We performed three-dimensional simulations to study the motion and interaction of microswimmers (pulling- and pushing-type squirmers) and spheres for Reynolds numbers ranging from 0.01 to 1 under conditions in which all particles were axially aligned with each other. We show that pullers are attractive and pushers are repulsive, in terms of the pressure at the front and rear of the squirmers. Correspondingly, the pullers always come close to each other and form a string that swims slightly faster than does a single puller. A possible reason for this finding is discussed. In contrast, whether a leading puller touches a trailing pusher depends primarily on its strength. When the two have similar strengths, they come into contact and form a stable doublet with finite inertia. The speed of the doublet is substantially higher than that of a single pusher owing to the additional force stemming from the fore and aft pressure differences of the doublet. We also demonstrate how a leading pusher interacts with a trailing puller, which is quite different. In contrast, a sphere can be directly or hydrodynamically ‘pushed’ to run by a puller or a pusher. In particular, we reveal that the sphere exhibits the highest speed when ‘pulled’ by a leading puller and ‘pushed’ by a trailing pusher simultaneously. Grouping behaviours reflect the interacting nature of the microswimmers and spheres from different aspects. A bunch of pushers/pullers eventually appears in pairs or forms a string depending on the Reynolds number, similar to groups of pushers/spheres and pullers/spheres.

This study investigates droplet impact on elastic plates using a two-phase lattice Boltzmann method in both two-dimensional (2-D) and three-dimensional (3-D) configurations, with a focus on rebound dynamics and contact time. The 2-D simulations reveal three distinct rebound modes – conventional bounce, early bounce and rim rising – driven by fluid–structure interaction. Among them, the early bounce mode uniquely achieves a significant reduction in contact time, occurring only at moderate plate oscillation frequency. Momentum analysis shows a non-monotonic relationship between vertical momentum transfer and rebound efficiency: increased momentum does not necessarily promote rebound if it concentrates in a central jet, which contributes minimally to lift-off. This introduces a novel rebound mechanism governed by momentum distribution morphology rather than total magnitude. A theoretical model treating the droplet–plate system as coupled oscillators is developed to predict contact time in the early bounce regime, showing good agreement with numerical results. The mechanism and model are further validated through fully 3-D simulations, confirming the robustness of the findings.

Plane unsteady potential flows of an ideal incompressible fluid with a free boundary are considered in the absence of external forces and surface tension. At the initial time, the flow occupy a wedge with an angle at the apex. For different initial flow velocities and values of the angle at the vertex, a family of exact solutions is found. A method for finding solutions based on reducing the boundary-value problems to systems of ordinary differential equations.

Groundwater is a critical support system for agriculture, domestic and industrial consumption in India, but escalating depletion and climatic stresses underscore the need for scientifically robust groundwater potential zone (GWPZ) mapping. In response to the aggravating water security issues in India, this study presents a critical and systematic-methodical review of research articles focused on GWPZ mapping. The primary goal of this research is to integrate input parameters, modeling techniques and validation methods to produce an evidence-based framework for selecting appropriate and effective GWPZ mapping strategies. Six prominent thematic categories – topography, geology, hydrology, climate, land cover and aquifer properties – seem to be inevitably predominant in different physiographic zones. Methodological tendencies suggest a shift from conventional Multi-Criteria Decision-Making models, that is, Analytical Hierarchy Process and Frequency Ratio, toward sophisticated machine learning techniques like Random Forests, Support Vector Machine and Extreme Gradient Boosting. Validation practices are dominated by a high incidence of receiver operating characteristic curve analysis and area under the curve metrics, with occasional addition of precision, recall, F1-score and root mean square error. Across the studies reviewed, field-derived data, well yield, groundwater depth, aquifer thickness and resistivity surveys remain critical for ground-truthing model results. Our view is that even though Indian GWPZ research has taken significant methodological strides, regional data heterogeneity, aquifer complexity and climatic variability issues continue to pose a key challenge in GWPZ mapping. We suggest future strategies involving high-resolution datasets, three-dimensional subsurface modeling, climate-resilient algorithms and more diversified validation frameworks. Through this critical synthesis, the article presents an integrated guide to support planners select cost-effective mapping techniques, inform policymakers on strategic investments and data collection priorities and direct researchers toward the most critical scientific gaps in India’s increasingly dynamic hydro-environmental context.

Hysteresis in the transition between regular reflection (RR) and Mach reflection (MR) has been predicted theoretically and numerically for decades, yet successful experimental demonstrations have remained limited to wedge-angle-variation-induced hysteresis. This work presents the first successful experimental demonstration of Mach-number-variation-induced hysteresis. Utilising a newly developed continuously variable Mach 5–8 wind-tunnel nozzle, Mach-sweep experiments were conducted on a pair of wedges at three different angles ($25^{\circ }$, $27^{\circ }$ and $28^{\circ }$). A stable RR was first established at Mach 7 within the dual-solution domain for each angle, and then the Mach number was decreased to 5. For the $27^{\circ }$ and $28^{\circ }$ cases, transition from RR to MR was observed at Mach 5.3 and 5.9, respectively, during the downward Mach sweep, and the MR state persisted throughout the upward sweep back to Mach 7. During the $25^{\circ }$ case, a stable RR was maintained throughout the entire Mach sweep, prompting further experiments into the effect of free-stream disturbances on the stability of the RR state. Preliminary results revealed a free-stream-disturbance-induced hysteresis and that the RR state is metastable with potential stochastic behaviour.

A heaving and pitching wing encountering effective angle-of-attack perturbations at the Reynolds numbers of 2000 and 20 000 is numerically studied by using an immersed boundary–lattice Boltzmann method. The perturbations are introduced as an abrupt heaving or pitching motion superposed on the baseline motion. It is found that the lift increment scales with the increase in the perturbation effective angle of attack, especially during the heaving perturbation. The pitching perturbation is more likely to disrupt this scaling due to the transition of the leading-edge vortex (LEV) detachment mechanism, where the detachment mechanism of the LEV transitions from bluff-body shedding dominant to vorticity layer eruption dominant. Despite the same variation in the effective angle of attack for the heaving and pitching perturbations, vorticity layer eruption is more likely to occur under the fast pitching perturbation. When the Reynolds number is increased to 20 000, the time histories of aerodynamic force are similar to those at the Reynolds number of 2000. Moreover, the boundary layer under the LEV is more resistant to the adverse pressure gradient, leading to greater variability in vorticity layer eruption.

Transonic buffet is a complex and strongly nonlinear unstable flow sensitive to variations in the incoming flow state. This poses great challenges for establishing accurate-enough reduced-order models, limiting the application of model-based control strategies in transonic buffet control problems. To address these challenges, this paper presents a time-variant modelling approach that incorporates rolling sampling, recursive parameter updating and inner iteration strategies under dynamic incoming flow conditions. The results demonstrate that this method successfully overcomes the difficulty in designing appropriate training signals and obtaining unstable steady base flow. Additionally, it improves the global predictive capability and identification efficiency of linear models for nonlinear flow-system responses by more than one order of magnitude. Furthermore, two adaptive control strategies – minimum variance control and generalised predictive control – are validated as effective based on the time-variant reduced-order model through numerical simulations of the transonic buffet flow over the NACA 0012 aerofoil. The adaptive controllers effectively regulate the unstable eigenvalues of the flow system, achieving the desired control outcomes. They ensure that the shock wave buffet phenomenon does not recur after control is applied, and that the actuator deflection, specifically the trailing-edge flap, returns to zero. Moreover, the control results further confirm the global instability essence of transonic buffet flow from a control perspective, thereby deepening the cognition of this nonlinear unstable flow.

The low Reynolds number solution of the wind–wave interaction problem is found in Cimarelli et al. (2023 J. Fluid Mech. vol. 956, A13), to be characterised by a skewed pattern of small-elevation waves on the bottom of a turbulent wind where drag reduction is caused by a wave-induced Stokes sublayer. The inhomogeneous, anisotropic and multiscale phenomena at the basis of this interesting solution are analysed here by means of the generalised Kolmogorov equation. It is found that the large and coherent structures populating the wind are the result of an upward shift of the self-sustaining production mechanisms of turbulence and of intense reverse energy cascade phenomena. The upward shift of production and the intensification of the reverse cascade are recognised to be the result of a periodically distributed pumping of scale energy induced by the pressure field associated with the wave-induced Stokes sublayer. The low dissipative nature of the wind–wave interface region is also investigated and is found to be related to a layering effect generated by the simultaneous presence of wave-induced pressure fluctuations and of wind-induced velocity fluctuations that interact with each other in an incoherent manner. Finally, the theoretical framework provided by the generalised Kolmogorov equation is also used to rigorously define two relevant cross-over scales for the filtering formalism, the shear scale identifying the energy-containing motion and the split energy cascade scale identifying the cross-over between forward and backward cascades. Well-defined quantitative criteria for the definition of spatial resolution and for the selection of turbulence closures in coarse-grained approaches to the wind–wave problem are provided.

We explore the fundamental flow structure of temporally evolving inclined gravity currents with direct numerical simulations. A velocity maximum naturally divides the current into inner and outer shear layers, which are weakly coupled by momentum and buoyancy exchanges on time scales that are much longer than the typical time scale characterising either layer. The outer layer evolves to a self-similar state and can be described by theory developed for a current on a free-slip slope (Van Reeuwijk et al. 2019, J. Fluid Mech., vol. 873, pp. 786–815) when expressed in terms of outer-layer properties. The inner layer evolves to a quasi-steady state and is essentially unstratified for shallow slopes, with flow statistics that are virtually indistinguishable from fully developed open channel flow. We present the classic buoyancy–drag force balance proposed by Ellison & Turner (1959, J. Fluid Mech., vol. 6, pp. 423–448) for each layer, and find that buoyancy forces in the outer layer balance entrainment drag, while buoyancy forces in the inner layer balance wall friction drag. Using scaling laws within each layer and a matching condition at the velocity maximum, the entire flow system can be solved as a function of the slope angle, in good agreement with the simulation data. We further derive an entrainment law from the solution, which exhibits relatively high accuracy across a wide range of Richardson numbers, and provides new insights into the long runout of oceanographic gravity currents on mild slopes.

Understanding the flow behaviour of wet granular materials is essential for comprehending the dynamics of numerous geological and physical phenomena, but remains a significant challenge, especially the transition of these flow regimes. In this study, we perform a series of rotating drum experiments to systematically investigate the dynamic observables and flow regimes of wet mono-dispersed particles. Two typical continuous flows including rolling and cascading regimes are identified and analysed, concentrating on the impact of fluid density and rotation speed. The probability density functions of surface angles, $\theta _{\textit{top}}$ and $\theta _{\textit{lo}w\textit{er}}$, reveal distinct patterns for these two flow regimes. A morphological parameter thus proposed, termed angle divergence, is used to characterise the rolling–cascading regime transition quantitatively. By integrating quantitative observables, we construct the flow phase diagram and flow curve to delineate the transition rules governing these regimes. Notably, the resulting nonlinear phase boundary demonstrates that higher fluid densities significantly enhance the likelihood of the system transitioning into the cascading regime. This finding is further supported by corresponding variations in flow fluctuations. Our results provide new insights into the fundamental dynamics of wet granular matter, offering valuable implications for understanding the complex rheology of underwater landslides and related phenomena.