我们使用扩散波光谱（DWS）首次对湍流边界处的耗散率 ε 进行了直接的空间和时间分辨测量。我们在先前发表的文章中已经证明，该技术能够提供牛顿流体耗散率的空间分布图。本文中，我们将该技术应用于由叶轮在方形箱体内搅拌流体所产生的湍流边界处。尽管测量仅在边界附近的小区域内进行，我们仍表明耗散率与注入功率保持正比，并遵循湍流标度律 ε∝Re³，其中雷诺数 Re 的范围为 1.5×10⁴ 至 6×10⁵。对于该流动，无需对数修正即可重现平坦边界附近的耗散行为。此外，我们的实验装置还允许测量边界附近耗散率的时空涨落。这些涨落相当大（相对涨落约为 50%），并且很好地符合对数正态分布，这与均匀各向同性湍流（HIT）体相中耗散率的预期一致，但功率密度谱（PDS）并不符合 HIT 所预期的谱形。
英文摘要：
We use Diffusing Wave Spectroscopy (DWS) to perform the first direct space- and time-resolved measurement of the dissipation rate~$ε$ at the boundary of a turbulent flow. We have shown in a previous publication that this technique provides maps of the dissipation rate of Newtonian fluids~\cite{Francisco}. Here, we apply the technique at the boundary of a turbulent flow generated in a square box by an impeller stirring the fluids. Although the measurement is made on a small region near the boundary, we show that the dissipation remains proportional to the injected power and follows the turbulent scaling $ε\propto \mathrm{Re}^3$, with Re being the Reynolds number ranging from $1.5 \times 10^4$ to $6 \times 10^5$. With this flow, there is no need for logarithmic corrections to reproduce the dissipation near the flat boundary. In addition, our setup allows us to measure the spatio-temporal fluctuations of the dissipation near the boundary. These fluctuations are quite large (the relative fluctuations are about 50\%) and are well described by a log-normal distribution, as expected for the dissipation rate in the bulk of homogeneous and isotropic turbulence (HIT) but Power Density Spectra (PDS) do not correspond to those expected for HIT \cite{Li07,Graham16,K62}
We develop a passive control strategy for suppressing thermoacoustic instability in a bluff-body stabilized premixed turbulent combustor. When the equivalence ratio is varied, there is a transition from combustion noise to thermoacoustic instability via intermittency in the combustor. We perform simultaneous acoustic pressure, 2D-PIV, and CH$^*$ chemiluminescence measurements to capture the pressure fluctuations, the velocity field, and the heat release rate (HRR) field during the transition. We measure the spatial distribution of the amplitude of turbulent velocity at the acoustic frequency, …
We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and multifractal, both in space and time, as it is demanded by the phenomenology of turbulence at infinite Reynolds numbers. We then solve numerically the flow equations for a differentiable version of this field. We observe that trajectories get also rough, characterized by nearly the same Hurst exponent as the one of our prescribed advecting field. Moreover, eve…
Estimation of the initial state of turbulent channel flow from limited data is investigated using an adjoint-variational approach. The data are generated from a reference direct numerical simulation (DNS) which is sub-sampled at different spatiotemporal resolutions. When the velocity data are at 1/4096 the spatiotemporal resolution of DNS, the correlation coefficient between the true and adjoint-variational estimated state exceeds 99 percent. The robustness of the algorithm to observation noise is demonstrated. In addition, the impact of the spatiotemporal density of the data on estimation qua…
University of Cambridge（剑桥大学）；Delft University of Technology（代尔夫特理工大学）；Imperial College London（帝国理工学院）；The Alan Turing Institute（艾伦·图灵研究所）
The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state for a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live (i.e., it is a numerical approximation of the turbulent attractor). The latent space is found by a series of …
The outward propagation of asymmetries introduced to originally axisymmetric turbulent flows is investigated, where 3D Batchelor vortices at high Reynolds numbers and with arbitrary swirl numbers are chosen as test cases. It is well known that disturbances (asymmetries) added to a 2D axisymmetric flow propagate radially outward, in order to re-axisymmetrize the vortex, but cease to travel at a critical distance, known as the stagnation radius. We utilize direct numerical simulations (DNS) and an inviscid model developed by linearizing the momentum and vorticity transport equations around the b…
A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems
Department of Applied and Computational Mathematics and Statistics, University of University of Notre Dame（应用与计算数学与统计学系，诺特大学）；Department of Environmental and Civil Engineering, University of Notre Dame（环境与土木工程系，诺特大学）
Particle Image Velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on Rapid Distortion Theory (RDT) and Taylor's Hypothesis (TH) to reconstruct the time evolution of a turbulent flow field in the intermediate period between consecutive PIV snapshots obtained using a non-time resolved system. The linear governing equations are evolved forwards and backwards in time using the PIV snapshots as initial conditions. The flow field in the intervenin…
Wall-bounded turbulent flows can be challenging to measure within experiments due to the breadth of spatial and temporal scales inherent in such flows. Instrumentation capable of obtaining time-resolved data (e.g., Hot-Wire Anemometers) tends to be restricted to spatially-localized point measurements; likewise, instrumentation capable of achieving spatially-resolved field measurements (e.g., Particle Image Velocimetry) tends to lack the sampling rates needed to attain time-resolution in many such flows. In this study, we propose to fuse measurements from multi-rate and multi-fidelity sensors w…
Differentially pumped capillaries, i.e., capillaries operated in a pressure gradient environment, are widely used for nonlinear pulse compression. In this work, we show that strong pressure gradients and high gas throughputs can cause spatiotemporal instabilities of the output beam profile. The instabilities occur with a sudden onset as the flow evolves from laminar to turbulent. Based on the experimental and numerical results, we derive guidelines to predict the onset of those instabilities and discuss possible applications in the context of nonlinear flow dynamics.
Spectral-Refiner: Accurate Fine-Tuning of Spatiotemporal Fourier Neural Operator for Turbulent Flows
School of Science and Engineering University of Missouri-Kansas City（科学与工程学院，密苏里大学-堪萨斯城分校）；Department of Mathematics Emory University（数学系，埃默里大学）；Center for Applied Scientific Computing Lawrence Livermore National Laboratory（应用科学计算中心，劳伦斯利弗莫尔国家实验室）
Target Parameterization in Diffusion Models for Nonlinear Spatiotemporal System Identification
Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, institut FEMTO-ST（玛丽-路易·巴斯蒂安大学，SUPMICROTECH，法国国家科学研究中心，FEMTO-ST研究所）；LLF, CNRS, Université Paris Cité（LLF，法国国家科学研究中心，巴黎cité大学）
Bayesian Conditional Diffusion Models for Versatile Spatiotemporal Turbulence Generation
University of Notre Dame（圣母大学）；Harvard University（哈佛大学）；Tufts University（塔夫茨大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；The Ohio State University（俄亥俄州立大学）
(abridged) Context: Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems. Aims: Our goal is to compute turbulent viscosity and magnetic diffusivity, relevant for diffusing large-scale flows and magnetic fields, respectively, and their ratio, the turbulent magnetic Prandtl number, ${\rm Pm}_{\rm t}$, for isotropically forced homogeneous turbulence. Methods: We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity is computed either from …
We analyse the long-time evolution of the three-dimensional flow in a closed cubic turbulent Rayleigh-Bénard convection cell via a Koopman eigenfunction analysis. A data-driven basis derived from diffusion kernels known in machine learning is employed here to represent a regularized generator of the unitary Koopman group in the sense of a Galerkin approximation. The resulting Koopman eigenfunctions can be grouped into subsets in accordance with the discrete symmetries in a cubic box. In particular, a projection of the velocity field onto the first group of eigenfunctions reveals the four stabl…
The effect of slip surfaces on the laminar-turbulent separatrix of plane Poiseuille flow is studied by direct numerical simulation. Turbulence lifetimes, the likelihood that turbulence is sustained, is investigated for transitional flows with various slip lengths. Slip surfaces decrease the likelihood of sustained turbulence compared to the no-slip case, and likelihood is further decreased as slip length is increased. A deterministic analysis of the effects of slip surfaces on transition to turbulence is performed using nonlinear traveling wave solutions to the Navier-Stokes equations, also kn…
Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic `active turbulence'. Here, we study these phenomena using the framework of Exact Coherent Structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact Coherent Structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant Exact Coherent Stru…
Learning Temporally Consistent Turbulence Between Sparse Snapshots via Diffusion Models
School of Engineering, The University of Manchester（工程学院，曼彻斯特大学）；School of Mathematics, The University of Manchester（数学学院，曼彻斯特大学）；IBM Research Europe, Daresbury, Warrington（IBM欧洲研究院，达尔斯伯里，沃林顿）
Neural Multigrid Memory For Computational Fluid Dynamics
Ecole Polytechnique（巴黎综合理工学院）；University of Engineering and Technology, Vietnam National University, Hanoi（河内越南国立大学工程技术大学）；Microsoft（微软）；OpenAI；Google（谷歌）；Littelfuse（力特公司）；Halıcıoğlu Data Science Institute, University of California, San Diego（加州大学圣地亚哥分校哈利哲奥卢数据科学研究所）
Plumes in a convective flow are considered to be relevant to the turbulent transport in convection. The effective mass, momentum, and heat transports in the convective turbulence are investigated in the framework of time--space double averaging procedure, where a field quantity is decomposed into three parts: the spatiotemporal mean (spatial average of the time-averaged) field, the dispersion or coherent fluctuation, and the random or incoherent fluctuation. With this framework, turbulent correlations in the mean-field equations are divided into the dispersion/coherent and random/incoherent co…
A realistic inflow boundary condition is essential for successful simulation of the developing turbulent boundary layer or channel flows. Recent advances in artificial intelligence (AI) have enabled the development of an inflow generator that performs better than the synthetic methods based on intuitions. In the present work, we applied generative adversarial networks (GANs), a representative of unsupervised learning, to generate an inlet boundary condition of turbulent channel flow. Upon learning the two-dimensional spatial structure of turbulence using data obtained from direct numerical sim…
Buoyancy effect on low-flow condition convective heat transfer of non-conventional coolants, such as liquid metal and molten salts, is a crucial safety factor to advanced reactors under transient or accidental scenarios. The distinct heat transfer characteristics of non-unitary Prandtl fluids and the inherent complexity of the low-flow mixed convection phenomena requires the development of novel turbulent and heat transfer models that are adaptive to different spatiotemporal scales involved in the mixed convection heat transfer. In this work, direct numerical simulation of low-flow mixed conve…
Super-resolution reconstruction of turbulent flows from a single Lagrangian trajectory
Northwestern Polytechnical University（西北工业大学）；National Key Laboratory of Aircraft Configuration Design, Key Laboratory for Extreme Mechanics of Aircraft of Ministry of Industry and Information Technology（飞机外形设计全国重点实验室，工业和信息化部飞机极端力学重点实验室）
