ETC2019 17th European Turbulence Conference Submission

16:15 Numerical Methods and Data Analysis 2

16:15 15 mins #470	TURBULENCE MODELING USING ARTIFICIAL NEURAL NETWORK Yuji Yuji Hattori, Satoshi Miyazaki Abstract: Large-eddy simulation (LES) is an important tool of numerical simulation in a wide variety of fields where turbulent flows appear. In LES the effects of the fluctuations of unresolved scales on the resolved-scale flow field appear as the residual or SGS stress tensor which should be modeled. Although a number of subgrid models have been proposed since the Smagorinsky model, a new subgrid model which is much better than the existing ones is still wanted. In order to pursue such a subgrid model essentially new ideas of modeling would be required; however, there has been no such idea since the prototypes of the existing models were proposed about four or five decades ago. In our previous work [1] we used artificial neural network (ANN) to construct a subgrid model using DNS (direct numerical simulation) data of a turbulent channel flow; it has been shown that ANN works in principle; however, the accuracy was limited for rather small filter width. In this paper, we seek how to improve the performance of ANN and thereby to construct a better subgrid model. We use DNS data of homogeneous isotropic turbulence instead of turbulent channel flow to train and test ANN; the SGS stress obtained by filtering DNS data is used in training and a priori test. The model established by ANN is also applied to LES calculation (a posteriori test). A priori test showed that ANN succeeded in estimating SGS stress in isotropic homogeneous turbulence (figure 1). The performance of ANN has been improved by a sampling method which takes account of the intermittency of the data. It was also improved by adding the second-order derivatives of the velocity to the set of input variables which is originally composed of the first-order derivatives. This result suggests that the model established by ANN is similar to the gradient model and its extension [2]. In fact, the correlation between the ANN model and the gradient model is higher than the correlation between the ANN model and the correct SGS stress. The gradient model has better correlation with the correct SGS stress than the ANN model; however, the ANN model has smaller error than the gradient model. In a posteriori test, like the gradient model, the ANN model turned out to be numerically unstable; it has to be stabilized. The stabilization is achieved by prohibiting backscatter or the energy transfer from the unresolved scale to the resolved scale. The stabilized ANN model was used to simulate homogeneous isotropic turbulence and the evolution of the threedimensional Taylor Green vortex. The results are compared to the Smagorinsky model, the Bardina model and filtered DNS. The flow obtained by the ANN model is in good agreement with filtered DNS results. References [1] M. Gamahara and Y. Hattori. Searching for turbulence models by artificial neural network. Phys. Rev. Fluids 2: 054694, 2017. [2] W. Yeo. Ph.D thesis Ohio State Univ., 1987 etc.
16:30 15 mins #537	Predictions of turbulent shear flows by neural networks and application to off-wall boundary conditions Luca Guastoni, Prem Anand Srinivasan, Hossein Azizpour, Philipp Schlatter, Ricardo Vinuesa Abstract: In the present work we assess the capabilities of neural networks to predict temporally evolving turbulent flows. In particular, we use the nine-equation shear flow model by Moehlis et al. (2004) to generate training data for two types of neural networks: the multilayer perceptron (MLP) and the long short-term memory (LSTM) network. We tested a number of neural network architectures by varying the number of layers, number of units per layer, dimension of the input, weight initialization and activation functions in order to obtain the best configurations for flow prediction. Due to its ability to exploit the sequential nature of the data, the LSTM network outperformed the MLP. The LSTM led to excellent predictions of turbulence statistics (with relative errors of 0.45% and 2.49% in mean and fluctuations, respectively) and of the dynamical behaviour of the system (characterized by Poincaré maps and Lyapunov exponents). The proposed machine-learning framework lays the foundation for future applications, in particular the generation of off-wall boundary conditions for wall-bounded turbulence simulations. The LSTM network, combined with other types of neural network, can be trained to predict, based on data from the outer region, a two-dimensional velocity field, to be used as an off-wall boundary condition for the flow.
16:45 15 mins #630	From Deep to Physics-Informed Learning of Turbulence: Diagnostics Michael Chertkov, Arvind Mohan Abstract: We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of turbulence. Even the bare DL solutions, which do not take into account any physics of turbulence explicitly, are impressively good overall when it comes to qualitative description of important features of turbulence. However, the early tests have also uncovered some caveats of the DL approaches. We observe that DL schemes trained on spatial snapshots of turbulence, fails to reproduce intermittency of turbulent fluctuations at small scales and details of the turbulence geometry at large scales. We show that dynamic NN schemes trained on a temporal sequence of turbulence snapshots are capable to correct for the caveats of the static NN. We suggest a path forward towards improving reproducibility of the large-scale geometry of turbulence with NN. This presentation extends our earlier results reported in https://arxiv.org/abs/1810.07785 .
17:00 15 mins #62	Can Artificial Neural Networks trained through Deep Reinforcement Learning become a tool in Active Flow Control and Turbulence? Jean Rabault, Miroslav Kuchta, Alexander Kuhnle, Atle Jensen, Bernd R. Noack Abstract: The non-linearity, high dimensionality, and time dependence implied by the Navier-Stockes equations make them a particularly difficult problem. The resulting complexity is hardly tamed [1], either the aim is to perform simulations [4] or to control flow dynamics at intermediate to high Reynolds numbers [1]. One can argue that similar challenges are observed across many research fields which aim at studying complex problems presenting the same ingredients of non-linearity and high dimensionality. A notable citation on the difficulty of such problems comes from Stephen Hawking, who said to believe that ’the next century will be the century of complexity’ [2]. However, several breakthroughs were recently achieved in other fields of research where complexity is present, with the success of AlphaGo winning against the world champion at the game of Go being probably the most famous example [5]. Therefore, it is natural to investigate the applicability of the same methods used for these breakthroughs (namely, Artificial Neural Networks (ANNs) and Deep Reinforcement Learning (DRL)), also on the complexity arising from the Navier- Stockes equations. A first illustration of the applicability of ANNs/DRL for Active Flow Control was recently presented in the literature [3], see Fig. 1 for an illustration. However, the corresponding work focuses on a simple flow, more specifically the control of 2D vortex shedding at moderate Reynolds number. This is far from reaching the level of complexity observed in turbulent flows. Following these results, new work has been performed on several models of PDEs recognized as a benchmark for control algorithms [1] that reproduce some of the ingredients at the heart of turbulence, namely exponential modal growth and cross talks. Results are there also conclusive, and indicate that ANNs/DRL can control systems with weak, non-linear cross talks where some traditional methods based on linearization of the system fail. In the present talk, we will start by offering an overview of the ANN/DRL field of research and presenting the results achieved in Active Flow Control on the simple vortex shedding system. Then, we will focus on the results obtained recently on the more challenging PDE systems and we will discuss why, and to which extent, these results indicate that ANNs/DRL are a promising tool to further investigate also for the control of fully turbulent systems. References [1] Thomas Duriez, Steven L Brunton, and Bernd R Noack. Machine Learning Control-Taming Nonlinear Dynamics and Turbulence. Springer, 2017. [2] Stephen Hawking. What is complexity? http://www.complexsys.org/downloads/whatiscomplexity.pdf, accessed 01.18.2019. [3] Jean Rabault, Miroslav Kuchta, Atle Jensen, Ulysse Reglade, and Nicolas Cerardi. Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. arXiv preprint arXiv:1808.07664, accepted for publication, JFM, 2018. [4] Robert S Rogallo and Parviz Moin. Numerical simulation of turbulent flows. Annual review of fluid mechanics, 16(1):99–137, 1984. [5] David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, Arthur Guez, Thomas Hubert, Lucas Baker, Matthew Lai, Adrian Bolton, et al. Mastering the game of go without human knowledge. Nature, 550(7676):354, 2017. Figure 1. Snapshot of the velocity field in the baseline case (no actuation, top) and with active flow control (bottom) obtained in [3]. The wake configuration is clearly changed by the active control, resulting in reduced drag. In the current presentation, we will discuss how this simple control example can be extended to turbulent flows.
17:15 15 mins #157	Optimal sub-grid-scale models for inertial range turbulence Michele Buzzicotti, Luca Biferale, Fabio Bonaccorso, Kartik Iyer Abstract: A class of spectral sub-grid models based on a purely self-similar and reversible closure is studied with the aim to minimize the impact of dissipative effects on the inertial range scaling properties of fully developed turbulence. In this manner we improve the inertial range extension where anomalous scaling is observed by roughly one order of magnitude, when compared to direct numerical simulations or other popular sub-grid closures at comparable resolutions [1]. As a result, the computational effort required to achieve the same accuracy of a direct numerical simulation decreases by three orders of magnitude. In Fig.1 we compare the energy spectra of the modelled simulations on a grid of 1024^3 collocation points with the energy spectra of fully resolved simulations with a resolution up to 8192^3 collocation points [2]. Aside from the unprecedented improvement in the scaling properties, our study contributes to clarify the robustness of the inertial range with respect to small-scale closures and opens the way to apply similar protocols to many other turbulent systems, e.g. in stratified media, under rotation, along the homogeneous directions in bounded domains or even for notoriously stiff problems as the kinematic dynamo in the limit of small Prandtl numbers.
17:30 15 mins #571	Wavelet-Convolutional LSTM: An Efficient Deep Learning Paradigm for High Fidelity Turbulence Arvind Mohan, Don Daniel, Daniel Livescu, Michael Chertkov Abstract: High fidelity simulation of turbulence with DNS/LES presents many challenges for real-world flows due to their prohibitive computing costs. Recently, deep learning based approaches such as Convolutional LSTM (ConvLSTM) neural networks have shown considerable promise in modeling 2D spatio-temporal datasets for weather and medical imaging applications. The authors recently proposed a variant of this method Compressed ConvLSTM (CC-LSTM) [1] to model 3D turbulence, which is orders of magnitude cheaper than DNS. In this work, we propose a novel paradigm called wavelet-ConvLSTM, where the complementary strengths of wavelet transforms and ConvLSTM are leveraged to learn dynamics of 3D homogeneous isotropic turbulence at a much lower cost than current high dimensional deep learning approaches. The accuracy of predicted flow from the wavelet-ConvLSTM model is analyzed in the Figure at three different eddy turnover times by computing a) Energy spectra with 5/3 law comparison, b) PDF of velocity gradient and c) Normalized Q-R plane dynamics of a local Lagrangian velocity-gradient volume, coarse grained by a scale 'r'. This allows us to study dynamics of various scales individually, and r=0,8,32 are chosen here to delineate small, inertial and large scales respectively [2]. The results show excellent and nearly identical agreement in large and inertial scales of turbulence, with some errors occurring in the small scales that can be minimized by suitable wavelet thresholding [3]. Results indicate that wavelet-ConvLSTM predicts stable, long-term temporal realizations and is an order of magnitude faster compared to primitive flow variables in CC-LSTM, due to the superior entropy/information gain in wavelet bases. Its adaptive, low dimensional nature leads to comparatively scarce memory utilization for wavelet thresholding, enabling higher resolution models to be built at lower cost. Finally, we show the strengths of wavelet-ConvLSTM to model a variety of turbulent flows with data sizes ranging from 128^3 to 1024^3, with the eventual goal of modeling real-world flows. [1] R. King, O. Hennigh, A.T. Mohan, and M. Chertkov. From deep to physics-informed learning of turbulence: Diagnostics. arXiv:1810.07785, 2018. [2] M. Chertkov, A. Pumir, and B. Shraiman. Lagrangian tetrad dynamics and the phenomenology of turbulence. Phy. Fluids, 11(8):2394–2410, 1999. [3] J. Pulido, D. Livescu, J. Woodring, J. Ahrens, and B. Hamann. Survey and analysis of multiresolution methods for turbulence data. Comput. Fluids, 125:39–58, 2016.
17:45 15 mins #155	Data-driven investigations of scale interactions in turbulent flows Nikki Vercauteren, Thomas von Larcher, Abhishek Paraswarar Harikrishnan, Johannes von Lindheim, Gitta Kutyniok, Rupert Klein Abstract: The most established phenomenological characterisation of turbulent flows is that of a cascading process which transfers energy from large to small scales in a self-similar manner. In wall-bounded flows, turbulence structures are strongly distorted near confining walls, and in stably stratified atmospheric boundary layers (ABL), turbulence additionally coexists with internal waves and large-scale quasi two-dimensional flow structures. Such near-wall effects and the influence of additional physical processes influences the way in which the small and large scales interact, e.g., by causing global intermittency of turbulence. In this study we determine the associated regime changes of scale interactions using advanced multiscale data analysis techniques. Specifically, we seek to characterise local and non-local scale interactions in Direct Numerical Simulation (DNS) data and in data from atmospheric turbulence measurements under stably stratified conditions. Based on non-stationary timeseries analysis methods, multiple regimes of scale interactions are clustered in the different datasets and their specifics are subsequently identified. In direct simulation data of turbulent channel flow, we detect different regimes of how small unresolved scales affect the larger scales. At sufficiently high resolution, a clustering algorithm [1] identifies three distinct regimes associated with the channel core, the near-wall layer(s), and with an intermediate transition zone between the two. We demonstrate that data from a discrete stencil of coarse-grained cells comparable to those utilised in large eddy simulations suffice to essentially determine the full turbulent fluxes across a cell face in the center of the stencil. The weights associated with the stencil entries turn out to depend on the core-, transition-, and near-wall-regimes. In stably stratified atmospheric flows we detect, by similar methods, regimes in which large-scale wave-like velocity fluctuations modulate the intensity of local turbulence and find signs of a direct energy transfer between wave-like motions and turbulence. We find that regimes with modulation of the turbulence by wave-like motions are characterised by highly anisotropic Reynolds stresses. Our next goal is to achieve a data-driven characterisation of turbulent structures in DNS datasets, focusing in particular on the spatial structure of turbulent eddies. We present preliminary results using shearlet decompositions to detect anisotropic structures in DNS datasets. Shearlets are closely related to wavelets and curvelets. They differ from wavelets in that they allow multiscale resolution in arbitrary, grid-independent directions – a feature that is important for capturing, e.g., meandering vortices in a turbulent flow. The automatic extraction method is a first step to a detailed geometrical characterisation of turbulent structures and will enable quantitative characterisations of self-similar and intermittent turbulent structures. References [1] von Larcher Th., Beck A., Klein R., Horenko I., Metzner Ph., Waidmann M., Igdalov D., Gassner G., Munz C.-D., A framework for the stochastic modelling of subgrid scale fluxes for large eddy simulation, Met. Zeitschr., 24, 313-342 (2015)
18:00 15 mins #76	INFERRING PHYSICAL PARAMETERS IN TURBULENCE: FROM NUDGING TO MACHINE LEARNING Luca Biferale, Michele Buzzicotti, Fabio Bonaccorso, Patricio Clark di Leoni Abstract: Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling and astrophysics. We adopt here two different protocols, one based on the Nudging of the equations of motion and the second on a supervised Machine Learning (ML) approach to classify turbulent configurations. Nudging is a general data-driven algorithm to learn from sparse measurements in a dynamical way and with a broad range of applications. The idea is to use the Navier Stokes equations with a Newton relaxation feedback term, which imposes a linear reward/penalisation depending if the evolved hydrodynamical fields are close/far from the data to be assimilated. ML is equation-free and based on the idea that a complex enough Artificial Neural Network is able to learn the basic statistical observables that discriminate among different turbulent configurations. We discuss both methods for the case of turbulence under rotation, and we show that in both cases we are able to infer the rotation intensity of the ﬂow ﬁeld, with different degrees of success and accuracy.