A typical feature of thermal convection is the formation of large-scale flow (LSF) structures of the order of system size. How this structure affects global heat transport is an important issue in the study of thermal convection. We present an experimental study of the coupling between the flow structure and heat transport in liquid metal convection with different degrees of spatial confinement, characterized by the aspect ratio $\varGamma$ of the convection cell. Combining measurements in two convection cells with $\varGamma =1.0$ and 0.5, the study shows that a large-scale circulation (LSC) transports ${\sim }35\,\%$ more heat than a twisted LSC. It is further found that when the LSF is in the form of the LSC state, the system is in a fully developed turbulence state with a $Nu\sim Ra^{0.29}$ scaling for the heat transport. However, the twisted LSC state with a heat transport scaling of $Nu\sim Ra^{0.37}$ appears when the system is not in the fully developed turbulence state. Bistability is observed when the system evolves from the twisted-LSC-dominated to the LSC-dominated state.

Preferential flow in a porous medium is commonly encountered in many practical applications. Our previous studies have discovered the preferential flow-induced non-monotonic wettability effect on displacement (J. Fluid Mech, vol. 942, 2022a, R5), but whether this non-monotonic rule is consistent for different disordered media and the impact of the interplay between the disorder and wettability under preferential flow conditions is still not well understood. Here, we combine microfluidic experiments, pore-scale simulations and theoretical analysis to study the impact of the disorder on the invading process where wettability varies from strongly water wet to strongly oil wet. Even though the strongly disordered matrix varies to a uniform state, the generality of the preferential flow-induced non-monotonic wettability effect is still proved. However, the previous pore-scale dynamics based on the strongly disordered matrix cannot explain the invading behaviour in the uniform matrix under preferential flow conditions. New mechanisms for the uniform matrix are further investigated by pore-scale modelling, which indicates that the balance of microscopic imbibition ability and the macroscopic interfacial stability dominate the invading process. We derive a theoretical model to describe the wettability effect and predict the optimal contact angle, which fits well with experimental and simulation results. Our work extends the understanding of the impact of preferential flow conditions on the wettability effect and is also of practical significance for engineering applications, such as geological CO2 sequestration, enhanced hydrocarbon recovery, soil wetting, liquid-infused material fabrication and microfluidic device design.

Despite decades of research, a universal method for prediction of roughness-induced skin friction in a turbulent flow over an arbitrary rough surface is still elusive. The purpose of the present work is to examine two possibilities; first, predicting equivalent sand-grain roughness size $k_s$ based on the roughness height probability density function and power spectrum (PS) leveraging machine learning as a regression tool; and second, extracting information about relevance of different roughness scales to skin-friction drag by interpreting the output of the trained data-driven model. The model is an ensemble neural network (ENN) consisting of 50 deep neural networks. The data for the training of the model are obtained from direct numerical simulations (DNS) of turbulent flow in plane channels over 85 irregular multi-scale roughness samples at friction Reynolds number $Re_\tau =800$. The 85 roughness samples are selected from a repository of 4200 samples, covering a wide parameter space, through an active learning (AL) framework. The selection is made in several iterations, based on the informativeness of samples in the repository, quantified by the variance of ENN predictions. This AL framework aims to maximize the generalizability of the predictions with a certain amount of data. This is examined using three different testing data sets with different types of roughness, including 21 surfaces from the literature. The model yields overall mean error 5 %–10 % on different testing data sets. Subsequently, a data interpretation technique, known as layer-wise relevance propagation, is applied to measure the contributions of different roughness wavelengths to the predicted $k_s$. High-pass filtering is then applied to the roughness PS to exclude the wavenumbers identified as drag-irrelevant. The filtered rough surfaces are investigated using DNS, and it is demonstrated that despite significant impact of filtering on the roughness topographical appearance and statistics, the skin-friction coefficient of the original roughness is preserved successfully.

Using a combination of proper variable transformation and integral methods, we rigorously derive an analytical formulation for the mean wall-normal velocity in turbulent boundary layers (TBLs) subjected to arbitrary pressure gradients. The accuracy and robustness of this novel formulation are validated extensively through comparisons with two independent sets of numerical simulation data, demonstrating excellent agreement in both near-equilibrium and non-equilibrium TBLs. In addition, the robustness of the analytical formulations to various choices of boundary-layer edge definition is further confirmed in non-equilibrium TBLs. Our formulation includes a streamwise derivative term, which has minimal significance in near-equilibrium TBLs but plays a crucial role in determining the mean wall-normal velocity in non-equilibrium TBLs. Moreover, we investigate the physical significance of the pre-factors associated with the mean wall-normal velocity components, and unveil a close connection between a previously defined pressure gradient parameter and the ratio of these pre-factors in the analytical equation governing the mean wall-normal velocity. The insights gained from the examination of the pre-factors and their connection to the pressure gradient parameter offer valuable knowledge for interpreting and predicting the behaviour of turbulent boundary layers in various practical applications.