is also true of the APE flux, except that at larger scales, regions of strong alignment are associated with an upscale APE flux. The TKE and APE dissipation rates, and the mixing coefficient also show a strong dependence on the alignment, especially for $Pr=1$. Finally, we explore the connection between the local alignment and stability of the flow, and we find a non-trivial relationship, with regions of strong alignment surprisingly occurring most often in stable regions. This demonstrates that the dynamical significance of the alignments on the flow energetics cannot be understood through a simple connection between the local alignments and local stability of the flow.

physics.flu-dyn↗

arXiv2026

Evolution of passive scalar mixing layers in stratified and unstratified homogeneous turbulence

High-resolution large-eddy simulations of decaying stratified and unstratified homogeneous turbulence are used to understand the mixing of passive scalars in stably stratified flows. Two passive scalar mixing layers, one in the vertical direction and the other in the transverse direction, are a model for a plume that is very large relative to the length scale of the velocity. In the transverse direction, the evolution of the passive scalar is broadly similar in the stratified and unstratified cases, although it does spread slightly faster when stratified. Also, the intensity of the scalar fluctuations is higher in the stratified case, and the turbulent/non-turbulent interface is more intermittent. In the vertical direction, though, the stratified case has almost no mixing because the stratification prevents large-scale stirring. Initially, the stratified passive layer grows until its width is proportional to the vertical integral length of the horizontal velocity, which is itself constrained to maintain the vertical Froude number order one. After this early growth, there is little additional spreading of the passive scalar. Modelling of the stratified scalar flux in the transverse direction is done effectively with a one-constant model if the mean profile is known, and a two-constant model if the profile shape must be assumed. In the latter case, the model is good only if the scalar is in quasi-equilibrium with the velocity field such that the length scale of the scalar can be scaled from the kinetic energy. In this study, the Prandtl number of the active and passive scalars is 0.7. It is anticipated that the reverse buoyancy flux resulting from higher Prandtl numbers will affect the passive scalar mixing.

physics.flu-dyn↗

arXiv2026

Tensor network compression using fluid dynamics as a testbed: Analytical foundations in one dimension

High performance computers produce extreme-scale data sets that require sampling or compression if they are to be used to their full potential. Existing data compression techniques typically exploit features such as sparsity in the data, homogeneity in the data, or {\it a priori} knowledge of what subsets of data are of most interest. Fluid dynamics data in general do not exhibit these features and so are attractive test beds for generic compression techniques that are objective, robust, and tuneable with respect to information lost due to compression. Presented here is a method based on tensor networks, specifically matrix product states or tensor trains, that meets these requirements. The method is demonstrated for compression in one-dimension and is extensible to higher dimensionality. Lossless compression is demonstrated for random Fourier series for sufficiently high bond dimension of the tensor network, with the memory required to store the tensor network scaling directly proportional to the bond dimension. The lossy compression exhibited at lower bond dimension can be well within the relative error of many fluid simulations. The compression algorithm is tested for the time evolution of Burger's equation with excellent results. We additionally demonstrate the capability to perform computations in the compressed form through a tensor network periodic convolution that can be orders of magnitude faster than using fast Fourier transforms and the convolution theorem. In addition to being an attractive method for working with data sets generated by existing computers, the tensor network methods utilised are directly translatable to the emerging paradigm of quantum computing.

physics.comp-ph↗

arXiv2025

Mechanism generating reverse buoyancy flux at the small scales of stably stratified turbulence

Previous studies have shown that at the small-scales of stably stratified turbulence, the scale-dependent buoyancy flux reverses sign, such that there is a conversion of turbulent potential energy (TPE) back into turbulent kinetic energy (TKE) at these scales. Moreover, the magnitude of the reverse flux becomes stronger with increasing Prandtl number $Pr$. Using a filtering analysis we demonstrate analytically how this flux reversal is connected to the mechanism identified in Bragg \& de Bruyn Kops (JFM 2024 Vol 991 A10) that is responsible for the surprising observation that the TKE dissipation rate increases while the TPE dissipation rate decreases with increasing $Pr$ in stratified turbulence. The mechanism identified by Bragg \& de Bruyn Kops, which is connected to the formation of ramp-cliff structures in the density field, is shown to give the scale-local contribution to the buoyancy flux. At the smallest-scales this local contribution dominates and explains the flux reversal, while at larger scales a non-local contribution is important. Direct numerical simulations (DNS) of 3D statistically stationary, stably stratified turbulence in the strongly stratified regime confirm the theoretical analysis, and indicate that while on average the local contribution only dominates the buoyancy flux at the smallest scales, it remains strongly correlated with the buoyancy flux at all scales. The results show that ramp-cliffs are not only connected to the reversal of the local buoyancy flux but also the non-local part. At the small scales (approximately below the Ozmidov scale), ramp structures contribute exclusively to reverse buoyancy flux events, whereas cliff structures contribute to both forward and reverse buoyancy flux events.

physics.flu-dyn↗

arXiv2025

Pixel-Resolved Long-Context Learning for Turbulence at Exascale: Resolving Small-scale Eddies Toward the Viscous Limit

Turbulence plays a crucial role in multiphysics applications, including aerodynamics, fusion, and combustion. Accurately capturing turbulence's multiscale characteristics is essential for reliable predictions of multiphysics interactions, but remains a grand challenge even for exascale supercomputers and advanced deep learning models. The extreme-resolution data required to represent turbulence, ranging from billions to trillions of grid points, pose prohibitive computational costs for models based on architectures like vision transformers. To address this challenge, we introduce a multiscale hierarchical Turbulence Transformer that reduces sequence length from billions to a few millions and a novel RingX sequence parallelism approach that enables scalable long-context learning. We perform scaling and science runs on the Frontier supercomputer. Our approach demonstrates excellent performance up to 1.1 EFLOPS on 32,768 AMD GPUs, with a scaling efficiency of 94%. To our knowledge, this is the first AI model for turbulence that can capture small-scale eddies down to the dissipative range.

physics.flu-dyn↗

arXiv2024

Machine-Learned Closure of URANS for Stably Stratified Turbulence: Connecting Physical Timescales & Data Hyperparameters of Deep Time-Series Models

We develop time-series machine learning (ML) methods for closure modeling of the Unsteady Reynolds Averaged Navier Stokes (URANS) equations applied to stably stratified turbulence (SST). SST is strongly affected by fine balances between forces and becomes more anisotropic in time for decaying cases. Moreover, there is a limited understanding of the physical phenomena described by some of the terms in the URANS equations. Rather than attempting to model each term separately, it is attractive to explore the capability of machine learning to model groups of terms, i.e., to directly model the force balances. We consider decaying SST which are homogeneous and stably stratified by a uniform density gradient, enabling dimensionality reduction. We consider two time-series ML models: Long Short-Term Memory (LSTM) and Neural Ordinary Differential Equation (NODE). Both models perform accurately and are numerically stable in a posteriori tests. Furthermore, we explore the data requirements of the ML models by extracting physically relevant timescales of the complex system. We find that the ratio of the timescales of the minimum information required by the ML models to accurately capture the dynamics of the SST corresponds to the Reynolds number of the flow. The current framework provides the backbone to explore the capability of such models to capture the dynamics of higher-dimensional complex SST flows.

physics.flu-dyn↗

arXiv2024

Asymptotic analysis of mixing in stratified turbulent flows, and the conditions for an inertial sub-range

In an important study, Maffioli et al. (J. Fluid Mech., Vol. 794 , 2016) used a scaling analysis to predict that in the weakly stratified flow regime $Fr_h\gg1$ ($Fr_h$ is the horizontal Froude number), the mixing coefficient $Γ$ (defined as the ratio of the dissipation rates of potential to kinetic energy) scales as $Γ\sim O(Fr_h^{-2})$. Direct numerical simulations confirmed this result, and also indicated that for the strongly stratified regime $Fr_h\ll 1$, $Γ\sim O(1)$. Furthermore, the study argued that $Γ$ does not depend on the buoyancy Reynolds number $Re_b$, but only on $Fr_h$. We present an asymptotic analysis to predict theoretically how $Γ$ should behave for $Fr_h\ll1$ and $Fr_h\gg1$ in the limit $Re_b\to\infty$. To correctly handle the singular limit $Re_b\to\infty$ we perform the asymptotic analysis on the filtered Boussinesq-Navier-Stokes equations, and demonstrate the precise sense in which the inviscid scaling analysis of Billant \& Chomaz (Phys. Fluids, vol. 13, 1645-1651, 2001) applies to viscous flows with $Re_b\to\infty$. The analysis yields $Γ\sim O(Fr_h^{-2}(1+Fr_h^{-2}))$ for $Fr_h\gg1$ and $Γ\sim O(1+Fr_h^{2})$ for $Fr_h\ll 1$, providing a theoretical basis for the numerical observation made by Maffioli et al, as well as predicting the sub-leading behavior. Our analysis also shows that the Ozmidov scale $L_O$ does not describe the scale below which buoyancy forces are sub-leading, which is instead given by $O(Fr_h^{1/2} L_O)$, and that the condition for there to be an inertial sub-range when $Fr_h\ll 1$ is not $Re_b\gg1$, but the more restrictive condition $Re_b\gg Fr_h^{-4/3}$.

physics.flu-dyn↗

arXiv2023

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a 'layered anisotropic stratified turbulence' (LAST) regime, characterised by relatively deep and well-mixed density 'layers' separated by relatively thin 'interfaces' of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study 'LAST' mixing, as it is associated with Reynolds numbers $Re := UL/ν\gg 1$ and Froude numbers $Fr :=(2πU)/(L N) \ll 1$, ($U$ and $L$ being characteristic velocity and length scales, $ν$ being the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := ε/(νN^{2}) \gg 1$ where $ε$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := ν/κ= \mathcal{O}(10)$ in thermally-stratified water (where $κ$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ($Fr=0.5, 2$) and Prandtl numbers ($Pr=1, 7$) forced so that $Re_{b}=50$, with resolutions up to $30240 \times 30240 \times 3780$. We find that, as $Pr$ increases, emergent 'interfaces' become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed 'layers'. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $χ_0$) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$.

physics.flu-dyn↗

arXiv2023

Understanding the effect of Prandtl number on momentum and scalar mixing rates in neutral and stably stratified flows using gradient field dynamics

Recently, direct numerical simulations (DNS) of stably stratified turbulence have shown that as the Prandtl number ($Pr$) is increased from 1 to 7, the mean turbulent potential energy dissipation rate (TPE-DR) drops dramatically, while the mean turbulent kinetic energy dissipation rate (TKE-DR) increases significantly. Through an analysis of the equations governing the fluctuating velocity and density gradients we provide a mechanistic explanation for this surprising behavior and test the predictions using DNS. We show that the mean density gradient gives rise to a mechanism that opposes the production of fluctuating density gradients, and this is connected to the emergence of ramp-cliffs. The same term appears in the velocity gradient equation but with the opposite sign, and is the contribution from buoyancy. This term is ultimately the reason why the TPE-DR reduces while the TKE-DR increases with increasing $Pr$. Our analysis also predicts that the effects of buoyancy on the smallest scales of the flow become stronger as $Pr$ is increased, and this is confirmed by our DNS data. A consequence of this is that the standard buoyancy Reynolds number does not correctly estimate the impact of buoyancy at the smallest scales when $Pr$ deviates from 1, and we derive a suitable alternative parameter. Finally, an analysis of the filtered gradient equations reveals that the mean density gradient term changes sign at sufficiently large scales, such that buoyancy acts as a source for velocity gradients at small scales, but as a sink at large scales.

physics.flu-dyn↗

arXiv2023

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically-stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyze spatial correlations between the vertical density gradient $\partialρ/\partial z$ and the dissipation rates of kinetic energy $ε$ and scalar variance $χ$, the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $ε$ alone. While the majority of the domain is characterized by the canonical flux coefficient $Γ\equivχ/ε=0.2$, often assumed in ocean mixing parameterizations, extreme values of $χ$ within the statically-stable interfaces, associated with elevated $Γ$, strongly skew the bulk statistics. Our findings suggest that current parameterizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.

physics.flu-dyn↗

arXiv2021

Probabilistic neural networks for predicting energy dissipation rates in geophysical turbulent flows

Motivated by oceanographic observational datasets, we propose a probabilistic neural network (PNN) model for calculating turbulent energy dissipation rates from vertical columns of velocity and density gradients in density stratified turbulent flows. We train and test the model on high-resolution simulations of decaying turbulence designed to emulate geophysical conditions similar to those found in the ocean. The PNN model outperforms a baseline theoretical model widely used to compute dissipation rates from oceanographic observations of vertical shear, being more robust in capturing the tails of the output distributions at multiple different time points during turbulent decay. A differential sensitivity analysis indicates that this improvement may be attributed to the ability of the network to capture additional underlying physics introduced by density gradients in the flow.

physics.flu-dyn↗

arXiv2021

Analysis of scale-dependent kinetic and potential energy in sheared, stably stratified turbulence

Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analyzed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyze data from direct numerical simulation (DNS) at buoyancy Reynolds number $Re_b=O(100)$. The mean TKE exceeds TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average and their instantaneous values are positively correlated, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contribution to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain-self amplification, vortex stretching, and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered. Unlike isotropic turbulence, as $\ell$ increases the sheared-drop shape of the PDF disappears and the PDF becomes symmetric about $R=0$, meaning regions of vortex stretching and compression become equi-probable, as well as regions of strain amplification or suppression.

physics.flu-dyn↗

arXiv2019

Area of Scalar Isosurfaces in Homogeneous Isotropic Turbulence as a Function of Reynolds and Schmidt Numbers

A fundamental effect of fluid turbulence is turbulent mixing, which results in the stretching and wrinkling of scalar isosurfaces. Thus, the area of isosurfaces is of interest in understanding turbulence in general with specific applications in, e.g., combustion and the identification of turbulent/non-turbulent interfaces. We report measurements of isosurface areas in 28 direct numerical simulations (DNSs) of homogeneous isotropic turbulence with a mean scalar gradient resolved on up to $14256^3$ grid points with Taylor Reynolds number $Re{_λ}$ ranging from 24 to 633 and Schmidt number $Sc$ ranging from 0.1 to 7. More precisely, we measure layers with very small but finite thickness. The continuous equation we evaluate converges exactly to the area in the limit of zero layer thickness. We demonstrate a method for numerically integrating this equation that, for a test case with an analytical solution, converges linearly towards the exact solution with decreasing layer width. By applying the technique to DNS data and testing for convergence with resolution of the simulations, we verify the resolution requirements for DNS recently proposed by \citet{yeung18}. We conclude that isosurface areas scale with the square root of the Taylor Péclet number $Pe_λ$ between approximately 50 and 4429 with some departure from power law scaling evident for $2.4 < Pe_λ < 50$. No independent effect of either $Re_λ$ or $Sc$ is observed. The excellent scaling of area with $Pe_λ^{1/2}$ occurs even though the probability density function (p.d.f.) of the scalar gradient is very close to exponential for $Re_λ=98$ but approximately lognormal when $Re_λ=633$.

physics.flu-dyn↗