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Bioengineering Fluid Mechanics

W.a.t.e.r. – a structured approach for training on advanced measurement and experimental research.

Abstract. W.A.T.E.R. stands for Workshop on Advanced measurement Techniques and Experimental Research. It is an initiative started in 2016, in the scope of the Experimental Methods and Instrumentation (EMI) committee of the International Association for Hydroenvironment Research (IAHR) aimed to advance the use of experimental techniques in hydraulics and fluid mechanics research. It provides a structured approach for the learning and training platform to postgraduate students, young researchers, and professionals with an experimental background in fluid mechanics. It offers an opportunity to learn about state-of-the-art instrumentation and measurement techniques and the latest developments in the field by partnering with manufacturers. The W.A.T.E.R. brings together academics, instrumentation manufacturers, and public sectors in a structured setting to share knowledge and to learn from good practices. It is about training people that already have certain knowledge and skill level but need to go deeper and/or wider in the field of measurement and experimental research.

Fluid Mechanics

Morphological aspect in translating thermodynamic terminology.

Several studies on translation have been carried out, namely on the problem of untranslation, translation of terms from various fields, and the formation of target language terms with spelling adjustments. One of them is the field of thermodynamics which is part of the field of Mechanical Engineering, which has many terms borrowed from Dutch and English. Therefore, the researchers are interested in investigating the morphological aspects of the translation of thermodynamic terms using the natural borrowing technique. This study used qualitative research methods. Researchers took terminology data from two books, namely The Fundamental of Engineering Thermodynamics and Fluid Mechanics. The results showed that the forms of borrowing that occurred were (1) borrowing by adjusting spelling and pronunciation adjustments; (2) borrowing with spelling adjustment without pronunciation adjustment; (3) borrowing without spelling adjustment, but with pronunciation adjustment; (4) adjustments to the spelling of prefixes and bound forms found 15 forms of adjustment; (5) suffix spelling adjustments found 20 forms of adjustment; and (6) a combination of translation and borrowing. In short, morphological aspects in translating thermodynamics terms are very important because they relate to the technique used.

Applying machine learning to study fluid mechanics

Abstract This paper provides a short overview of how to use machine learning to build data-driven models in fluid mechanics. The process of machine learning is broken down into five stages: (1) formulating a problem to model, (2) collecting and curating training data to inform the model, (3) choosing an architecture with which to represent the model, (4) designing a loss function to assess the performance of the model, and (5) selecting and implementing an optimization algorithm to train the model. At each stage, we discuss how prior physical knowledge may be embedding into the process, with specific examples from the field of fluid mechanics. Graphic abstract

Fundamentals of fluid mechanics

Editorial for special issue on “oldroyd at 100: celebrating the impact of j. g. oldroyd on non-newtonian fluid mechanics, the fluid mechanics of liquid democracy.

Liquid democracy is the principle of making collective decisions by letting agents transitively delegate their votes. Despite its significant appeal, it has become apparent that a weakness of liquid democracy is that a small subset of agents may gain massive influence. To address this, we propose to change the current practice by allowing agents to specify multiple delegation options instead of just one. Much like in nature, where—fluid mechanics teaches us—liquid maintains an equal level in connected vessels, we seek to control the flow of votes in a way that balances influence as much as possible. Specifically, we analyze the problem of choosing delegations to approximately minimize the maximum number of votes entrusted to any agent by drawing connections to the literature on confluent flow. We also introduce a random graph model for liquid democracy and use it to demonstrate the benefits of our approach both theoretically and empirically.

Ocular Fluid Mechanics and Drug Delivery: A Review of Mathematical and Computational Models

The progress of fluid mechanics application in architecture design, export citation format, share document.

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Fluid dynamics is the study of the motion of liquids, gases and plasmas. Flow is dependent on the intrinsic properties of the matter itself, such as compressibility, viscosity and density. Example systems are a liquid flowing through a pipe or capillary, air moving across an aeroplane wing, and plasma motion in a stars magnetic field.

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Artificial intelligence in fluid mechanics

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• Published: 20 January 2022
• Volume 37 , pages 1715–1717, ( 2021 )

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• Wei-Wei Zhang 1 &
• Bernd R. Noack 2  

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Recent progress in machine learning and big data not only forms a new research paradigm, but also provides opportunity to solve grand challenges in fluid mechanics. Following the disciplinary development, this thematic issue of artificial intelligence (AI) in fluid mechanics came into being. This perspective briefly summarizes the development trend of intelligent fluid mechanics (IFM), discusses the opportunities and challenges, and introduces relevant papers in this thematic issue.

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The transformative potential of machine learning for experiments in fluid mechanics

Applying machine learning to study fluid mechanics

Enhancing computational fluid dynamics with machine learning

Liu, W.K., Karniadakis, G., Tang, S.Q., et al.: A computational mechanics special issue on: data-driven modeling and simulation—theory, methods, and applications. Comput. Mech. 64 , 275–277 (2019)

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Perdikaris, P., Tang, S.Q.: Mechanistic machine learning: theory, methods, and applications. Theor. Appl. Mech. Lett. 10 , 141–142 (2020)

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Kariadakis, G.E., Hesthaven, J.: Machine learning for physical systems. J. Comput. Phys. https://www.sciencedirect.com/journal/journal-of-computational-physics/special-issue/10QSWHT6XHF

Brunton, S.: Applying machine learning to study fluid mechanics. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01143-6

Cai, S.Z., Mao, Z.P., Wang, Z.C., et al.: Physics-informed neural networks (PINNs) for fluid mechanics: a review. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01148-1

Jiang, Q.H., Zhu, L.L., Shu, C., et al.: Multilayer perceptron neural network activated by adaptive Gaussian radial basis function and its application to predict lid-driven cavity flow. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01144-5

Zhao, T., Chen, G., Wang, X., et al.: Aerodynamic modeling using an end-to-end learning attitude dynamics network for flight control. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01151-6

Maruyama, D., Bekemeyer, P., Görtz, S., et al.: Data-driven bayesian inference of turbulence model closure coefficients incorporating epistemic uncertainty. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01152-5

Guo, X.W., Xia, Z.H., Chen, S.Y.: Practical framework for data-driven RANS modeling with data augmentation. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01147-2

Yuan, Z.L., Wang, Y.P., Xie, C.Y., et al.: Deconvolutional artificial-neural-network framework for subfilter-scale models of compressible turbulence. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01150-7

Blanchard, A.B., Cornejo Maceda, G.Y., Fan, D.W., et al.: Bayesian optimization for active flow control. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01149-0

Yu, J.N., Fan, D.W., Noack, B.R., et al.: Genetic-algorithm-based artificial intelligence control of a turbulent boundary layer. Acta Mech. Sin. (2021). https://doi.org/10.1007/s10409-021-01145-4

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Acknowledgements

We appreciate the efforts made by all the contributors for this thematic issue. We are grateful to Prof. Xiao-Jing Zheng, the Editor-in-Chief of Acta Mechanica Sinica (AMS), for inviting us as the guest editors of this thematic issue. We also thank the staff of the editorial office of AMS for managing, assistance, and support.

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Zhang, WW., Noack, B.R. Artificial intelligence in fluid mechanics. Acta Mech. Sin. 37 , 1715–1717 (2021). https://doi.org/10.1007/s10409-021-01154-3

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Special Issue Papers

Shigeo Kida

The steady flow in a rotating sphere is investigated by asymptotic analysis in the limit of strong precession. The whole spherical body is divided into three regions in terms of the flow characteristics: the critical band, which is the close vicinity surrounding the great circle perpendicular to the precession axis, the boundary layer, which is attached to the whole sphere surface and the inviscid region that occupies the majority of the sphere. The analytic expressions, in the leading order of the asymptotic expansion, of the velocity field are obtained in the former two, whereas partial differential equations for the velocity field are derived in the latter, which are solved numerically. This steady flow structure is confirmed by the corresponding direct numerical simulation.

Mitsuaki Funakoshi

Andrés Franco-Gómez , Alice B Thompson , Andrew L Hazel and Anne Juel

We study the propagation of finite bubbles in a Hele-Shaw channel, where a centred occlusion (termed a rail) is introduced to provide a small axially uniform depth constriction. For bubbles wide enough to span the channel, the system's behaviour is similar to that of semi-infinite fingers and a symmetric static solution is stable. Here, we focus on smaller bubbles, in which case the symmetric static solution is unstable and the static bubble is displaced towards one of the deeper regions of the channel on either side of the rail. Using a combination of experiments and numerical simulations of a depth-averaged model, we show that a bubble propagating axially due to a small imposed flow rate can be stabilised in a steady symmetric mode centred on the rail through a subtle interaction between stabilising viscous forces and destabilising surface tension forces. However, for sufficiently large capillary numbers Ca , the ratio of viscous to surface tension forces, viscous forces in turn become destabilising thus returning the bubble to an off-centred propagation regime. With decreasing bubble size, the range of Ca for which steady centred propagation is stable decreases, and eventually vanishes through the coalescence of two supercritical pitchfork bifurcations. The depth-averaged model is found to accurately predict all the steady modes of propagation observed experimentally, and provides a comprehensive picture of the underlying steady bifurcation structure. However, for sufficiently large imposed flow rates, we find that initially centred bubbles do not converge onto a steady mode of propagation. Instead they transiently explore weakly unstable steady modes, an evolution which results in their break-up and eventual settling into a steady propagating state of changed topology.

Farhana Afroz and Muhammad A R Sharif

Generation of adverse pressure gradient (APG) in the boundary layer over a plane wall using a rotating cylinder close to the wall has been numerically investigated for a range of the freestream Reynolds number (50 ≤  Re  ≤ 400), the cylinder rotation rate (0 ≤  α  ≤ 2), and the cylinder to wall gap (0.125 ≤  G / D  ≤ 2). Various combinations of these flow parameters have been considered and the transient flow is computed using the ANSYS Fluent CFD code. The magnitude of the APG has been quantified. The influence of the freestream Reynolds number on the dynamics of flow separation and cylinder wake has been examined. Reynolds number has strong effect on bubble size properties and APG magnitude. Drag and lift force coefficient on the cylinder are also computed which are found to be strong function of the Reynolds number. Higher Reynolds number results in complex laminar separation bubble on the wall. A parametric demarcation map showing the threshold combinations of the flow parameters for transition from steady to periodic unsteady flow is generated.

Toshiyuki Doi

Slow flows of a rarefied gas between two plane parallel walls with nonuniform surface properties are studied based on kinetic theory. It is assumed that one wall is a diffuse reflection boundary and the other wall is a Maxwell-type boundary whose accommodation coefficient varies periodically in the direction perpendicular to the flow. The time-independent Poiseuille, thermal transpiration and Couette flows are considered. The flow behavior is numerically studied based on the linearized Bhatnagar–Gross–Krook–Welander model of the Boltzmann equation. The flow field, the mass and heat flow rates in the gas, and the tangential force acting on the wall surface are studied over a wide range of the gas rarefaction degree and the parameters characterizing the distribution of the accommodation coefficient. The locally convex velocity distribution is observed in Couette flow of a highly rarefied gas, similarly to Poiseuille flow and thermal transpiration. The reciprocity relations are numerically confirmed over a wide range of the flow parameters.

Linwei Shen , Eng-Soon Chan and Yan Wei

In this paper, beating phenomenon of a circular cylinder in vortex-induced vibration is studied by numerical simulations in a systematic manner. The cylinder mass coefficients of 2 and 10 are considered, and the Reynolds number is 150. Two distinctive frequencies, namely cylinder oscillation and vortex shedding frequencies, are obtained from the harmonic analysis of the cylinder displacement. The result is consistent with that observed in laboratory experiments. It is found that the cylinder oscillation frequency changes with the natural frequency of the cylinder while the reduced velocity is varied. The added-mass coefficient of the cylinder in beating motion is therefore estimated. Meanwhile, the vortex shedding frequency does not change dramatically in the beating situations. In fact, it is very close to 0.2. Accordingly, the lift force coefficient has two main components associated with these two frequencies. Besides, higher harmonics of the cylinder oscillation frequency appear in the spectrum of the lift coefficient. Moreover, the vortex shedding timing is studied in the beating motion by examining the instantaneous flow fields in the wake, and two scenarios of the vortex formation are observed.

Lili Ma , Yangyang Gao , Zhen Guo and Lizhong Wang

An experimental investigation on flow past nine cylinders in a square configuration was carried out using the particle image velocimetry technique and load cell in a water channel. The center-to-center spacing ratio L / D was in the range of 1.5–3.0 and the Reynolds number Re was varied from 1500 to 5000. The effects of spacing ratio and Reynolds number on the instantaneous time-averaged flow fields and force coefficients are investigated. The results show that three distinct flow regimes are categorized with variation of the spacing ratios and Reynolds numbers, namely, shielding flow regime, transition flow regime and vortex shedding flow regime. Depending on the interferences of shear layers around the nine cylinders, each flow regime is further divided into two types of flow patterns. An interesting feature of bistable flow pattern with different flow modes is observed at small spacing ratio L / D  = 1.5. The non-dimensional vortex shedding frequencies appear to be more associated with the individual shear layers rather than the multiple cylinders. Moreover, force analysis, streamline topologies and Reynolds stress contours are presented to elucidate the effects of spacing ratio and Reynolds number on the complex wake interference among the nine cylinders. The flow characteristics and force coefficients are found to be more sensitive to L / D rather than Re .

Ethirajan Rathakrishnan

The effect of nozzle aspect ratio on the mixing promotion capability of limiting tabs fixed at the exit of a Mach 2 convergent−divergent elliptical nozzle has been investigated experimentally. Limiting tabs of flat, triangular, circular arc and circular (crosswire) geometry placed along major and minor axes were studied in the presence of various levels of pressure gradient corresponding to NPR 4 to 8. These NPRs for Mach 2 flow correspond to highly overexpanded to marginally underexpanded states at the nozzle exit. In each case, the blockage offered by a limiting tab at the nozzle exit was 5% of the nozzle exit area. Among the tabs studied, the triangular tab was found to be the most efficient mixing promoter for this Mach 2 elliptical jet. The triangular tab promotes mixing to the largest extent when placed along the minor axis, leading to a core length reduction of about 82%, in the presence of adverse pressure gradient of about 36%, at the nozzle exit—that is, at NPR 5. At this NPR, circular arc and flat tabs protect the core—that is, these tabs retard the jet mixing, leading to an elongation of the core by 8.7% and 42.4% respectively, whereas the core reduction caused by crosswire is only 36.8% at this NPR. The triangular tab is also found to be most efficient mixing promoter for tab orientation along the major axis, but for this orientation the best core length reduction caused is only 73.4%, at NPR 8. The efficient mixing promotion caused by the triangular tab does not introduce any abnormal level of asymmetry to jet propagation.

M Nayamatullah , Narasimha Rao Pillalamarri and Kiran Bhaganagar

A numerical investigation was performed to understand the flow dynamics of 2D density currents over sloping surfaces. Large eddy simulation was conducted for lock-exchange (L-E) release currents and overflows. 2D Navier–Stokes equations were solved using the Boussinesq approximation. The effects of the lock aspect-ratio (height/length of lock), slope, and Reynolds number on the flow structures and turbulence mixing have been analyzed. Results have confirmed buoyancy within the head of the two-dimensional currents is not conserved which contradicts the classical thermal theory. The lock aspect-ratio dictates the fraction of initial buoyancy which is carried by the head of the current at the beginning of the slumping (horizontal) and accelerating phase (over a slope), which has important implications on turbulence kinetic energy production, and hence mixing in the current. For L-E flows over a slope, increasing slope angle enhances the turbulence production. Increasing slope results in shear reversal within the density current resulting in shear-instabilities. Differences in turbulence production mechanisms and flow structures exist between the L-E and constant-flux release currents resulting in significant differences in the flow characteristics between different releases.

Suhail Abbas , Li Yuan and Abdullah Shah

P R Resende and A S Cavadas

The evolution of viscoelastic turbulent models, in the last years, has been significant due to the direct numeric simulation (DNS) advances, which allowed us to capture in detail the evolution of the viscoelastic effects and the development of viscoelastic closures. New viscoelastic closures are proposed for viscoelastic fluids described by the finitely extensible nonlinear elastic-Peterlin constitutive model. One of the viscoelastic closure developed in the context of isotropic turbulent models, consists in a modification of the turbulent viscosity to include an elastic effect, capable of predicting, with good accuracy, the behaviour for different drag reductions. Another viscoelastic closure essential to predict drag reduction relates the viscoelastic term involving velocity and the tensor conformation fluctuations. The DNS data show the high impact of this term to predict correctly the drag reduction, and for this reason is proposed a simpler closure capable of predicting the viscoelastic behaviour with good performance. In addition, a new relation is developed to predict the drag reduction, quantity based on the trace of the tensor conformation at the wall, eliminating the need of the typically parameters of Weissenberg and Reynolds numbers, which depend on the friction velocity. This allows future developments for complex geometries.

Rahim Shamsoddini

An incompressible smoothed particle hydrodynamics algorithm is proposed to model and investigate the thermal effect on the mixing rate of an active micromixer in which the rotating stirrers enhance the mixing rate. In liquids, mass diffusion increases with increasing temperature, while viscosity decreases; so, the local Schmidt number decreases considerably with increasing temperature. The present study investigates the effect of wall temperature on mixing rate with an improved SPH method. The robust SPH method used in the present work is equipped with a shifting algorithm and renormalization tensors. By introducing this new algorithm, the several mass, momentum, energy, and concentration equations are solved. The results, discussed for different temperature ratios, show that mixing rate increases significantly with increased temperature ratio.

Tomoaki Hirakawa and Makoto Okamura

Wei Chen , Kai Wang , Lei Wang , Guoxiang Hou and Wenjun Leng

Slip flow over structured superhydrophobic surface with transverse slots is investigated by the lattice Boltzmann method. The Shan–Chen multiphase model is employed to simulate the flow over gas bubbles in the slots. The Carnahan–Starling equation of state is applied to obtain large density ratio. The interface thickness of the multiphase model is discussed. We find that the Cahn number Cn should be smaller than 0.02 when the temperature T  = 0.5 T c to restrict the influence of interface thickness on slip length. Influences of slot fraction on slip length is then studied, and the result is compared with single LB simulation of which the interface is treated as free-slip boundary. The slip length obtained by the multiphase model is a little smaller. After that, the shape of the liquid–gas interface is considered, and simulations with different initial protrusion angles and capillary numbers are performed. Effective slip length as a function of initial protrusion angle is obtained. The result is in qualitative agreement with a previous study and main features are reproduced. Furthermore, the influence of Capillary number Ca is studied. Larger Ca causes larger interface deformation and smaller slip length. But when the interface is concaving into the slot, this influence is less obvious.

S Malekzadeh , I Mirzaee and N Pourmahmoud

In this article, the effects of Reynolds number on three-dimensional flow over a square cylinder with flow control are discussed at moderate Reynolds numbers, i.e. Re W  = 200–1000 (based on the width of the square cylinder and the inlet flow velocity). The flow is controlled by a thin vertical plate placed upstream of the cylinder. The vorticity structures at different Reynolds numbers, turbulent kinetic energy, Reynolds stresses, and mean and fluctuating fluid forces on the square cylinder in the presence of the control plate are investigated in order to determine the characteristics of the transient flow regime at the wake region behind the square cylinder. The results show that the transitional process of the flow regime from laminar to turbulent in the wake region behind the square cylinder at Re W  = 300–600 causes the pulsation phenomena to happen in the instantaneous lift signals of the square cylinder, and both of spanwise instability modes of A and B , as well as the dislocation phenomena are presented in the wake region behind the cylinder. It is also found that the mean and fluctuating fluid forces of the square cylinder in the presence of the control plate decrease in comparison to the single square cylinder, except for the rms drag coefficient at Re W  = 300.

Takao Yoshinaga

M A Manna , A Latifi and R A Kraenkel

The Miles' quasi laminar theory of waves generation by wind in finite depth h is presented. In this context, the fully nonlinear Green–Naghdi model equation is derived for the first time. This model equation is obtained by the non perturbative Green–Naghdi approach, coupling a nonlinear evolution of water waves with the atmospheric dynamics which works as in the classic Miles' theory. A depth-dependent and wind-dependent wave growth γ is drawn from the dispersion relation of the coupled Green–Naghdi model with the atmospheric dynamics. Different values of the dimensionless water depth parameter δ = gh / U 1 , with g the gravity and U 1 a characteristic wind velocity, produce two families of growth rate γ in function of the dimensionless theoretical wave-age c 0 : a family of γ with h constant and U 1 variable and another family of γ with U 1 constant and h variable. The allowed minimum and maximum values of γ in this model are exhibited.

Hongjie Huang , Minghou Liu , Hailin Gu , Xinlong Li , Xiaoqiang Wu and Feiyang Sun

The laminar flow (Reynolds number ranging from 60 to 180) past a hydrophobic circular cylinder is conducted by the time-dependent simulation with focus on the effect of dimensionless slip length, L S (ranging from 0.01 to 0.25), on total, viscous and pressure drag coefficients. It is found that the viscous drag plays a major role in drag reduction, for low Reynolds ( Re  < 100) and small slip length ( L S  < 0.02). When the Reynolds number and slip length are large enough, the decrease of total drag mainly depends on the pressure drag. The pressure drag coefficient increases with the Reynolds number when L S ranges from 0 to 0.02. For L S of 0.05, however, it has a different trend. Due to small proportion of viscous drag to total drag coefficient, the effect of viscous drag on the total drag is less important. The adverse pressure gradient appears on the circular cylinder and increases with the slip length. The pressure distribution is mainly affected by the vorticity gradient, fluid convection and the stability. Meanwhile, as Reynolds number equals to 100, the separation point moves downstream. This results in the increase of vortex shedding frequency and the decrease of vortex intensity at L S ranging from 0 to 0.11. As slip length increases to 0.25, the flow is stable. These results can provide useful information on the drag reduction control of the cylinder surface.

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Machine Learning in Fluid Mechanics Invited Papers

Physical Review Fluids publishes a collection of invited papers which advance the use of machine learning in fluid mechanics.

Invited 25 citations

Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows, suraj pawar and omer san, phys. rev. fluids 6 , 050501 (2021) – published 12 may 2021.

Modeling the effect of subgrid-scale processes is one of the main obstacles in the accurate prediction of multiscale systems. An investigation considers how machine learning methods can be applied to model subgrid-scale processes and integrated within sequential data assimilation methods. It is found that the use of machine-learning-based closure modeling in conjunction with data assimilation improves the prediction of multiscale systems and can be considered a promising approach to numerical weather prediction tasks in the age of data.

Invited 22 citations

Embedded training of neural-network subgrid-scale turbulence models, jonathan f. macart, justin sirignano, and jonathan b. freund, phys. rev. fluids 6 , 050502 (2021) – published 12 may 2021.

The weights of a deep neural-network model are optimized over the governing flow equations to provide a model for the subgrid-scale stresses in a turbulent plane jet. The training, which is done in a p o s t e r i o r i large-eddy simulations (LES), solves the adjoint Navier-Stokes equations to provide end-to-end sensitivities. Out-of-sample testing on multiple dual-jet configurations confirms that the required grid resolution is half that needed by dynamic models for comparable accuracy. The coupled formulation is generalized to train based only on the mean flow and Reynolds stresses, which are more readily available from experiments.

Invited 33 citations

Reconstruction of turbulent data with deep generative models for semantic inpainting from turb-rot database, m. buzzicotti, f. bonaccorso, p. clark di leoni, and l. biferale, phys. rev. fluids 6 , 050503 (2021) – published 12 may 2021.

Investigations show that convolutional neural networks (CNNs) are able to reconstruct missing data in turbulence. Different types of input information impact the performance of the algorithm. CNNs are able to reconstruct original data with errors comparable to equation-informed tools such as nudging, even in the presence of large gaps.

Invited 125 citations

Perspectives on machine learning-augmented reynolds-averaged and large eddy simulation models of turbulence, karthik duraisamy, phys. rev. fluids 6 , 050504 (2021) – published 12 may 2021.

Perspectives are presented on the use of machine learning to augment models of turbulent flows. Particular emphasis is placed on techniques that promote consistency of the machine learning model with the underlying physical model in view of the possibility of using sparse computational and experimental data. This is followed by a discussion of physics-informed and mathematical considerations on the choice of the feature space and imposition of constraints. Machine learning should be viewed as one tool in the turbulence modeler’s toolkit. The associated modeling endeavor requires multidisciplinary advances.

Invited 26 citations

Learning to swim in potential flow, yusheng jiao, feng ling, sina heydari, nicolas heess, josh merel, and eva kanso, phys. rev. fluids 6 , 050505 (2021) – published 12 may 2021.

Fish swim by coordinating their shape changes with the fluid environment to produce forward swimming or turning gaits. We use model-free reinforcement learning to learn shape coordinations that lead to robust turning and forward swimming motions in the context of a simple three-link fish in a potential flow environment. We show that the optimal control policies arrived at by reinforcement learning are interpretable via shape space analysis in driftless environment and are robust to the presence of drift-related perturbations.

Invited 17 citations

Ensemble kalman filter for vortex models of disturbed aerodynamic flows, mathieu le provost and jeff d. eldredge, phys. rev. fluids 6 , 050506 (2021) – published 12 may 2021.

We use an ensemble Kalman filter (EnKF) to sequentially estimate low Reynolds number aerodynamic flows using an inviscid vortex model and distributed surface pressure readings. We look at two scenarios: an impulsively translating plate subject to flow actuation near the leading edge or placed in a cylinder wake. In each case, the ensemble transform Kalman filter (ETKF) - a deterministic version of the EnKF - is consistently more robust than the stochastic EnKF and is qualitatively better at representing the coherent structures of the true flow. We analyze the mapping from pressure discrepancies to state update through a singular value decomposition of the Kalman gain.

Invited 9 citations

Data-driven modeling of rotating detonation waves, ariana mendible, james koch, henning lange, steven l. brunton, and j. nathan kutz, phys. rev. fluids 6 , 050507 (2021) – published 12 may 2021.

A rotating detonation engine displays complex nonlinear shock front propagation dynamics which impede effective dimensionality reduction. A novel optimization is used to discover separate low-rank modes and interpretable dynamics for each front’s propagation. Koopman autoencoders similarly enable separation and forecasting of shock wave interactions.

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