We consider the scattering of acoustic waves emitted by an active source above a plane turbulent shear layer. The layer is modeled by a moving random medium with small spatial and temporal fluctuations of its mean velocity, and constant density and speed of sound. We develop a multi-scale perturbative analysis for the acoustic pressure field transmitted by the layer and derive its power spectral density when the correlation function of the velocity fluctuations is known. Our aim is to compare the proposed analytical model with some experimental results obtained for jet flows in open wind tunnels. We start with the Euler equations for an ideal fluid flow and linearize them about an ambient, unsteady inhomogeneous flow. We study the transmitted pressure field without fluctuations of the ambient flow velocity to obtain the Green's function of the unperturbed medium with constant characteristics. Then we use a Lippmann-Schwinger equation to derive an analytical expression of the transmitted pressure field, as a function of the velocity fluctuations within the layer. Its power spectral density is subsequently computed invoking a stationary-phase argument, assuming in addition that the source is time-harmonic and the layer is thin. We finally study the influence of the source tone frequency and ambient flow velocity on the power spectral density of the transmitted pressure field and compare our results with other analytical models and experimental data.
A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble simulations of high dimensional equations is effectively avoided by adopting a random batch decomposition of the wide spectrum of the fluctuation states which is a characteristic feature of the multiscale turbulent systems. The time update of each ensemble sample is then only subject to a small portion of the small-scale fluctuation modes in one batch, while th…
Cascades of turbulent kinetic energy and multicomponent scalars in a momentum-scalar coupling turbulence driven by multiscale forces under homogeneous and isotropic hypotheses
Turbulence remains an unsolved multidisciplinary science problem. As one of the most well-known examples in turbulent flows, knowledge of the logarithmic mean velocity profile (MVP), so called the log law of the wall, plays an important role everywhere turbulent flow meets the solid wall, such as fluids in any kind of channels, skin friction of all types of transportations, the atmospheric wind on a planetary ground, and the oceanic current on the seabed. However, the mechanism of how this log-law MVP is formed under the multiscale nature of turbulent shears remains one of the greatest interes…
The invariants of the velocity gradient tensor, $R$ and $Q$, and their enstrophy and strain components are studied in the logarithmic layer of an incompressible turbulent channel flow. The velocities are filtered in the three spatial directions and the results analyzed at different scales. We show that the $R$--$Q$ plane does not capture the changes undergone by the flow as the filter width increases, and that the enstrophy/enstrophy-production and strain/strain-production planes represent better choices. We also show that the conditional mean trajectories may differ significantly from the ins…
The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric f…
We use high resolution direct numerical simulations to study the anisotropic contents of a turbulent, statistically homogeneous flow with random transitions among multiple energy containing states. We decompose the velocity correlation functions on different sectors of the three dimensional group of rotations, SO(3), using a high-precision quadrature. Scaling properties of anisotropic components of longitudinal and transverse velocity fluctuations are accurately measured at changing Reynolds numbers. We show that independently of the anisotropic content of the energy containing eddies, small-s…
The deformation and dynamics of a single droplet in isotropic turbulence is studied using a Lattice Boltzmann diffuse interface model involving exact boundary flow conditions to allow for the creation of an external turbulent flow. We focus on a small, sub-Kolmogorov droplet, whose scale is much smaller than the Kolmogorov length scale of the turbulent flow. The external flow field is obtained via pseudo-spectral simulation data describing the trajectory of a passive tracer in isotropic turbulence. In this way we combine the microscopic scale of the droplet and the macroscopic scale of the tur…
Capturing multiscale interactions in fluid flow via Lagrangian coherent structures and modal analysis
University of Southern California（南加州大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of California, Los Angeles（加州大学洛杉矶分校）；Stanford University（斯坦福大学）；University of Washington（华盛顿大学）
The properties of bubble-laden turbulent flows at different scales are investigated experimentally, focusing on the flow kinetic energy, energy transfer, and extreme events. The experiments employed particle shadow velocimetry measurements to measure the flow in a column generated by a homogeneous bubble swarm rising in water, for two different bubble diameters ($2.7$ mm $\&$ $3.9$ mm) and moderate gas volume fractions ($0.26\%\sim1.31\%$). The two velocity components were measured at high-resolution, and used to construct structure functions up to twelfth order for separations spanning the sm…
A term-by-term variational multiscale method with dynamic subscales for incompressible turbulent aerodynamics
Computational Heat and Fluid Flow Lab, Universidad de Santiago de Chile（圣地亚哥智利大学计算热与流体流动实验室）；Department of Mechanical Engineering, University of Santiago de Chile（圣地亚哥智利大学机械工程系）；Chair for Computational Analysis of Technical Systems, RWTH Aachen University（亚琛工业大学技术系统计算分析教席）；Chair of Methods for Model-based Development in Computational Engineering, RWTH（亚琛工业大学计算工程基于模型开发方法教席）；Center for Simulation and Data Science (JARA-CSD), RWTH Aachen University（亚琛工业大学仿真与数据科学中心（JARA-CSD））
After decades of experimental, theoretical, and numerical research in fluid dynamics, many aspects of turbulence remain poorly understood. The main reason for this is often attributed to the multiscale nature of turbulent flows, which poses a formidable challenge. There are, however, properties of these flows whose roles and inter-connections have never been clarified fully. In this article, we present a new connection between the pressure drop, viscous dissipation, and the turbulent energy spectrum, which, to the best of our knowledge, has never been established prior to our work. We use this…
We present a wavelet-based adaptive method for computing 3D multiscale flows in complex, time-dependent geometries, implemented on massively parallel computers. While our focus is on simulations of flapping insects, it can be used for other flow problems, including turbulence, as well. The incompressible fluid is modeled with an artificial compressibility approach in order to avoid solving elliptical problems. No-slip and in/outflow boundary conditions are imposed using volume penalization. The governing equations are discretized on a locally uniform Cartesian grid with centered finite differe…
The small-scale statistical properties of velocity circulation in classical homogeneous and isotropic turbulent flows are assessed through a modeling framework that brings together the multiplicative cascade and the structural descriptions of turbulence. We find that vortex structures exhibit short-distance repulsive correlations, which is evidenced when they are "tomographically" investigated, by means of planar cuts of the flow, as two-dimensional vortex gases. This phenomenon is suggested from model improvements which allow us to obtain an accurate multiscale description of the intermittent…
In a seminal article, \citet[J. Fluid Mech., 174:441-465]{maxey87} presented a theoretical analysis showing that enhanced particle settling speeds in turbulence occur through the preferential sweeping mechanism, which depends on the preferential sampling of the fluid velocity gradient field by the inertial particles. However, recent Direct Numerical Simulation (DNS) results in \citet[J. Fluid Mech., 796:659--711]{ireland16b} show that even in a portion of the parameter space where this preferential sampling is absent, the particles nevertheless exhibit enhanced settling velocities. Further, th…
This study presents a deep learning-based framework to reconstruct high-resolution turbulent velocity fields from extremely low-resolution data at various Reynolds numbers using the concept of generative adversarial networks (GANs). A multiscale enhanced super-resolution generative adversarial network (MS-ESRGAN) is applied as a model to reconstruct the high-resolution velocity fields, and direct numerical simulation (DNS) data of turbulent channel flow with large longitudinal ribs at various Reynolds numbers are used to evaluate the performance of the model. The model is found to have the cap…
An iterface structure between turbulence and laminar flow is investigated in two-dimensional channel flow. This spatially localized structure not only sustains itself, but also converts laminar state into turbulence actively. In other words, this coherent structure has a functionality to generate inhomogeneity by its inner dynamics. The dynamics of this functional coherent structure is isolated using the filtered simulation, and a physical perspective of its dynamics is summarized in a phenomenological model called an "ejection-jet" cycle, which includes multiscale interaction process.
High-fidelity Three-Dimensional Flow Field Reconstruction Driven by Turbulent Fluid Dynamics
State Key Lab of Brain-Machine Intelligence, Zhejiang University（浙江大学脑机智能全国重点实验室）；Shanghai Innovation Institute（上海创新研究院）；Zhejiang Key Laboratory of Industrial Intelligence and Digital Twin, Eastern Institute of Technology（东方理工工程学院工业智能与数字孪生浙江省重点实验室）；Zhejiang Sci-Tech University（浙江理工大学）
We compare different approaches towards an effective description of multi-scale velocity field correlations in turbulence. Predictions made by the operator product expansion, the so-called fusion rules, are placed in juxtaposition to an approach that interprets the turbulent energy cascade in terms of a Markov process of velocity increments in scale. We explicitly show that the fusion rules are a direct consequence of the Markov property provided that the structure functions exhibit scaling in the inertial range. Furthermore, the limit case of joint velocity gradient and velocity increment sta…
Anisotropy and multifractality in velocity and temperature time series sampled at multiple heights in the roughness sublayer (RSL) over a boreal mixed-coniferous forest are reported. In particular, a turbulent-stress invariant analysis along with a scalewise version of it are conducted to elucidate the nature of relaxation of large-scale anisotropy to quasi-isotropic states at small scales. As the return to isotropy is linked to nonlinear interactions and correlations between different fluctuating velocity components across scales, we study the velocity and temperature time series by using mul…
One of the more promising recent approaches to turbulence modelling is the Variational Multiscale Large Eddy Simulation (VMS LES) method proposed by Hughes et al. [Comp. Visual. Sci., vol. 3, pp. 47-59, 2000]. This method avoids several conceptual issues of traditional filter-based LES by employing a priori scale partitioning in the discretization of the Navier-Stokes equations. Most applications of VMS LES reported to date have been based on hierarchical bases, in particular global spectral methods, in which scale partitioning is straightforward. In the present work we describe the implementa…
This study proposes a newly-developed deep-learning-based method to generate turbulent inflow conditions for spatially-developing turbulent boundary layer (TBL) simulations. A combination of a transformer and a multiscale-enhanced super-resolution generative adversarial network is utilized to predict velocity fields of a spatially-developing TBL at various planes normal to the streamwise direction. Datasets of direct numerical simulation (DNS) of flat plate flow spanning a momentum thickness-based Reynolds number, Re_theta = 661.5 - 1502.0, are used to train and test the model. The model shows…
We highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length-scales larger than $\ell$ by smaller scale (subscale) turbulence. %subscale flux/stress which appear in the evolution of coarse-grained (resolved) scalars/momentum account for the effect of (subgrid) scales smaller than the coarse-graining length $\ell$. We use the first term in a multiscale gradient expansion due to Eyink \cite{Eyink06a}, which exhibits excellent correlation with the exact subscale physics when the partitioning length $\ell$ is any scale smaller than that of the spect…
A series of Direct Numerical Simulations (DNS) of lean methane/air flames was conducted in order to investigate the enhancement of the turbulent flame speed and modifications to the reaction layer structure associated with the systematic increase of the integral scale of turbulence $l$ while the Karlovitz number and the Kolmogorov scale are kept constant. Four turbulent slot jet flames are simulated at increasing Reynolds number and up to $Re \approx 22000$, defined based on the bulk velocity, slot width, and the reactants' properties. The turbulent flame speed $S_T$ is evaluated locally at se…
We have experimentally quantified the temporal structural diversity from the coordinate fluctuations of a laser beam propagating through isotropic optical turbulence. The main focus here is on the characterization of the long-range correlations in the wandering of a thin Gaussian laser beam over a screen after propagating through a turbulent medium. To fulfill this goal, a laboratory-controlled experiment was conducted in which coordinate fluctuations of the laser beam were recorded at a sufficiently high sampling rate for a wide range of turbulent conditions. Horizontal and vertical displacem…
We study the experimental properties of exchange flows in a stratified inclined duct (SID), which are simultaneously turbulent, strongly stratified by a mean vertical density gradient, driven by a mean vertical shear, and continuously forced by gravity. We focus on the core shear layer away from the duct walls, where these flows are excellent experimentally-realisable approximations of canonical hyperbolic-tangent stratified shear layers, whose forcing allows mean and turbulent properties to reach quasi steady states. We analyse state-of-the-art data sets of the time-resolved density and veloc…
A new computational framework for the simulation of turbulent flow through complex objects and along irregular boundaries is presented. This is motivated by the application of metal foams in compact heat-transfer devices, or as catalyst substrates in process-engineering. The flow-consequences of such complicated objects are incorporated by adding explicit multiscale forcing to the Navier-Stokes equations. The forcing represents the simultaneous agitation of a wide spectrum of length-scales when flow passes through the complex object. It is found that a considerable modulation of the traditiona…
For one-way coupled (1WC) flows, Tom & Bragg (J. Fluid Mech., 871, pp. 244-270, 2019) advanced the analysis of Maxey (J. Fluid Mech., 174, pp. 441-465, 1987), which applied to weakly inertial particles, to particles of arbitrary inertia, and the new theoretical result revealed the role that different scales play in the preferential sweeping mechanism that leads to enhanced particle settling in turbulent flows. Monchaux & Dejoan (Phys. Rev. Fluids, 2, 104302, 2017) showed using direct numerical simulations (DNS) that while for low particle loading the effect of two-way coupling (2WC) on the glo…
Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows
Centre for Computational Science, University College London, London, UK；Department of Earth Science；Engineering, Imperial College London, London, UK；Department of Chemical Engineering, University College London, London, UK；Department of Physics, Eindhoven University of Technology, Eindhoven, Netherlands；School of Civil \& Environmental Engineering, Queensland University of Technology, Brisbane, Australia；Australian Centre for Water；Environmental Biotechnology, The University of Queensland, Brisbane, Australia；Institute for Mechanics, Computational Mechanics Group, Technical University of Darmstadt, Germany；Centre for Advanced Research Computing, University College London, London, UK
We assess the ability of three different approaches based on high-order discontinuous Galerkin methods to simulate under-resolved turbulent flows. The capabilities of the mass conserving mixed stress method as structure resolving large eddy simulation solver are examined. A comparison of a variational multiscale model to no-model or an implicit model approach is presented via numerical results. In addition, we present a novel approach for turbulent modeling in wall-bounded flows. This new technique provides a more accurate representation of the actual subgrid scales in the near wall region and…
In this paper, we investigate the hemodynamics of a left atrium (LA) by proposing a computational model suitable to provide physically meaningful fluid dynamics indications and detailed blood flow characterization. In particular, we consider the incompressible Navier-Stokes equations in Arbitrary Lagrangian Eulerian (ALE) formulation to deal with the LA domain under prescribed motion. A Variational Multiscale (VMS) method is adopted to obtain a stable formulation of the Navier-Stokes equations discretized by means of the Finite Element method and to account for turbulence modeling based on Lar…
Superstatistical Approach to Turbulent Circulation Fluctuations
Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）；Instituto de Física, Universidade Federal do Rio de Janeiro（里约热内卢联邦大学物理研究所）；Department of Mechanical and Aerospace Engineering, New York University（纽约大学机械与航空航天工程系）；Department of Physics and Courant Institute of Mathematical Sciences, New York University（纽约大学物理系与库朗数学科学研究所）；Santa Fe Institute（圣塔菲研究所）；Complexity Science Hub Vienna（维也纳复杂性科学中心）；Dipartimento di Fisica e Astronomia Ettore Majorana, University of Catania（卡塔尼亚大学埃托雷·马约拉纳物理与天文学系）
