Recent theoretical and experimental investigations have revealed that flapping compliant membrane wings can significantly enhance propulsive performance (e.g. Tzezana & Breuer J. Fluid Mech., 2019, vol. 862, pp. 871–888) and energy harvesting efficiency (e.g. Mathai et al. J. Fluid Mech., 2022, vol. 942, p. R4) compared with rigid foils. Here, we numerically investigate the effects of the in-plane stretching stiffness (or aeroelastic number), $K_{\!S}$, the flapping frequency, ${\textit{St}}_c$, and the pitching amplitude, $\theta _0$, on the propulsive performance of a compliant membrane undergoing combined heaving and pitching in uniform flow. Distinct optimal values of $K_{\!S}$ are identified that respectively maximise thrust and efficiency: thrust can be increased by 200 %, and efficiency by 100 %, compared with the rigid case. Interestingly, these optima do not occur at resonance but at frequency ratios (flapping to natural) below unity, and this ratio increases with flapping frequency. Using a force decomposition based on the second invariant of the velocity gradient tensor $Q$, which measures the relative strength between the rotation and deformation of fluid elements, we show that thrust primarily arises from $Q$-induced and body-acceleration forces. The concave membrane surface can trap the leading-edge vortex (LEV) generated during the previous half-stroke, generating detrimental $Q$-induced drag. However, moderate concave membrane deformation weakens this LEV and enhances body-acceleration-induced thrust. Thus, the optimal $K_{\!S}$ for maximum thrust occurs below resonance, balancing beneficial deformation against excessive drag. Furthermore, by introducing the membrane’s deformation into a tangential angle at the leading edge and substituting it into an existing scaling law developed for rigid plates, we obtain predictive estimates for the thrust and power coefficients of the membrane. The good agreement confirms the validity of this approach and offers insights for performance prediction.

Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control or other problem parameters. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise comparisons but can fail to distinguish distributional changes in flow fields. To address this limitation, we employ optimal transport (OT) theory, which is a mathematical framework built on probability and measure theory. By aligning Euclidean distances between flow fields in a latent space learned by an autoencoder with the corresponding OT geodesics, we seek to learn low-dimensional representations of flow fields that are interpretable from the perspective of unbalanced OT. As a demonstration, we utilise this OT-based analysis on separated flows past a NACA 0012 airfoil with periodic heat flux actuation near the leading edge. The cases considered are at a chord-based Reynolds number of 23 000 and a free-stream Mach number of 0.3 for two angles of attack (AoA) of $6^\circ$ and $9^\circ$. For each angle of attack, we identify a two-dimensional embedding that succinctly captures the different effective regimes of flow responses and control performance, characterised by the degree of suppression of the separation bubble and secondary effects from laminarisation and trailing-edge separation. The interpretation of the latent representation was found to be consistent across the two AoA, suggesting that the OT-based latent encoding was capable of extracting physical relationships that are common across the different suites of cases. This study demonstrates the potential utility of optimal transport in the analysis and interpretation of complex flow fields.

Experimental deep reinforcement learning (DRL) control of a turbulent boundary layer is conducted for the first time at $Re_\tau$ = 1196, with the aim of friction-drag reduction. Two hot films, an impinging plasma jet actuator array and two wall hot wires act as the state detector, flow disturber and reward evaluator, respectively. The control law parametrised by a radial basis function network is executed in real time on a field programmable gate array and optimised using a classical value-based algorithm (deep Q-network). Results show that DRL control requires only 30 s to train a closed-loop control law with satisfactory drag-reduction performance. Compared with open-loop control where only fine-tuned periodical forcing can reduce the friction drag, the experimental efficiency is improved significantly. Proper setting of the hyper-parameters is crucial in DRL. Particularly, the reward time delay and control frequency need to match the convection time scale and the characteristic frequency of the turbulent boundary layer. The optimal DRL control setting achieves 6.7 % relative drag reduction, almost three times that of the best open-loop control (2.3 %). Physically, plasma actuation induces alternating low-speed and high-speed zones that confine the sidewise motion of turbulent streaks. The final control law optimised by DRL can be simplified as a threshold control, firing the plasma actuator after perceiving a streak burst event and a long-lasting high-speed zone. Control benefits are attributed to the increase in the occurrence probability of high-reward states and the elevation of mean reward at different clusters.

In this work, we propose a lattice Boltzmann model (LBM) to simulate diverse particle deposition patterns induced by isothermal droplet evaporation. The model is composed of two distributions, for the multiphase flow with phase change, and the particle transport with deposition, coupled with a contact angle hysteresis model for the contact line stick-slip dynamics. The model is validated by two benchmarks, and our simulations agree well with the theoretical solutions or experimental results. With the validated LBM, we first reproduced diverse deposition patterns, ranging from the coffee ring, uniform, to mountain-type patterns in single and multiple symmetrical/unsymmetrical forms. Then a parametric study is conducted to investigate how the solvent/particle/substrate properties affect the evaporation dynamics and resultant deposition patterns. Afterwards, we apply the average ratio ($r_{\phi ,a}$) of particles deposited at the droplet periphery and the centre to quantitatively classify the diverse emerging patterns. We show that $r_{\phi ,a}$ is controlled by the competition between the capillary transport and particle diffusion, leading to a linear dependence on the average Péclet number $\textit{Pe}_{a}$. Finally, we validated the scaling by lattice Boltzmann simulations with the proposed $\textit{Pe}_{a}$ spanning over three orders of magnitude, supplemented by discussions from the aspect of the particle transport equation.

This article presents experimental measurements of breaking wave impact loads on a vertical cylinder. The focus is on the influence of some of the breaking wave properties on the measured force. These properties are the distance to breaking, $\delta$, defined as the distance between the breaking location and the front face of the cylinder, and the breaking strength, characterised here by the $\varGamma$ parameter proposed by Derakhti et al. (J. Fluid Mech., 2018, vol. 848, p. R2). The wave characteristics are obtained through numerical simulations of the breaking waves using a fully nonlinear potential flow solver. Seven breaking waves with different breaking strengths have been considered. For each wave, the distance to breaking has been systematically varied and the resulting impact force time-history was measured. It is found that except for the two less intense breaking cases, corresponding to values of $\varGamma$ lower than one, there is a value of $\delta$ for which the magnitude of the impact force is maximum. Small variations of the distance to breaking $\delta$ strongly influence the impact force time-history and its maximum. A linear relationship is observed between the maximum force and the breaking strength $\varGamma$. For the wave cases with values of $\varGamma$ higher than one, the maximum impact force is observed when the distance to breaking $\delta$ is close to 5 % of the wavelength.

The acoustic fields of a contra-rotating propeller and isolated propellers producing the same overall thrust are compared at both design and off-design working conditions. The sound levels are reconstructed by using the Ffowcs Williams–Hawkings acoustic analogy, exploiting results of computations conducted on a cylindrical grid consisting of $4.6 \times {10}^9$ points and a large-eddy simulation technique. The analysis shows that, although the blades of the contra-rotating propeller are less loaded and produce less intense flow structures, the levels of radiated sound are reinforced, compared with the propellers working alone. This is due to the loading sound, originating from the pressure fluctuations on the surface of the blades of the propellers. The higher levels of linear sound are attributable to the interplay between the front and rear rotors of the contra-rotating system. This interaction is able to reinforce the unsteady component of the loads acting on the blades of the propellers and the resulting linear component of sound. While the shear occurring between the tip vortices shed by the front and rear rotors gives rise to a complex system of isolated vortex rings in the wake, increasing the quadrupole component of sound, these phenomena are balanced by the lower intensity of the vortices shed by the contra-rotating system.

We derive the far-field and near-field solutions for the Green’s function of a point force acting perpendicular to a no-slip wall in a Brinkman fluid, focusing on the regime where the distance between the force and the wall is much smaller than the screening length. The general solution is obtained in closed form up to a single integral, and can be systematically expanded in a Taylor series in both the far-field and near-field limits. The flow can then be expressed as a series of source-multipole singularities with an additional, analytically known, correction in the proximity of the wall. Comparisons with numerical integration demonstrate the accuracy and reliability of the asymptotic expansions. The results are also applicable to the unsteady Stokes flow driven by a localised assembly of forces, such as a beating cilium protruding from a flat surface.

This study experimentally investigates the bleeding flow characteristics downstream of isotropic porous square cylinders as a function of permeability and pore configuration across a broad range of Darcy numbers ($2.4 \times 10^{-5} \lt \textit{Da} \lt 2.9 \times 10^{-3}$). The porous cylinders, constructed with a simple cubic lattice design, were fabricated using a high-resolution three-dimensional printing technique. This novel design method, based on a periodic and scalable lattice structure, allows fine control over the number of lattice pores along the cylinder width, $D$, and the corresponding permeability, independently of porosity. Permeability was carefully determined by measuring the pressure drop and superficial velocity for each porous structure considered in this study. High-resolution particle image velocimetry measurements were conducted in an open-loop wind tunnel to characterize the downstream flow structures. The results reveal that bleeding flow characteristics near the cylinder trailing edge are strongly influenced by both permeability and pore configuration. These structural behaviours are further explored using an analogy to multiple plane turbulent jets. This approach identifies three distinct flow regions downstream of porous square cylinders, determined by the structural pattern of the bleeding flow. Additionally, an analytical framework is developed to model the longitudinal extent of the merging region by integrating the momentum equation, incorporating the Darcy–Brinkman–Forchheimer model, with a boundary layer assumption. The analytical model is validated against experimental data, demonstrating its capability to predict the key dynamics of bleeding flow evolution. Our results provide new insights into the fluid dynamics of porous bluff bodies, establishing pore configuration and permeability as dominant parameters governing downstream flow structures.

This paper develops scaling laws for wall-pressure root mean square and the streamwise turbulence intensity peak, accounting for both variable-property and intrinsic compressibility effects – those associated with changes in fluid volume due to pressure variations. To develop such scaling laws, we express the target quantities as an expansion series in powers of an appropriately defined Mach number. The leading-order term is represented using the scaling relations developed for incompressible flows, but with an effective Reynolds number. Higher-order terms capture intrinsic compressibility effects and are modelled as constant coefficients, calibrated using flow cases specifically designed to isolate these effects. The resulting scaling relations are shown to be accurate for a wide range of turbulent channel flows and boundary layers.

Numerical simulations and theoretical analysis are conducted to investigate the Atwood-number dependence of perturbation evolution in a shocked heavy fluid layer. For layers without reverberating waves, a higher Atwood number of one interface significantly enhances its coupling effect on the perturbation growth at the opposite interface. A theoretical model incorporating the startup, linear and nonlinear stages is developed to predict the interface mixing width. Dimensionless formulae are derived, identifying eight distinct modulation regimes of multi-interface instability. When reverberating waves are present, the individual effects of the upstream ($A_1$) and downstream ($A_2$) Atwood numbers are examined. The model is further modified to account for additional reverberating waves required at higher $A_2$ values for accurate amplitude prediction. Both theory and simulations demonstrate that perturbation growth at one interface can be actively controlled by adjusting the Atwood number of the opposite interface. These findings provide insights for mitigating instabilities in applications such as inertial confinement fusion through appropriate material selection.

We carry out an experimental study of granular flow in a quasi-two-dimensional wedge-shaped hopper, with glass front and back walls, using videography, along with image analysis and particle tracking. Results are presented for different orifice sizes and roughnesses of the sidewalls for nearly spherical glass and steel particles of different sizes. The data for the radial velocity in the hopper (wedge angle $2\theta _w$) are well described by $v_r(r,\theta )=v_{r0}(r)[1-F(r)(\theta /\theta _w)^2],$ in cylindrical coordinates $(r,\theta )$, with the origin at the apex of the wedge. The centreline velocity is given by $v_{r0}=(a_0/r+a_1)$, and the effective wall friction by $F=(b_0+b_1r)$, where $a_0$ and $a_1$ increase with orifice width, while $b_0$ increases with roughness. For the smooth wall system, we obtain $F\in (0,1)$, however, for the rough walls $F\gt 1$ for most cases, with the velocity at the wall being zero, and a few layers of slow-moving particles adjacent to the wall. The mass flow rate scaled by the particle density and the radial velocity profile are independent of the particle density, for a threefold increase in the density, implying insignificant inertial effects. Discrete element method simulations are carried out using glass particles for a system of the same size as the experimental hopper, with the simulation parameters calibrated to closely match the experimental results. The simulation results indicate that the variation in the direction normal to the plane of the flow is small and the radial velocity profiles without the front and back walls are similar to the experimental profiles.

The effects arising from interactions between two identical starting jets on their propulsive characteristics have been investigated numerically for different dimensionless distances $S/D$ (the distance between two jet axes normalised by nozzle diameter, from 1.1 to 4) and stroke ratios $L/D$ (the length-to-diameter ratio of jet column, from 2 to 5). The two jets are arranged in parallel and initiated simultaneously with identical conditions. Their leading vortical structures evolve from an axisymmetric to a plane-symmetric configuration, with deceleration in regions where the two jet wakes approach each other. The generation of axial thrust is affected, primarily dominated by variations in the pressure thrust component. This results from the combination of the mutually induced pressure (MIP) and the coupling effects of vortex rings (CEVR for $S/D\gt1.5$ and CEVR-R for $S/D\lt1.5$). The MIP governs the fluctuations introduced into thrust development, while CEVR (CEVR-R) is responsible for the reduction in average thrust. These effects become more pronounced as $S/D$ decreases, but remain almost unaffected by $L/D$. Adjusting the acceleration and deceleration rates of the velocity program shows limited effects on either the thrust fluctuations or the average thrust reduction. Furthermore, the interaction induces two lateral force components with equal magnitude but opposite directions on the outer walls of the two nozzles, with their magnitude exceeding $15\,\%$ of the axial thrust. The introduction of an additional vertical wall within the nozzle exit plane effectively eliminates the lateral force. However, it consequently enhances both the average thrust reduction and the thrust fluctuations induced by the interaction.

This work presents an analytical solution for the steady laminar wake generated by a finite wall segment acting as a sink for heat or mass transfer. The classical Lévêque solution is extended to include the wake region downstream of the active surface by employing Laplace transform methods to couple Dirichlet and Neumann boundary value problems through convolution identities. This yields a unified closed-form expression for the scalar field that reduces to the Lévêque result above the sink and provides a new analytical expression for the wake region. Numerical simulations confirm the analytical solution, with errors decreasing systematically under mesh refinement. The derived expressions enable direct calculation of scalar recovery at any point in the wake, providing essential information for designing segmented systems where wake interference between adjacent active elements must be predicted. The solution also serves as a benchmark for numerical methods solving mixed boundary value problems in convective transport.

Negatively electrified liquid cone jets supported on capillary tubes with 30–36 $ \,\unicode{x03BC} \text{m}$ tip diameters are investigated in vacuo with four ionic liquids (ILs) selected for their high electrical conductivity and low viscosity. All four use the same cation 1-ethyl-3-methylimidazolium$^+$ ($ \text{EMI}^+$), paired with the four anions $\textrm{SCN}^-$, $\text{N}(\text{CN})_2^-$, $\text{C}(\text{CN})_3^-$ and $ \text{BF}_4^-$. Purely ionic (PI) emissions are not unambiguously achieved with any of the four, but are closely approached by all under a broad range of conditions. In this unusual quasi-ionic (QI) regime, drops contribute minimally to the current ($\sim$ 0.5 %–3 %) but substantially to the mass flow. A sharp QI$\rightarrow$PI transition below a critical liquid flow rate has been demonstrated for capillary emitters by Caballero-Perez et al. (2025) J. Propul. Power, for 1-butyl-3-methylimidazolium-C(CN)$_3$ (BMI-C(CN)$_3$) by using 15 $\unicode{x03BC}$m capillary tips able to stabilise unusually small liquid flow rates. None of their other 3 ILs achieves the QI regime, indicating the singularity of BMI-C(CN)$_3$ and our four ILs. We focus on the peculiarities of the QI regime, the likely mechanism for the QI$\rightarrow$PI transition and argue that ILs reaching the QI regime will probably also attain the PI regime when sprayed from sufficiently small capillary tips. Paradoxically, while high conductivity and low viscosity appear to favour the QI mode, for a liquid operating in this regime, inverting these properties by lowering the emitter temperature appears to better approach the PI regime.

We investigate the linear stability of a Plateau border and the existence of solitary waves. Firstly, we formulate a new non-orthogonal coordinate system that describes the specific geometry of a Plateau border. Within the framework of this coordinate system, the equations of motion for the fluid potential and free surface are derived. By performing a linear stability analysis we find that the Plateau border is stable under small perturbations. Next, a weakly nonlinear theory is developed, leading to a Korteweg–de Vries equation for the free surface profile. Our weakly nonlinear evolution equation predicts depression solitary waves, such as those observed by Bouret et al. (Phys. Rev. Fluids., 2016, vol. 1 no. 4, p. 043902).

Cavitation inception in the wake of propulsor systems often arises from the interaction between multiple vortices. We use large-eddy simulation (LES) to study cavitation during the canonical interaction of a pair of unequal strength counter-rotating vortices generated in the wake of a hydrofoil pair at a chord-based Reynolds number ($ \textit{Re}$) of $1.7 \times 10^6$. The simulations reproduce the experimental observations by Knister et al. (In 33rd Symposium on Naval Hydrodynamics, Osaka, Japan, 2020) of spatially and temporally intermittent inception events occurring in the weaker vortex. Sinusoidal instabilities representing the Crow instability develop on the weaker vortex beyond one chord length downstream of the hydrofoils, causing it to bend and wrap around the stronger vortex. The inviscid stretching causes a significant reduction of the weaker core pressure and inception occurs as it approaches close to the stronger core. These intermittent inception events correspond to $3{-}4$ fold pressure reduction from the unperturbed value, with the instantaneous pressures reaching $40\,\%{-}60\,\%$ lower than the mean minimum pressure. However, the loss of circulation (${\gt} 20\,\%$) in both cores during the later stages of interaction reduces the possibility of further inception events. Statistical analysis reveals that inception occurs once per Crow cycle and is most likely to occur near the central regions of the Crow wavelength. Conditional averages show that the axial stretching is non-uniform along the weaker vortex axis, with the stretching intensities in the central regions being four times larger than the wavelength-averaged value. Probability distribution analysis shows that only a small portion of the weaker core experiences inception pressures and these regions have relatively lower axial stretching intensities compared with the bulk of the core.

This research investigates the hydrodynamics of a physical boundary transition from free slip to no slip, which usually occurs in ice-jams, large wood and debris accumulation in free-surface flows. Using direct numerical simulation coupled with a volume penalisation method, a series of numerical simulations is performed for an open-channel flow covered with a layer of floating spherical particles, replicating the laboratory set-up of Yan Toe et al. (2025 J. Hydraul. Eng., vol. 151, 04025010). Flow transition from the open channel to the closed channel induces a new boundary-layer development at the top surface, accompanied by a flow separation and an increased bottom shear stress that enhances particle mobility at the bottom. Analysis of a fully developed flow in an asymmetric roughness channel (rough surface at the top boundary and smooth surface at the bottom boundary) also shows that the vertical position of maximum velocity is higher than the position of zero Reynolds shear stress, which supports the experimental observation of Hanjalić & Launder (J. Fluid Mech., vol. 51, 1972, pp. 301–335), demonstrating the shortcoming of traditional turbulence closure models such as the $k{-}\varepsilon$ model. Finally, the stagnation force acting on a particle at the leading edge of the accumulation layer is compared with the analytical prediction of Yan Toe et al. Understanding the flow transition improves the prediction of the stability threshold of the accumulation layer and design criteria for debris-collection devices.