Fully-convolutional neural networks (FCN) were proven to be effective for predicting the instantaneous state of a fully-developed turbulent flow at different wall-normal locations using quantities measured at the wall. In Guastoni et al. (J Fluid Mech 928:A27, 2021. https://doi.org/10.1017/jfm.2021.812), we focused on wall-shear-stress distributions as input, which are difficult to measure in experiments. In order to overcome this limitation, we introduce a model that can take as input the heat-flux field at the wall from a passive scalar. Four different Prandtl numbers Pr=ν/α=(1,2,4,6) are considered (where ν is the kinematic viscosity and α is the thermal diffusivity of the scalar quantity). A turbulent boundary layer is simulated since accurate heat-flux measurements can be performed in experimental settings: first we train the network on aptly-modified DNS data and then we fine-tune it on the experimental data. Finally, we test our network on experimental data sampled in a water tunnel. These predictions represent the first application of transfer learning on experimental data of neural networks trained on simulations. This paves the way for the implementation of a non-intrusive sensing approach for the flow in practical applications.

The wall cycle in wall-bounded turbulent flows is a complex turbulence regeneration mechanism that remains not fully understood. This study explores the potential of deep reinforcement learning (DRL) for managing the wall regeneration cycle to achieve desired flow dynamics. To create a robust framework for DRL-based flow control, we have integrated the StableBaselines3 DRL libraries with the open-source direct numerical simulation (DNS) solver CaNS. The DRL agent interacts with the DNS environment, learning policies that modify wall boundary conditions to optimise objectives such as the reduction of the skin-friction coefficient or the enhancement of certain coherent structures’ features. The implementation makes use of the message-passing-interface (MPI) wrappers for efficient communication between the Python-based DRL agent and the DNS solver, ensuring scalability on high-performance computing architectures. Initial experiments demonstrate the capability of DRL to achieve drag reduction rates comparable with those achieved via traditional methods, although limited to short time intervals. We also propose a strategy to enhance the coherence of velocity streaks, assuming that maintaining straight streaks can inhibit instability and further reduce skin-friction. Our results highlight the promise of DRL in flow-control applications and underscore the need for more advanced control laws and objective functions. Future work will focus on optimising actuation intervals and exploring new computational architectures to extend the applicability and the efficiency of DRL in turbulent flow management.

We study drag reduction in a minimal turbulent channel flow using scientific multi-agent reinforcement learning (SMARL). The flow is controlled by blowing and suction at the wall of an open channel, with observable states derived from flow velocities sensed at adjustable heights. We explore the actions, state, and reward space of SMARL using the off-policy algorithm V-RACER. We compare single- and multi-agent setups, and compare the identified control policies against the well-known mechanism of opposition-control. Our findings demonstrate that off-policy SMARL reduces drag in various experimental setups, surpassing classical opposition-control by up to 20 percentage points.

We introduce a reinforcement learning (RL) environment to design and benchmark control strategies aimed at reducing drag in turbulent fluid flows enclosed in a channel. The environment provides a framework for computationally efficient, parallelized, high-fidelity fluid simulations, ready to interface with established RL agent programming interfaces. This allows for both testing existing deep reinforcement learning (DRL) algorithms against a challenging task, and advancing our knowledge of a complex, turbulent physical system that has been a major topic of research for over two centuries, and remains, even today, the subject of many unanswered questions. The control is applied in the form of blowing and suction at the wall, while the observable state is configurable, allowing to choose different variables such as velocity and pressure, in different locations of the domain. Given the complex nonlinear nature of turbulent flows, the control strategies proposed so far in the literature are physically grounded, but too simple. DRL, by contrast, enables leveraging the high-dimensional data that can be sampled from flow simulations to design advanced control strategies. In an effort to establish a benchmark for testing data-driven control strategies, we compare opposition control, a state-of-the-art turbulence-control strategy from the literature, and a commonly used DRL algorithm, deep deterministic policy gradient. Our results show that DRL leads to 43% and 30% drag reduction in a minimal and a larger channel (at a friction Reynolds number of 180), respectively, outperforming the classical opposition control by around 20 and 10 percentage points, respectively.

The objective of the present study is to provide a numerical database of thermal boundary layers and to contribute to the understanding of the dynamics of passive scalars at different Prandtl numbers. In this regard, a direct numerical simulation (DNS) of an incompressible zero-pressure-gradient turbulent boundary layer is performed with the Reynolds number based on momentum thickness Re-theta ranging up to 1080. Four passive scalars, characterized by the Prandtl numbers Pr=1,2,4,6 are simulated using the pseudo-spectral code SIMSON (Chevalier et al., SIMSON : a pseudo-spectral solver for incompressible boundary layer flows. Tech. Rep. TRITA-MEK 2007:07. KTH Mechanics, Stockholm, Sweden, 2007). To the best of our knowledge, the present DNS provides the thermal boundary layer with the highest Prandtl number available in the literature. It corresponds to that of water at similar to 24(degrees)C, when the fluid temperature is considered as a passive scalar. Turbulence statistics for the flow and thermal fields are computed and compared with available numerical simulations at similar Reynolds numbers. The mean flow and scalar profiles, root-mean-squared velocity and scalar fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order statistics agree well with the numerical data reported in the literature. Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of the passive scalars are computed, providing a quantitative description of the energy distribution at the different length scales for various wall-normal locations. The energy distribution of the heat-flux fields at the wall is concentrated on longer temporal structures with increasing Prandtl number. This is due to the thinner thermal boundary layer as thermal diffusivity decreases and, thereby, the longer temporal structures exhibit a different footprint at the wall.

The objective of this study is to assess the capability of convolution-based neural networks to predict the wall quantities in a turbulent open channel flow, starting from measurements within the flow. Gradually approaching the wall, the first tests are performed by training a fully-convolutional network (FCN) to predict the two-dimensional velocity-fluctuation fields at the inner-scaled wall-normal location ytarget+, using the sampled velocity fluctuations in wall-parallel planes located farther from the wall, at yinput+. The predictions from the FCN are compared against the predictions from a proposed R-Net architecture as a part of the network investigation study. Since the R-Net model is found to perform better than the FCN model, the former architecture is optimized to predict the two-dimensional streamwise and spanwise wall-shear-stress components and the wall pressure from the sampled velocity-fluctuation fields farther from the wall. The data for training and testing is obtained from direct numerical simulation (DNS) of open channel flow at friction Reynolds numbers Reτ=180 and 550. The turbulent velocity-fluctuation fields are sampled at various inner-scaled wall-normal locations, i.e. y+={15,30,50,100,150}, along with the wall-shear stress and the wall pressure. At Reτ=550, both FCN and R-Net can take advantage of the self-similarity in the logarithmic region of the flow and predict the velocity-fluctuation fields at y+=50 using the velocity-fluctuation fields at y+=100 as input with about 10% error in prediction of streamwise-fluctuations intensity. Further, the network model trained in this work is also able to predict the wall-shear-stress and wall-pressure fields using the velocity-fluctuation fields at y+=50 with around 10% error in the intensity of the corresponding fluctuations at both Reτ=180 and 550. These results are an encouraging starting point to develop neural-network-based approaches for modelling turbulence near the wall in numerical simulations, especially large-eddy simulations (LESs).

In the present thesis, the application of deep learning and deep reinforcement learning to turbulent-flow simulations is investigated. Deep-learning models are trained to perform temporal and spatial predictions, while deep reinforcement learning is applied to a flow-control problem, namely the reduction of drag in an open channel flow. Long short-term memory (LSTM, Hochreiter & Schmidhuber 1997) networks and Koopman non-linear forcing (KNF) models are optimized to perform temporal predictions in two reduced-order-models of turbulence, namely the nine-equations model proposed by Moehlis et al. (2004) and a truncated proper orthogonal decomposition (POD) of a minimal channel flow (Jiménez & Moin 1991). In the first application, both models are able to produce accurate short-term predictions. Furthermore, the predicted system trajectories are statistically correct. KNF models outperform LSTM networks in short-term predictions, with a much lower training computational cost. In the second task, only LSTMs can be trained successfully, predicting trajectories that are statistically accurate. Spatial predictions are performed in two turbulent flows: an open channel flow and a boundary-layer flow. Fully-convolutional networks (FCNs) are used to predict two-dimensional velocity-fluctuation fields at a given wall-normal location using wall measurements (and vice versa). Thanks to the non-linear nature of these models, they provide a better reconstruction performance than optimal linear methods like extended POD (Borée 2003). Finally, we show the potential of deep reinforcement learning in discovering new control strategies for turbulent flows. By framing the fluid-dynamics problem as a multi-agent reinforcement-learning environment and by training the agents using a location-invariant deep deterministic policy-gradient (DDPG) algorithm, we are able to learn a control strategy that achieves a remarkable 30% drag reduction, improving over existing strategies by about 10 percentage points.

I den förinställda avhandlingen undersöks tillämpningen av djupinlärning och djupförstärkningsinlärning på turbulenta flödessimuleringar. Modeller för djupinlärning tränas för att utföra tids- och rumsförutsägelser, medan djupförstärkningsinlärning tillämpas på ett flödeskontrollproblem, nämligen minskningen av motståndet i ett öppet kanalflöde. Long short-term memory (LSTM, Hochreiter & Schmidhuber 1997) nätverk och Koopman non-linear forcing (KNF) modeller optimeras för att utföratidsförutsägelser i två turbulensmodeller med reducerad ordning, nämligen nio-ekvationsmodellen som föreslagits av Moehlis et al. (2004) och en trunkerad proper orthogonal decomposition (POD) av ett minimalt kanalflöde (Jiménez & Moin 1991). I den första applikationen kan båda modellerna producera korrekta korttidsförutsägelser, dessutom är de förutsagda trajektorierna statistiskt korrekta. KNF-modeller överträffar LSTM-nätverk i kortsiktiga förutsägelser, med en mycket lägre utbildningsberäkningskostnad. I den andra uppgiften kan endast LSTM nätverken tränas framgångsrikt, med trajektorier som är statistiskt korrekta. Spatiala förutsägelser utförs i två turbulenta flöden, en öppen kanal flöde och en gränsskikt. Fully-convolutional networks (FCN) används för att förutsäga tvådimensionella hastighetsfluktuationsfält vid givet avstånd från väggen med hjälp av väggmätningar (och vice versa). Tack vare deras icke-linjär karaktär ger dessa modeller bättre rekonstruktionsprestanda än optimala linjära metoder som extended POD (Borée 2003). Slutligen visar vi potentialen med djup förstärkningsinlärning för att upptäcka nya kontrollstrategier i turbulenta flöden. Genom att inrama strömningsmekaniska problemet som en förstärknings-inlärningsmiljö med flera agenter och genom att träna agenterna med hjälp av en positionsinvariant deep deterministic policy gradient (DDPG) algoritm, kan vi lära oss en kontrollstrategi som uppnår en anmärkningsvärd 30% minskning av luftmotståndet, vilket jämfört med existerande strategier är en förbättring med cirka 10 procentenheter.

Flow-control techniques are extensively studied in fluid mechanics, as a means to reduce energy losses related to friction, both in fully-developed and spatially-developing flows. These techniques typically rely on closed-loop control systems that require an accurate representation of the state of the flow to compute the actuation. Such representation is generally difficult to obtain without perturbing the flow. For this reason, in this work we propose a fully-convolutional neural-network (FCN) model trained on direct-numerical-simulation (DNS) data to predict the instantaneous state of the flow at different wall-normal locations using quantities measured at the wall. Our model can take as input the heat-flux field at the wall from a passive scalar with Prandtl number Pr = ν/α = 6 (where ν is the kinematic viscosity and α is the thermal diffusivity of the scalar quantity). The heat flux can be accurately measured also in experimental settings, paving the way for the implementation of a non-intrusive sensing of the flow in practical applications.

The success of recurrent neural networks (RNNs) has been demonstrated in many applications related to turbulence, including flow control, optimization, turbulent features reproduction as well as turbulence prediction and modeling. With this study we aim to assess the capability of these networks to reproduce the temporal evolution of a minimal turbulent channel flow. We first obtain a data-driven model based on a modal decom-position in the Fourier domain (which we denote as FFT-POD) of the time series sampled from the flow. This particular case of turbulent flow allows us to accurately simulate the most relevant coherent structures close to the wall. Long-short-term-memory (LSTM) networks and a Koopman-based framework (KNF) are trained to predict the temporal dynamics of the minimal-channel-flow modes. Tests with different configurations highlight the limits of the KNF method compared to the LSTM, given the complexity of the flow under study. Long-term prediction for LSTM show excellent agreement from the statistical point of view, with errors below 2% for the best models with respect to the reference. Furthermore, the analysis of the chaotic behaviour through the use of the Lyapunov exponents and of the dynamic behaviour through Poincare' maps emphasizes the ability of the LSTM to reproduce the temporal dynamics of turbulence. Alternative reduced-order models (ROMs), based on the identification of different turbulent structures, are explored and they continue to show a good potential in predicting the temporal dynamics of the minimal channel.

Two models based on convolutional neural networks are trained to predict the two-dimensional instantaneous velocity-fluctuation fields at different wall-normal locations in a turbulent open-channel flow, using the wall-shear-stress components and the wall pressure as inputs. The first model is a fully convolutional neural network (FCN) which directly predicts the fluctuations, while the second one reconstructs the flow fields using a linear combination of orthonormal basis functions, obtained through proper orthogonal decomposition (POD), and is hence named FCN-POD. Both models are trained using data from direct numerical simulations at friction Reynolds numbers Re-tau = 180 and 550. Being able to predict the nonlinear interactions in the flow, both models show better predictions than the extended proper orthogonal decomposition (EPOD), which establishes a linear relation between the input and output fields. The performance of the models is compared based on predictions of the instantaneous fluctuation fields, turbulence statistics and power-spectral densities. FCN exhibits the best predictions closer to the wall, whereas FCN-POD provides better predictions at larger wall-normal distances. We also assessed the feasibility of transfer learning for the FCN model, using the model parameters learned from the Re-tau = 180 dataset to initialize those of the model that is trained on the Re-tau = 550 dataset. After training the initialized model at the new Ret, our results indicate the possibility of matching the reference-model performance up to y(+) = 50, with 50% and 25% of the original training data. We expect that these non-intrusive sensing models will play an important role in applications related to closed-loop control of wall-bounded turbulence.