As the Reynolds number is increased, a laminar fluid flow becomes turbulent, and the range of time and length scales associated with the flow increases. Yet, in a turbulent reactive flow system, as we increase the Reynolds number, we observe the emergence of a single dominant time scale in the acoustic pressure fluctuations, as indicated by its loss of multifractality. Such emergence of order from chaos is intriguing and has hardly been studied. We perform experiments in a turbulent reactive flow system consisting of flame, acoustic, and hydrodynamic subsystems interacting nonlinearly. We study the evolution of short-time correlated dynamics between the acoustic field and the flame in the spatiotemporal domain of the system. The order parameter, defined as the fraction of the correlated dynamics, increases gradually from zero to one. We find that the susceptibility of the order parameter, correlation length, and correlation time diverge at a critical point between chaos and order. Our results show that the observed emergence of order from chaos is a continuous phase transition. Moreover, we provide experimental evidence that the critical exponents characterizing this transition fall in the universality class of directed percolation. Our study demonstrates how a real-world complex, non-equilibrium turbulent reactive flow system exhibits universal behavior near a critical point.
Passive scalar mixing, produced by Lagrangian chaos generated a) by quasi-periodic (integrable) motion of three quasi-point vortices and b) by chaotic motion of three and six quasi-point vortices, has been studied and compared with turbulent mixing of passive scalar in 2D and 3D steady isotropic homogeneous turbulence and in turbulent wakes behind grid and behind cylinder. Results of numerical and laboratory experiments have been used and effective diffusivity approximation as well as distributed chaos approach have been applied to this problem.
Multiple chaotic and turbulent regimes in Rayleigh-Bénard convection have been studied and classified from the onset of deterministic chaos to the fully developed turbulence using the distributed chaos approach supported by results of laboratory experiments and numerical simulations. It is shown that the regimes can replace each other depending on value of the Rayleigh number and location in the convection cell (in the bulk of the flow or in the boundary layers). The inertial-buoyancy and helicity based invariants play crucial role in the formation of the regimes. Transition from the classical…
Spatio-temporal deterministic chaos at small Taylor-Reynolds numbers $Re_λ \lesssim 40$ and distributed chaos at turbulent $Re_λ \gtrsim 40$ in passive scalar dynamics have been studied using results of direct numerical simulations of homogeneous incompressible flows (with and without mean gradient of the passive scalar) for $8 \leq Re_λ < 700$ and of a reacting turbulent mixing layer. It is shown that the deterministic chaos in the passive scalar fluctuations at the small $Re_λ$ is characterized by exponential spatial (wavenumber) spectrum: $E(k) \propto \exp-(k/k_c)$, whereas the distributed…
Turbulence is still one of the main challenges for accurately predicting reactive flows. Therefore, the development of new turbulence closures which can be applied to combustion problems is essential. Data-driven modeling has become very popular in many fields over the last years as large, often extensively labeled, datasets became available and training of large neural networks became possible on GPUs speeding up the learning process tremendously. However, the successful application of deep neural networks in fluid dynamics, for example for subgrid modeling in the context of large-eddy simula…
A wind tunnel experiment is shown to examine the reproducibility of generated wind fields in the laboratory utilizing an active grid. A motion protocol of the grid, designed to mimic a measured atmospheric wind speed time series, is therefore repeated 50 times and the flow is measured by a 2D hotwire (x-wire) system. The acquired wind speed time series are analysed in two different ways to identify the reproducible time scales. A direct comparison using the cross covariance function combined with two filtering methods and a statistic approach using one and two point analysis. Like that the rep…
The spatio-temporal statistical structure of the turbulent dissipation field and its stochastic representation as a Gaussian Multiplicative Chaos
Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS, Laboratoire de Physique（里昂大学，巴黎高等师范学院里昂分校，克洛德·贝尔纳大学，法国国家科学研究中心，物理实验室）；CNRS, ICJ UMR5208, Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, Université Jean Monnet（法国国家科学研究中心，里昂中央理工学院，里昂国立应用科学学院，里昂克洛德·贝尔纳大学，让·莫内大学）
The statistical properties of species undergoing chemical reactions in a turbulent environment are studied. We focus on the case of reversible multi-component reactions of second and higher orders, in a condition close to chemical equilibrium sustained by random large-scale reactant sources, while the turbulent flow is highly developed. In such a state a competition exists between the chemical reaction that tends to dump reactant concentration fluctuations and enhance their correlation intensity and the turbulent mixing that on the contrary increases fluctuations and remove relative correlatio…
In this study we focus on the control of the dynamics of 3D turbulent wake downstream a square-back Ahmed body ($Re_H=3.9\times10^5$). The peculiar dynamics of such a wake are first characterized through the trajectories of the pressure barycenter over the rear part of the model as well as the recirculation barycenter in the wake. In particular it is shown that these dynamics allow the definition of three different states: the two so-called reflectional symmetry-breaking (RSB) modes and the transient symmetric (TS) mode. It was shown recently that the time-fluctuations of the pressure barycent…
Large eddy simulations with three-dimensional finite-volume Conditional Moment Closure (CMC) model are performed for a hydrogen / nitrogen lifted flame with detailed chemical meachanism. The emphasis is laid on the influences of mesh resolution and convection scheme of finite-volume CMC model on predictions of reactive scalar distribution and unsteady flame dynamics. The results show that the lift-off height is underestimated and the reactive scalars (e.g. temperature, H2 and OH) are over-predicted with coarser CMC mesh. It is also found that further refinement of the CMC mesh would not consid…
In pipes and channels, the onset of turbulence is initially dominated by localized transients, which lead to sustained turbulence through their collective dynamics. In the present work, we study the localized turbulence in pipe flow numerically and elucidate a state space structure that gives rise to transient chaos. Starting from the basin boundary separating laminar and turbulent flow, we identify transverse homoclinic orbits, the presence of which necessitates a homoclinic tangle and chaos. A direct consequence of the homoclinic tangle is the fractal nature of the laminar-turbulent boundary…
Extreme events that arise spontaneously in chaotic dynamical systems often have an adverse impact on the system or the surrounding environment. As such, their mitigation is highly desirable. Here, we introduce a novel control strategy for mitigating extreme events in a turbulent shear flow. The controller combines a probabilistic prediction of the extreme events with a deterministic actuator. The predictions are used to actuate the controller only when an extreme event is imminent. When actuated, the controller only acts on the degrees of freedom that are involved in the formation of the extre…
In order to better understand deviations from equilibrium in turbulent flows, it is meaningful to characterize the dynamics rather than the statistics of turbulence. To this end, the Lyapunov theory provides a useful description of turbulence through the study of the perturbation dynamics. In this work, the Lyapunov spectrum of forced homogeneous isotropic turbulent flows is computed. Using the Lyapunov exponents of a flow at different Reynolds numbers, the scaling of the dimension of the chaotic attractor for a three-dimensional homogeneous isotropic flow (HIT) is obtained for the first time …
Leveraging Scale Separation and Stochastic Closure for Data-Driven Prediction of Chaotic Dynamics
Sorbonne Université（索邦大学）；Institut Jean le Rond d’Alembert（让·勒朗·达朗贝尔研究所）；ISIR（智能机器人研究所）；SCAI（认知科学与人工智能中心）；Institut Universitaire de France（法国高等研究院）；M2N, Conservatoire National des Arts et Métiers（巴黎国立工艺学院）
Results of direct numerical simulations and laboratory experiments have been used in order to show that the buoyancy driven bubbly flows at high gas volume fraction are mixed by deterministic chaos with typical exponential spectrum of the liquid kinetic energy, whereas at moderate and small gas volume fraction it is a distributed chaos (turbulence or pseudo-turbulence) dominated by the third and second moments of helicity distribution with the stretched exponential spectra of the kinetic energy. Interaction of the bubbles with isotropic (behind an active grid) and near-wall turbulent flows has…
Contemporary paradigm of vascular hemodynamics considers normal blood flow to be pulsatile laminar flow. Transition to turbulence can cause diseases such as atherosclerosis or brain aneurysms. Recently, we demonstrated the existence of turbulence in experimental models of brain aneurysm; in the aneurysm sac as well as in the main artery. Thus, we were intrigued to explore if such a long-standing assumption of the laminarity of blood flow could be challenged. We have used methods and tools from chaos theory, hydrodynamic stability theory and turbulence physics to explore the existence of turbul…
We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, i…
The present work studies the non-linear dynamics of a shear layer, driven by a body force and confined between parallel walls, a simplified setting to study transitional and turbulent shear layers. It was introduced by Nogueira \& Cavalieri (J. Fluid Mech. 907, A32, 2021), and is here studied using a reduced-order model based on a Galerkin projection of the Navier-Stokes system. By considering a confined shear layer with free-slip boundary conditions on the walls, periodic boundary conditions in streamwise and spanwise directions may be used, simplifying the system and enabling the use of meth…
