A simple expression is derived of the componential contributions that different dynamical effects make to the frictional drag in turbulent channel, pipe and plane boundary layer flows. The local skin friction can be decomposed into four parts, i.e., laminar, turbulent, inhomogeneous and transient components, the second of which is a weighted integral of the Reynolds stress distribution. It is reconfirmed that the near-wall Reynolds stress is primarily important for the prediction and control of wall turbulence. As an example, the derived expression is used for an analysis of the drag modification by the opposition control and by the uniform wall blowing/suction.

We use machine learning to perform super-resolution analysis of grossly under-resolved turbulent flow field data to reconstruct the high-resolution flow field. Two machinelearning models are developed; namely the convolutional neural network (CNN) and the hybrid Downsampled Skip-Connection Multi-Scale (DSC/MS) models. These machinelearning models are applied to two-dimensional cylinder wake as a preliminary test and show remarkable ability to reconstruct laminar flow from low-resolution flow field data. We further assess the performance of these models for two-dimensional homogeneous turbulence. The CNN and DSC/MS models are found to reconstruct turbulent flows from extremely coarse flow field images with remarkable accuracy. For the turbulent flow problem, the machine-leaning based super-resolution analysis can greatly enhance the spatial resolution with as little as 50 training snapshot data, holding great potential to reveal subgrid-scale physics of complex turbulent flows. With the growing availability of flow field data from high-fidelity simulations and experiments, the present approach motivates the development of effective super-resolution models for a variety of fluid flows.

We present a theoretical prediction for the drag reduction rate achieved by superhydrophobic surfaces in a turbulent channel flow. The predicted drag reduction rate is in good agreement with results obtained from direct numerical simulations at Re τ 180 and 400. The present theory suggests that large drag reduction is possible also at Reynolds numbers of practical interest (Re τ ∼ 10 5 − 10 6) by employing a hydrophobic surface, which induces a slip length on the order of ten wall units or more.

We present a new nonlinear mode decomposition method to visualize the decomposed flow fields, named the mode decomposing convolutional neural network (MD-CNN). The proposed method is applied to a flow around a circular cylinder at Re D = 100 as a test case. The flow attributes are mapped into two modes in the latent space and then these two modes are visualized in the physical space. Since the MD-CNNs with nonlinear activation functions show lower reconstruction errors than the proper orthogonal decomposition (POD), the nonlinearity contained in the activation function is considered the key to improve the capability of the model. It is found by applying POD to each field decomposed using the MD-CNN with hyperbolic tangent activation that a single nonlinear MD-CNN mode contains multiple orthogonal bases, in contrast to the linear methods, i.e., POD and MD-CNN with linear activation. The present results suggest a great potential for the nonlinear MD-CNN to be used for feature extraction of flow fields in lower dimension than POD, while retaining interpretable relationships with the conventional POD modes.

Direct numerical simulation (DNS) of spatially developing turbulent boundary layer with uniform blowing (UB) or uniform suction (US) is performed aiming at skin friction drag reduction. The Reynolds number based on the free stream velocity and the 99 % boundary layer thickness at the inlet is set to be 3000. A constant wall-normal velocity is applied on the wall in the range, −0.01U ∞ 6 V ctr 6 0.01U ∞ . The DNS results show that UB reduces the skin friction drag, while US increases it. The turbulent fluctuations exhibit the opposite trend: UB enhances the turbulence, while US suppresses it. Dynamical decomposition of the local skin friction coefficient c f using the identity equation (FIK identity) (Fukagata, Iwamoto & Kasagi, Phys. Fluids, vol. 14, 2002, pp. L73-L76) reveals that the mean convection term in UB case works as a strong drag reduction factor, while that in US case works as a strong drag augmentation factor: in both cases, the contribution of mean convection on the friction drag overwhelms the turbulent contribution. It is also found that the control efficiency of UB is much higher than that of the advanced active control methods proposed for channel flows.

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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