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This paper surveys machine-learning-based super-resolution reconstruction for vortical flows. Super resolution aims to find the high-resolution flow fields from low-resolution data and is generally an approach used in image reconstruction. In addition to surveying a variety of recent super-resolution applications, we provide case studies of super-resolution analysis for an example of two-dimensional decaying isotropic turbulence. We demonstrate that physics-inspired model designs enable successful reconstruction of vortical flows from spatially limited measurements. We also discuss the challenges and outlooks of machine-learning-based super-resolution analysis for fluid flow applications. The insights gained from this study can be leveraged for super-resolution analysis of numerical and experimental flow data. [ABSTRACT FROM AUTHOR]

Direct numerical simulation of a fully developed turbulent channel flow controlled using a streamwise traveling wave having a periodicity not only in the streamwise direction but also in the spanwise direction, referred to as wave-machine-like traveling wave, is performed to investigate the impact of the spanwise variation of the streamwise traveling wave on the drag reduction effect. The maximum drag reduction rate attained in the present study is smaller than that in the case of the spanwise-uniform traveling wave. The drag reduction rate increases as the spanwise wavelength increases, and the drag reduction effect can be obtained in the range of λ z + > 400 . According to the analysis of the phased-averaged Reynolds shear stress (RSS), the wave-machine-like traveling wave makes the flow field more uniform in the streamwise direction and non-uniform in the spanwise direction, as compared to the case of spanwise-uniform traveling wave. While the turbulent component of RSS in the antinode plane is suppressed near the wall, that in the node plane is significantly suppressed far from the wall. An analysis using the Fukagata–Iwamoto–Kasagi identity shows that the drag reduction effect, which was primary due to the significant decrease in the contribution from the turbulent component of the RSS in the case of spanwise-uniform traveling wave, is partly deteriorated by the contribution from the periodic (i.e., dispersive) component of RSS in the case of wave-machine-like traveling wave. [ABSTRACT FROM AUTHOR]

Neural networks (NNs) and linear stochastic estimation (LSE) have widely been utilized as powerful tools for fluid-flow regressions. We investigate fundamental differences between them considering two canonical fluid-flow problems: (1) the estimation of high-order proper orthogonal decomposition coefficients from low-order their counterparts for a flow around a two-dimensional cylinder, and (2) the state estimation from wall characteristics in a turbulent channel flow. In the first problem, we compare the performance of LSE to that of a multi-layer perceptron (MLP). With the channel flow example, we capitalize on a convolutional neural network (CNN) as a nonlinear model which can handle high-dimensional fluid flows. For both cases, the nonlinear NNs outperform the linear methods thanks to nonlinear activation functions. We also perform error-curve analyses regarding the estimation error and the response of weights inside models. Our analysis visualizes the robustness against noisy perturbation on the error-curve domain while revealing the fundamental difference of the covered tools for fluid-flow regressions. [ABSTRACT FROM AUTHOR]

We demonstrate several techniques to encourage practical uses of neural networks for fluid flow estimation. In the present paper, three perspectives which are remaining challenges for applications of machine learning to fluid dynamics are considered: 1. interpretability of machine-learned results, 2. bulking out of training data, and 3. generalizability of neural networks. For the interpretability, we first demonstrate two methods to observe the internal procedure of neural networks, i.e., visualization of hidden layers and application of gradient-weighted class activation mapping (Grad-CAM), applied to canonical fluid flow estimation problems—(1) drag coefficient estimation of a cylinder wake and (2) velocity estimation from particle images. It is exemplified that both approaches can successfully tell us evidences of the great capability of machine learning-based estimations. We then utilize some techniques to bulk out training data for super-resolution analysis and temporal prediction for cylinder wake and NOAA sea surface temperature data to demonstrate that sufficient training of neural networks with limited amount of training data can be achieved for fluid flow problems. The generalizability of machine learning model is also discussed by accounting for the perspectives of inter/extrapolation of training data, considering super-resolution of wakes behind two parallel cylinders. We find that various flow patterns generated by complex interaction between two cylinders can be reconstructed well, even for the test configurations regarding the distance factor. The present paper can be a significant step toward practical uses of neural networks for both laminar and turbulent flow problems. [ABSTRACT FROM AUTHOR]

We focus on a convolutional neural network (CNN), which has recently been utilized for fluid flow analyses, from the perspective on the influence of various operations inside it by considering some canonical regression problems with fluid flow data. We consider two types of CNN-based fluid flow analyses: (1) CNN metamodeling and (2) CNN autoencoder. For the first type of CNN with additional scalar inputs, which is one of the common forms of CNN for fluid flow analysis, we investigate the influence of input placements in the CNN training pipeline. As an example, estimation of drag and lift coefficients of an inclined flat plate and two side-by-side cylinders in laminar flows is considered. For the example of flat plate wake, we use the chord Reynolds number Re c and the angle of attack α as the additional scalar inputs to provide the information on the complexity of wake. For the wake interaction problem comprising flows over two side-by-side cylinders, the gap ratio and the diameter ratio are utilized as the additional inputs. We find that care should be taken for the placement of additional scalar inputs depending on the problem setting and the complexity of flows that users handle. We then discuss the influence of various parameters and operations on the CNN performance, with the utilization of autoencoder (AE). A two-dimensional decaying homogeneous isotropic turbulence is considered for the demonstration of AE. The results obtained through the AE highly rely on the decaying nature. Investigation on the influence of padding operation at a convolutional layer is also performed. The zero padding shows reasonable ability compared to other methods which account for the boundary conditions assumed in the numerical data. Moreover, the effect of the dimensional reduction/extension methods inside CNN is also examined. The CNN model is robust against the difference in dimension reduction operations, while it is sensitive to the dimensional extension methods. The findings of this paper will help us better design a CNN architecture for practical fluid flow analysis. [ABSTRACT FROM AUTHOR]

We apply supervised machine learning techniques to a number of regression problems in fluid dynamics. Four machine learning architectures are examined in terms of their characteristics, accuracy, computational cost, and robustness for canonical flow problems. We consider the estimation of force coefficients and wakes from a limited number of sensors on the surface for flows over a cylinder and NACA0012 airfoil with a Gurney flap. The influence of the temporal density of the training data is also examined. Furthermore, we consider the use of convolutional neural network in the context of super-resolution analysis of two-dimensional cylinder wake, two-dimensional decaying isotropic turbulence, and three-dimensional turbulent channel flow. In the concluding remarks, we summarize on findings from a range of regression-type problems considered herein. [ABSTRACT FROM AUTHOR]

We propose a method to construct a reduced order model with machine learning for unsteady flows. The present machine-learned reduced order model (ML-ROM) is constructed by combining a convolutional neural network autoencoder (CNN-AE) and a long short-term memory (LSTM), which are trained in a sequential manner. First, the CNN-AE is trained using direct numerical simulation (DNS) data so as to map the high-dimensional flow data into low-dimensional latent space. Then, the LSTM is utilized to establish a temporal prediction system for the low-dimensionalized vectors obtained by CNN-AE. As a test case, we consider flows around a bluff body whose shape is defined using a combination of trigonometric functions with random amplitudes. The present ML-ROMs are trained on a set of 80 bluff body shapes and tested on a different set of 20 bluff body shapes not used for training, with both training and test shapes chosen from the same random distribution. The flow fields are confirmed to be well reproduced by the present ML-ROM in terms of various statistics. We also focus on the influence of two main parameters: (1) the latent vector size in the CNN-AE, and (2) the time step size between the mapped vectors used for the LSTM. The present results show that the ML-ROM works well even for unseen shapes of bluff bodies when these parameters are properly chosen, which implies great potential for the present type of ML-ROM to be applied to more complex flows. [ABSTRACT FROM AUTHOR]

Direct numerical simulation (DNS) of turbulent channel flow over a two-dimensional irregular rough wall with uniform blowing (UB) was performed. The main objective is to investigate the drag reduction effectiveness of UB on a rough-wall turbulent boundary layer toward its practical application. The DNS was performed under a constant flow rate at the bulk Reynolds number values of 5600 and 14000, which correspond to the friction Reynolds numbers of about 180 and 400 in the smooth-wall case, respectively. Based upon the decomposition of drag into the friction and pressure contributions, the present flow is considered to belong to the transitionally-rough regime. Unlike recent experimental results, it turns out that the drag reduction effect of UB on the present two-dimensional rough wall is similar to that for a smooth wall. The friction drag is reduced similarly to the smooth-wall case by the displacement of the mean velocity profile. Besides, the pressure drag, which does not exist in the smooth-wall case, is also reduced; namely, UB makes the rough wall aerodynamically smoother. Examination of turbulence statistics suggests that the effects of roughness and UB are relatively independent to each other in the outer layer, which suggests that Stevenson's formula can be modified so as to account for the roughness effect by simply adding the roughness function term. [ABSTRACT FROM AUTHOR]

A linearized analysis of the Reynolds-averaged Navier-Stokes (RANS) equations is proposed where the $$k-\epsilon $$ turbulence model is used. The flow near the forest is obtained as the superposition of the undisturbed incoming boundary layer plus a velocity perturbation due to the forest presence, similar to the approach proposed by Belcher et al. (J Fluid Mech 488:369-398, 2003). The linearized model has been compared against several non-linear RANS simulations with many leaf-area index values and large-eddy simulations using two different values of leaf-area index. All the simulations have been performed for a homogeneous forest and for four different clearing configurations. Despite the model approximations, the mean velocity and the Reynolds stress $$\overline{u'w'}$$ have been reasonably reproduced by the first-order model, providing insight about how the clearing perturbs the boundary layer over forested areas. However, significant departures from the linear predictions are observed in the turbulent kinetic energy and velocity variances. A second-order correction, which partly accounts for some non-linearities, is therefore proposed to improve the estimate of the turbulent kinetic energy and velocity variances. The results suggest that only a region close to the canopy top is significantly affected by the forest drag and dominated by the non-linearities, while above three canopy heights from the ground only small effects are visible and both the linearized model and the simulations have the same trends there. [ABSTRACT FROM AUTHOR]

We have developed a probe-system for simultaneous measurement of three velocity components and pressure in turbulent flows. A miniature total pressure probe is placed adjacent to the sensors of a triple hot-film probe in order to achieve the spatial resolution which is equivalent to that of the triple hot-film probe itself. The instantaneous static pressure is calculated from measured velocity and total pressure by means of a newly developed processing method based on the Bernoulli equation for unsteady flows. The measurements were undertaken in a turbulent wing-tip vortex flow. The look-up table method is employed for the calibration of the hot-film probe so accurate velocity data could be obtained over a wide range of the flow-attack angles. It is also demonstrated that the present probe-system is capable of measuring fluctuations in both velocity and pressure in the 20-650 Hz frequency range. The distribution of the fluctuating pressure obtained by this indirect method is in good agreement with the results from direct measurements of static pressure, demonstrating the promising performance of the present method. Furthermore, an improvement in the ability to make measurements of the velocity-pressure correlation across the wing-tip vortex is achieved. This improvement is possible because the effects of lateral velocity components are properly taken into account in the present formulation. The investigation regarding the transport equation budget for turbulent kinetic energy shows an anomalous structure of turbulence in this flow, mainly due to the meandering of the vortex, and the measurement of pressure diffusion is found to play an important role in the characterization of this kind of flow. [ABSTRACT FROM AUTHOR]