The presence of very-large-scale motions in wall-bounded turbulent flows is commonly associated with their footprint in the form of the superposition of the large scales at the wall and the additional amplitude modulation of small-scale near-wall turbulence. These two phenomena are currently understood to be interlinked, with the superposed large-scale velocity gradient causing the modulation of small-scale activity in the proximity of the wall. To challenge this idea, we devise a numerical strategy that selectively suppresses either superposition or amplitude modulation, in an effort to isolate and study the remaining phenomenon. Results from our direct numerical simulations indicate that a positive correlation between the amplitude of the small scales in the near-wall region and the large-scale signal in the outer flow persists even when near-wall large-scale motions are suppressed – i.e. in absence of superposition. Clearly, this kind of correlation cannot be caused by the near-wall large-scale velocity or its gradients, as both are absent. Conversely, when modulation is blocked, the near-wall footprints of the large scales seem to disappear. This study has been carried out on channel flows at friction Reynolds number $Re_\tau =1000$ in both standard simulation domains and minimal streamwise units (MSUs), where the streamwise fluctuation energy is enhanced. The consistency of the results obtained by the two approaches suggests that MSUs can capture correctly this kind of scale interaction at a much reduced cost.

The incompressible motion of viscoplastic fluid between two semi-infinite rigid plates, hinged at their ends and rotating towards one another at constant angular velocity, generates self-similar flow fields because there is no externally imposed length scale in the absence of inertia. The magnitude of the strain rate scales with the angular velocity of the plates and the dimensionless deviatoric stresses are functions only of the polar angle and a dimensionless measure of the yield stress; they are independent of the radial distance from the corner. These flows feature unyielded regions adjacent to the boundaries for sufficiently large angles between the plates. Moreover, when the dimensionless yield stress is large, there are viscoplastic boundary layers that are attached to the boundary or the plug, the asymptotic structures of which are constructed.

Machine learning frameworks such as genetic programming and reinforcement learning (RL) are gaining popularity in flow control. This work presents a comparative analysis of the two, benchmarking some of their most representative algorithms against global optimization techniques such as Bayesian optimization and Lipschitz global optimization. First, we review the general framework of the model-free control problem, bringing together all methods as black-box optimization problems. Then, we test the control algorithms on three test cases. These are (1) the stabilization of a nonlinear dynamical system featuring frequency cross-talk, (2) the wave cancellation from a Burgers’ flow and (3) the drag reduction in a cylinder wake flow. We present a comprehensive comparison to illustrate their differences in exploration versus exploitation and their balance between ‘model capacity’ in the control law definition versus ‘required complexity’. Indeed, we discovered that previous RL control attempts of controlling the cylinder wake were performing linear control and that the wide observation space was limiting their performances. We believe that such a comparison paves the way towards the hybridization of the various methods, and we offer some perspective on their future development in the literature of flow control problems.

Rain cleans pollution out of the atmosphere, as droplets collide with airborne particles during free fall. Such particle–droplet collisions have been presumed to be capture events, but the details of such collisions lack thorough investigation. We show that rain droplets and pollution particles interact through multiple collision behaviours, including captures on the droplet surface, cavity-forming droplet entries and ricochets. Rain drop diameter and free fall velocity, in addition to pollution particle density, size, wettability and droplet impact location, determine which capture or escape behaviour occurs. Our findings reveal that rain does not capture all airborne pollutants equally even upon collision, and certain pollutants prove more difficult to remove from the air than others. Consequently, we must account for both rain and pollution characteristics to understand pollution capture mechanisms and pollution fluxes in the environment.

When an aqueous drop contacts an immiscible oil film, it displays complex interfacial dynamics. When the spreading factor is positive, upon contact, the oil spreads onto the drop's liquid–air interface, first forming a liquid bridge whose curvature drives an apparent drop spreading motion and later engulfs the drop. We study this flow using both three-phase lattice Boltzmann simulations based on the conservative phase field model, and experiments. Inertially and viscously limited dynamics are explored using the Ohnesorge number $Oh$ and the ratio between the film height $H$ and the initial drop radius $R$. Both regimes show that the radial growth of the liquid bridge $r$ is fairly insensitive to the film height $H$, and scales with time $T$ as $r\sim T^{1/2}$ for $Oh\ll 1$, and as $r\sim T^{2/5}$ for $Oh\gg 1$. For $Oh\gg 1$, we show experimentally that this immiscible liquid bridge growth is analogous with the miscible drop–film coalescence case. Contrary to the growth of the liquid bridge, however, we find that the late-time engulfment dynamics and final interface profiles are significantly affected by the ratio $H/R$.

High-speed water entry is a transient hydrodynamic process that is accompanied by strongly compressible flow, free surface splash, cavity evolution and other nonlinear hydrodynamic phenomena. To address these problems, a novel fluid–structure interaction (FSI) scheme based on the immersed boundary method is proposed which is suitable for strongly compressible multiphase flows. In this scheme, considering the multiphase interfaces at the immersed boundary, an improved immersed boundary method for effectively suppressing the non-physical force oscillation is proposed. Additionally, a quaternion-based six degrees of freedom motion system is used to describe rigid body motion, and the multiphase flow Eulerian finite element method is applied as the fluid solver. Using analytical solutions, experimental data and literature data, the accuracy and robustness of the FSI scheme are validated. Finally, the high-speed water entry of the slender body with different noses is investigated, and the hydrodynamic loads including the axial and normal drag forces and the bending moment are extensively discussed. The hydrodynamic load and motion trajectory are determined by the nose configuration. The tail slamming phenomenon is the primary focus, and it is revealed that its formation is primarily related to the pitch moment formed at the stage of crossing the free surface. Tail slamming also causes violent impact loads, especially bending moments, which may cause slender projectiles to break off. Finally, to combine the features of the flat and hemispherical noses, the water entry of the projectile with a truncated hemispherical nose is simulated and discussed.

The dynamics of hydrogen bubbles produced by water electrolysis in an acidic electrolyte is studied using electrochemical and optical methods. A defined cyclic modulation of the electric potential is applied at a microelectrode to produce pairs of interacting H$_2$ bubbles in a controlled manner. Three scenarios of interactions are identified and studied systematically. The most prominent one consists of a sudden reversal in the motion of the first detached bubble, its return to the electrode, and finally its coalescence with the second bubble. Attested by Toepler's schlieren technique, an explanation of contactless motion reversal is provided by the competition between buoyancy and thermocapillary effects.

Nucleate boiling, a ubiquitous heat transfer mode, involves multiple vapour bubble nucleations on the heater surface and offers high heat transfer coefficients. The bubble growth process on a heating substrate involves the formation of microlayer, a thin liquid film trapped between the growing bubble and the heating substrate, and contributes to the bubble growth phenomenon through evaporation. Microlayer dynamics for a single bubble have been widely investigated in the pool and flow boiling conditions. However, the literature on multiple bubbles interactions and their associated microlayer information is scarce. Notably, in the case of flow boiling, where the microlayer dynamics are not symmetric due to the bubble's movement, the bubbles’ interaction and its influence on associated microlayer dynamics have never been reported. Therefore, microlayer and bubble dynamics in multiple interactions have been investigated experimentally using simultaneous application of thin-film interferometry and high-speed videography techniques in flow boiling with water as the working fluid. Our experimental investigation revealed that the secondary nucleation could cause a reduction in lift-off time and may assist or hinder the movement of the first bubble. The experimental results also demonstrated that the secondary nucleation could deplete the microlayer of the first bubble hydrodynamically even when the bubbles are far apart. Furthermore, it has been found that the microlayer depletion rate depends on the growth rate and the location of the secondary nucleation. Hence, this experimental study emphasises the need to consider the interaction of bubbles while modelling boiling flows to avoid overestimating the contribution of microlayer evaporation.

We study the linear stability of bubbles in a capillary tube under external flow. Yu et al. (J. Fluid Mech., vol. 911, 2021, pp. 1–19) showed that a rich variety of bubble dynamics occurs when a downward external flow is applied, opposing the buoyancy-driven ascent of the bubble. They found experimentally and numerically the existence of two branches of solutions that overlap over a finite range of the capillary number of the downward external flow in cases where the Reynolds number is small and the Bond number is larger than the critical value for which the bubble can rise spontaneously (Bretherton, J. Fluid Mech., vol. 10, issue 2, 1961, pp. 166–188). Furthermore, inertialess, symmetry-breaking steady-state shapes were found as the bubble transits near the tipping points of the solution branches. In this work, using steady axisymmetric simulations, we show that the reported multiplicity of solutions can be described using bifurcation diagrams with three branches of steady axisymmetric solutions and two limit points. The linear global stability analysis of the different branches of the stationary axisymmetric solutions demonstrates that the symmetry breaking is due to the development of three-dimensional instabilities with azimuthal wavenumber $|m|=1$.

The transition to dripping in the gravity-driven flow of a liquid film under an inclined plate is investigated at zero Reynolds number. Computations are carried out on a periodic domain assuming either a fixed fluid volume or a fixed flow rate for a hierarchy of models: two lubrication models with either linearised curvature or full curvature (the LCM and FCM, respectively), and the full equations of Stokes flow. Of particular interest is the breakdown of travelling-wave solutions as the plate inclination angle is increased. For any fixed volume, the LCM reaches the horizontal state where it attains a cosine-shaped profile. For sufficiently small volume, the FCM and Stokes solutions attain a weak Young–Laplace equilibrium profile, the approach to which is described by an asymptotic analysis generalising that of Kalliadasis & Chang (J. Fluid Mech., vol. 261, 1994, pp. 135–168) for the LCM. For large volumes, the bifurcation curves for the FCM and Stokes model have a turning point so that the fully inverted state is never reached. For fixed flow rate, the LCM blows up at a critical angle that is well predicted by asymptotic analysis. The bifurcation curve for the FCM either has a turning point or else reaches a point at which the surface profile has an infinite slope singularity, indicating the onset of multi-valuedness. The latter is confirmed by the Stokes model, which can be continued to obtain overturning surface profiles. Overall, the thin-film models either provide an accurate prediction for dripping onset or else supply an upper bound on the critical inclination angle.

This paper presents a numerical investigation of the effects of the moving ground and rotating wheels on the turbulent flow around a 1/10 scaled square-back van model. A comprehensive comparison among the partially averaged Navier–Stokes (PANS), large eddy simulation (LES) and particle image velocimetry (PIV) involving the aerodynamic drag, the wake topology, the velocity and the Reynolds stress profiles in the wake region is conducted. The proper orthogonal decomposition (POD) and fast Fourier transform (FFT) are applied to the shear layers shedding from the trailing edges to comment on the coherent structures and their frequency content. The Reynolds number for both simulations and experiments is set to Re = 2.5 × 105 based on the inlet velocity ${U_{inf}} = 9\;\textrm{m}\;{\textrm{s}^{ - 1}}$ and the width of the model W = 0.17 m. The results show that PANS accurately predicts the flow field measured in experiments and predicted by a resolved LES, even with a low-resolution grid. The superiority of the PANS approach could provide good guidance for industrial research in predicting the turbulent flow around the square-back van model with affordable computational grids. The ground and wheel motion mechanism on the aerodynamic forces has been revealed by analysing the surface pressure distribution, the wheels’ surrounding flow, the underbody flow characteristics and the turbulent wake structures. The effects of the ground and wheel motion on the frequency, evolution and development characteristics of the wake shear layers are analysed, thus providing relevant insights for future experimental investigations of square-back van models.

The impact of a heavier droplet falling into a deep pool of lighter liquid is investigated using three-dimensional numerical simulations. We demonstrate that the heavier droplets can hang from the surface of a lighter liquid using surface tension. The impact phenomenon and the evolution of the heavier droplet as a function of its size and release height are explored. A theoretical model is also formulated to understand the role of different forms of energy associated with the hanging droplet. We further solve the force balance equations for the hanging droplets analytically, and demonstrate that the results obtained from our simulations match very well the analytical solution. This research offers opportunities in many areas, including drug and gene delivery, encapsulation of biomolecules, microfluidics, soft robots, and remediation of oil spills.