1,720,990 research outputs found
Inertial range statistics of the entropic lattice Boltzmann method in three-dimensional turbulence
No full textWe present a quantitative analysis of the inertial range statistics produced by entropic lattice Boltzmann method (ELBM) in the context of three-dimensional homogeneous and isotropic turbulence. ELBM is a promising mesoscopic model particularly interesting for the study of fully developed turbulent flows because of its intrinsic scalability and its unconditional stability. In the hydrodynamic limit, the ELBM is equivalent to the Navier-Stokes equations with an extra eddy viscosity term. From this macroscopic formulation, we have derived a new hydrodynamical model that can be implemented as a large-eddy simulation closure. This model is not positive definite, hence, able to reproduce backscatter events of energy transferred from the subgrid to the resolved scales. A statistical comparison of both mesoscopic and macroscopic entropic models based on the ELBM approach is presented and validated against fully resolved direct numerical simulations. Besides, we provide a second comparison of the ELBM with respect to the well-known Smagorinsky closure. We found that ELBM is able to extend the energy spectrum scaling range preserving at the same time the simulation stability. Concerning the statistics of higher order, inertial range observables, ELBM accuracy is shown to be comparable with other approaches such as Smagorinsky model
Inferring turbulent environments via machine learning
No full textThe problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g., to precondition searching of optimal control policies in different turbulent backgrounds, to predict the probability of rare events and/or to infer physical parameters labeling different turbulent setups. To achieve such goal one can use different tools depending on the system’s knowledge and on the quality and quantity of the accessible data. In this context, we assume to work in a model-free setup completely blind to all dynamical laws, but with a large quantity of (good quality) data for training. As a prototype of complex flows with different attractors, and different multi-scale statistical properties we selected 10 turbulent ‘ensembles’ by changing the rotation frequency of the frame of reference of the 3d domain and we suppose to have access to a set of partial observations limited to the instantaneous kinetic energy distribution in a 2d plane, as it is often the case in geophysics and astrophysics. We compare results obtained by a machine learning (ML) approach consisting of a state-of-the-art deep convolutional neural network (DCNN) against Bayesian inference which exploits the information on velocity and entropy moments. First, we discuss the supremacy of the ML approach, presenting also results at changing the number of training data and of the hyper-parameters. Second, we present an ablation study on the input data aimed to perform a ranking on the importance of the flow features used by the DCNN, helping to identify the main physical contents used by the classifier. Finally, we discuss the main limitations of such data-driven methods and potential interesting applications
From two-dimensional to three-dimensional turbulence through two-dimensional three-component flows
Full text linkThe relevance of two-dimensional three-components (2D3C) flows goes well beyond their occurrence in nature, and a deeper understanding of their dynamics might be also helpful in order to shed further light on the dynamics of pure two-dimenional (2D) or three-dimensional (3D) flows and vice versa. The purpose of the present paper is to make a step in this direction through a combination of numerical and analytical work. The analytical part is mainly concerned with the behavior of 2D3C flows in isolation and the connection between the geometry of the nonlinear interactions and the resulting energy transfer directions. Special emphasis is given to the role of helicity. We show that a generic 2D3C flow can be described by two stream functions corresponding to the two helical sectors of the velocity field. The projection onto one helical sector (homochiral flow) leads to a full 3D constraint and to the inviscid conservation of the total (three dimensional) enstrophy and hence to an inverse cascade of the kinetic energy of the third component also. The coupling between several 2D3C flows is studied through a set of suitably designed direct numerical simulations (DNS), where we also explore the transition between 2D and fully 3D turbulence. In particular, we find that the coupling of three 2D3C flows on mutually orthogonal planes subject to small- scale forcing leads to stationary 3D out-of-equilibrium dynamics at the energy containing scales. The transition between 2D and 3D turbulence is then explored through adding a percentage of fully 3D Fourier modes in the volume
Multiscale properties of Large Eddy Simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities
Full text linkWe provide analytical and numerical results concerning multi-scale correlations be-tween the resolved velocity field and the subgrid-scale (SGS) stress-tensor in largeeddy simulations (LES). Following previous studies for Navier-Stokes equations(NSE), we derive the exact hierarchy of LES equations governing the spatio-temporalevolution of velocity structure functions of any order. The aim is to assess the influ-ence of the sub-grid model on the inertial range intermittency. We provide a seriesof predictions, within the multifractal theory, for the scaling of correlation involvingthe SGS stress and we compare them against numerical results from high-resolutionSmagorinsky LES and froma-priorifiltered data generated from direct numericalsimulations (DNS). We find that LES data generally agree very well with filteredDNS results and with the multifractal prediction for all leading terms in the balanceequations. Discrepancies are measured for some of the subleading terms involvingcross-correlation between resolved velocity increments and the SGS tensor or theSGS energy transfer, suggesting that there must be room to improve the SGS mod-elisation to further extend the inertial range properties for any fixed LES resoluti
Nonuniversal behaviour of helical two-dimensional three-component turbulence
Full text linkThe dynamics of two-dimensional three-component (2D3C) flows is relevant to describe the long-time evolution of strongly rotating flows and/or of conducting fluids with a strong mean magnetic field. We show that in the presence of a strong helical forcing, the out-of-plane component ceases to behave as a passive advected quantity and develops a nontrivial dynamics which deeply changes its large-scale properties. We show that a small-scale helicity injection correlates the input on the 2D component with the one on the out-of-plane component. As a result, the third component develops a nontrivial energy transfer. The latter is mediated by homochiral triads, confirming the strong 3D nature of the leading dynamical interactions. In conclusion, we show that the out-of-plane component in a 2D3C flow enjoys strong nonuniversal properties as a function of the degree of mirror symmetry of the small-scale forcing
A-priori study of the subgrid energy transfers for small-scale dynamo in kinematic and saturation regimes
Full text linkThe statistical properties of the subgrid energy transfers of homogeneous small-scale dynamo areinvestigated during the kinematic, nonlinear and statistically saturated stages. We carry out ana priorianalysis of data obtained from an ensemble of direct numerical simulations on 5123gridpoints and at unity magnetic Prandtl number. In order to provide guidance for subgrid-scale (SGS)modelling of different types of energy transfer that occur in magnetohydrodynamic dynamos, weconsider the SGS stress tensors originating from inertial dynamics, Lorentz force and the magneticinduction separately. We find that all SGS energy transfers display some degree of intermittencyas quantified by the scale-dependence of their respective probability density functions. Concerningthe inertial dynamics, a depletion of intermittency occurs in presence of a saturated dyna
Synchronizing subgrid scale models of turbulence to data
No full textLarge eddy simulations of turbulent flows are powerful tools used in many engineering and geophysical settings. Choosing the right value of the free parameters for their subgrid scale models is a crucial task for which the current methods present several shortcomings. Using a technique called nudging, we show that large eddy simulations can synchronize with data coming from a high-resolution direct numerical simulation of homogeneous and isotropic turbulence. Furthermore, we found that the degree of synchronization is dependent on the value of the parameters of the subgrid scale models utilized, suggesting that nudging can be used as a way to select the best parameters for a model. For example, we show that for the Smagorinsky model, synchronization is optimal when its constant takes the usual value of 0.16. Analyzing synchronization dynamics puts the focus on reconstructing trajectories in phase space, contrary to traditional a posteriori tests of large eddy simulations where the statistics of the flows are compared. These results open up the possibility of utilizing non-statistical analysis in a posteriori tests of large eddy simulations
Reconstruction of turbulent data with deep generative models for semantic inpainting from TURB-Rot database
No full textWe study the applicability of tools developed by the computer vision community for feature learning and semantic image inpainting to perform data reconstruction of fluid turbulence configurations. The aim is twofold. First, we explore on a quantitative basis the capability of convolutional neural networks embedded in a deep generative adversarial model (deep-GAN) to generate missing data in turbulence, a paradigmatic high dimensional chaotic system. In particular, we investigate their use in reconstructing two-dimensional damaged snapshots extracted from a large database of numerical configurations of three-dimensional turbulence in the presence of rotation, a case with multiscale random features where both large-scale organized structures and small-scale highly intermittent and non-Gaussian fluctuations are present. Second, following a reverse engineering approach, we aim to rank the input flow properties (features) in terms of their qualitative and quantitative importance to obtain a better set of reconstructed fields. We present two approaches both based on context encoders. The first one infers the missing data via a minimization of the L z pixel-wise reconstruction loss, plus a small adversarial penalization. The second, searches for the closest encoding of the corrupted flow configuration from a previously trained generator. Finally, we present a comparison with a different data assimilation tool, based on Nudging, an equation-informed unbiased protocol, well known in the numerical weather prediction community. The TURB-Rot database of roughly 300 K two-dimensional turbulent images is released and details on how to download it are given
Global cascade of kinetic energy in the ocean and the atmospheric imprint
No full textHere, we present an estimate for the ocean's global scale transfer of kinetic energy (KE), across scales from 10 to 40,000 km. Oceanic KE transfer between gyre scales and mesoscales is induced by the atmosphere’s Hadley, Ferrel, and polar cells, and the intertropical convergence zone induces an intense downscale KE transfer. Upscale transfer peaks at 300 gigawatts across mesoscales of 120 km in size, roughly one-third the energy input by winds into the oceanic general circulation. Nearly three quarters of this “cascade” occurs south of 15°S and penetrates almost the entire water column. The mesoscale cascade has a self-similar seasonal cycle with characteristic lag time of ≈27 days per octave of length scales; transfer across 50 km peaks in spring, while transfer across 500 km peaks in summer. KE of those mesoscales follows the same cycle but peaks ≈40 days after the peak cascade, suggesting that energy transferred across a scale is primarily deposited at a scale four times larger
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