An accurate prediction of turbulence has been very costly since it requires an infinitesimally small time step for advancing the governing equations to resolve the fast-evolving small-scale motions. With the recent development of various machine learning (ML) algorithms, the finite-time prediction of turbulence became one of promising options to relieve the computational burden. Yet, a reliable prediction of the small-scale motions is challenging. In this study, PredictionNet, a data-driven ML framework based on generative adversarial networks (GANs), was developed for fast prediction of turbulence with high accuracy down to the smallest scale using a relatively small number of parameters. In particular, we conducted learning of two-dimensional (2-D) decaying turbulence at finite lead times using direct numerical simulation data. The developed prediction model accurately predicted turbulent fields at a finite lead time of up to half the Eulerian integral time scale over which the large-scale motions remain fairly correlated. Scale decomposition was used to interpret the predictability depending on the spatial scale, and the role of latent variables in the discriminator network was investigated. The good performance of the GAN in predicting small-scale turbulence is attributed to the scale-selection and scale-interaction capability of the latent variable. Furthermore, by utilising PredictionNet as a surrogate model, a control model named ControlNet was developed to identify disturbance fields that drive the time evolution of the flow field in the direction that optimises the specified objective function.

Klotho is a protein that plays different functions in female fertility. We have previously reported that klotho protein supplementation during in vitro maturation improves porcine embryo development, while klotho knockout for somatic cell cloning completely blocks full-term pregnancy in vivo. However, the effects of the microinjection of klotho protein or klotho knockdown dual vector in porcine embryos at different time points and the specific molecular mechanisms remain largely unknown. In this study, we injected the preassembled cas9 + sgRNA dual vector, for klotho knockdown, into the cytoplasm of the germinal vesicle stage of oocytes and into porcine embryos after 6-h parthenogenetic activation. Similarly, the klotho protein was inserted into the cytoplasm of germinal vesicle stage oocytes and porcine embryos after 6-h parthenogenetic activation. Compared with the controls, the microinjection of klotho dual vector markedly decreased the blastocyst formation rates in germinal vesicle stage oocytes and activated embryos. However, the efficiency of blastocyst formation when klotho protein was inserted before in vitro maturation was significantly higher than that after klotho protein insertion into parthenogenetically activated embryos. These results indicated that klotho knockdown may impair embryo development into blastocyst irrespective of injection timing. In addition, klotho protein injection timing in pig embryos may be an important factor for regulating embryo development.

We propose an interpretable deep learning (DL) model that extracts physical features from turbulence data. Based on a conditional generative adversarial network combined with a new decomposition algorithm for the Prandtl number effect, we developed a DL model that is capable of predicting the local surface heat flux very accurately using only the wall-shear stress information and Prandtl number as inputs in channel turbulence. The considered range of Prandtl number is $Pr = 0.001 \sim 7$, with a focus on the subrange of $Pr = 0.1 \sim 7$. Through an investigation of the gradient maps of the trained prediction model, we were able to identify the nonlinear physical relationship between the wall-shear stresses and heat flux, which is quite diverse depending on the Prandtl number. Furthermore, the decomposition algorithm, which is used to separate the Prandtl number dependent field from the common field of the surface heat flux, helps not only in learning for good prediction of an arbitrary Prandtl number but also in analysing the effect of the Prandtl number on the determination of the heat flux for the given turbulent flow fields. We demonstrate that a physical interpretation of a trained network is possible.

Recent attempts to use deep learning for super-resolution reconstruction of turbulent flows have used supervised learning, which requires paired data for training. This limitation hinders more practical applications of super-resolution reconstruction. Therefore, we present an unsupervised learning model that adopts a cycle-consistent generative adversarial network (CycleGAN) that can be trained with unpaired turbulence data for super-resolution reconstruction. Our model is validated using three examples: (i) recovering the original flow field from filtered data using direct numerical simulation (DNS) of homogeneous isotropic turbulence; (ii) reconstructing full-resolution fields using partially measured data from the DNS of turbulent channel flows; and (iii) generating a DNS-resolution flow field from large-eddy simulation (LES) data for turbulent channel flows. In examples (i) and (ii), for which paired data are available for supervised learning, our unsupervised model demonstrates qualitatively and quantitatively similar performance as that of the best supervised learning model. More importantly, in example (iii), where supervised learning is impossible, our model successfully reconstructs the high-resolution flow field of statistical DNS quality from the LES data. Furthermore, we find that the present model has almost universal applicability to all values of Reynolds numbers within the tested range. This demonstrates that unsupervised learning of turbulence data is indeed possible, opening a new door for the wide application of super-resolution reconstruction of turbulent fields.

The dynamics of air bubbles in turbulent Rayleigh–Bénard (RB) convection is described for the first time using laboratory experiments and complementary numerical simulations. We performed experiments at $Ra=5.5\times 10^{9}$ and $1.1\times 10^{10}$, where streams of 1 mm bubbles were released at various locations from the bottom of the tank along the path of the roll structure. Using three-dimensional particle tracking velocimetry, we simultaneously tracked a large number of bubbles to inspect the pair dispersion, $R^{2}(t)$, for a range of initial separations, $r$, spanning one order of magnitude, namely $25\unicode[STIX]{x1D702}\leqslant r\leqslant 225\unicode[STIX]{x1D702}$; here $\unicode[STIX]{x1D702}$ is the local Kolmogorov length scale. Pair dispersion, $R^{2}(t)$, of the bubbles within a quiescent medium was also determined to assess the effect of inhomogeneity and anisotropy induced by the RB convection. Results show that $R^{2}(t)$ underwent a transition phase similar to the ballistic-to-diffusive ($t^{2}$-to-$t^{1}$) regime in the vicinity of the cell centre; it approached a bulk behavior $t^{3/2}$ in the diffusive regime as the distance away from the cell centre increased. At small $r$, $R^{2}(t)\propto t^{1}$ is shown in the diffusive regime with a lower magnitude compared to the quiescent case, indicating that the convective turbulence reduced the amplitude of the bubble’s fluctuations. This phenomenon associated to the bubble path instability was further explored by the autocorrelation of the bubble’s horizontal velocity. At large initial separations, $R^{2}(t)\propto t^{2}$ was observed, showing the effect of the roll structure.

With the recent rapid development of artificial intelligence (AI) and wide applications in many areas, some fundamental questions in turbulence research can be addressed, such as: ‘Can turbulence be learned by AI? If so, how and why?’ In order to provide answers to these questions, we applied deep learning to the prediction of turbulent heat transfer based only on wall information using data obtained from direct numerical simulations (DNS) of turbulent channel flow. Through this attempt, we investigated whether deep learning could help to improve our understanding of the physics of turbulent heat transfer. Under the assumption that the wall-normal local heat flux can be explicitly expressed through a multilayer nonlinear network in terms of the nearby wall-shear stresses and wall pressure fluctuations, we applied convolutional neural networks (CNNs) to predict the local heat flux. After optimizing the network hyperparameters using a grid searching method, we found that the network can predict the heat flux very accurately with a correlation coefficient of 0.980 between the DNS and the prediction by CNN for the trained Reynolds number, $Re_{\unicode[STIX]{x1D70F}}=180$, and shows similar accuracy at a Reynolds number three times higher than the trained number. This result indicates that relationships between the local heat flux and the nearby inputs are quite insensitive to the Reynolds number within the tested range. In addition, observing the gradient maps of the trained network, we identified the part of the input data that is essential for the local heat flux prediction and the spatial relationship between the local heat flux and the nearby input fields. In addition to obtaining an understanding of the underlying physics, we investigated whether our model could be utilized for turbulence modelling.

We performed two-way coupled direct numerical simulations of turbulent channel flow with Lagrangian tracking of small, heavy spheres at a dimensionless gravitational acceleration of 0.077 in wall units, which is based on the flow condition in the experiment by Gerashchenko et al. (J. Fluid Mech., vol. 617, 2008, pp. 255–281). We removed deposited particles after several collisions with the lower wall and then released new particles near the upper wall to observe direct interactions between particles and coherent structures of near-wall turbulence during gravitational settling through the mean shear. The results indicate that when the Stokes number is approximately 1 on the basis of the Kolmogorov time scale of the flow ($St_{K}\approx 1$), the so-called preferential sweeping occurs in association with coherent streamwise vortices, while the effect of crossing trajectories becomes significant for $St_{K}>1$. Consequently, in either case, the settling particles deposit on the wall without strong accumulation in low-speed streaks in the viscous sublayer. When particles settle through near-wall turbulence from the upper wall, more small-scale vortical structures are generated in the outer layer as low-speed fluid is pulled farther in the direction of gravity, while the opposite is true near the lower wall.

Two simple feedback control laws for drag reduction are derived by applying a suboptimal control theory to a turbulent channel flow. These new feedback control laws require pressure or shear-stress information only at the wall, and when applied to a turbulent channel flow at Reτ=110, they result in 16–22% reduction in the skin-friction drag. More practical control laws requiring only the local distribution of the wall pressure or one component of the wall shear stress are also derived and are shown to work equally well.