We compare an inviscid vortex sheet model with continuous leading-edge shedding with direct Navier–Stokes simulations over a wide range of unsteady plate motions at moderate Reynolds number (${\textit{Re}} \approx 1000$). Approximately $70$ distinct kinematic configurations are examined, spanning both body-dominated and flow-dominated regimes. In body-dominated motions, where the fluid dynamics are primarily driven by prescribed plate accelerations, the inviscid model accurately reproduces normal force histories and the qualitative structure of the induced vorticity field. In flow-dominated configurations, with quasi-periodic vortex shedding, agreement with force predictions is good but reduced at low angles of attack, reflecting the greater sensitivity of vortex shedding dynamics to physical and computational parameters. The ability of the present formulation to accommodate stable, continuous leading-edge vortex shedding enables uniform comparisons across diverse motions and clarifies the regimes in which inviscid vortex sheet models can be used reliably for force prediction and physical interpretation.

The method of three-dimensional curved characteristics (MOTC), built upon the three-dimensional curved shock theory (3D-CST-boos), is developed to uncover the downstream flow physics of three-dimensional shock-dominated supersonic flows. Starting from the post-shock pressure gradients and streamline curvatures supplied by 3D-CST-boos at the shock surface, MOTC advances these quantities along streamlines and characteristics to construct the complete downstream flowfield. The methodology derives a comprehensive set of governing equations, including gradient terms, along streamlines and characteristics. A key advantage over conventional osculating methods lies in its retention of the lateral pressure gradient and cross-flow information, which substantially enhances the accuracy of three-dimensional flowfield simulations. The method is verified against inviscid CFD for both external and internal flow configurations, achieving errors below 0.5 %. More importantly, the retained gradient information reveals a cross-over of the streamwise compression: near the shock, the pressure gradient is governed by the transverse shock curvature; while further downstream, the lateral pressure gradient drives flow convergence or divergence, reversing the compression ordering across different shock geometries. The lateral pressure gradient distribution is controlled by the shock axial ratio, providing a guideline for shock shape selection in forebody or inlet design. For internal flows, the reflected shock asymmetry is governed by the same shock-curvature-to-transverse-flow transition, offering a physical basis for centre-body design. The combination of accuracy, computational efficiency and the ability to trace flow physics from the shock to the far-field positions MOTC as a powerful tool for analysis and inverse design of supersonic flowfields.

This work provides new lower bounds on the global (nonlinear) stability limit of pressure-driven two-dimensional plane Poiseuille flow, improving on the energy stability limit $\textit{Re}_E$ originally computed by Orr in 1907. Using a computer, we carefully construct quartic Lyapunov functionals of the velocity perturbations about the laminar profile, which certify the nonlinear stability of the flow to arbitrary perturbations. The formulation combines a decomposition of the velocity into finitely many energy eigenmodes, referred to as a ‘mode set’, and an infinite-dimensional ‘tail’, together with explicit bounds that recast the Lyapunov inequality conditions as semidefinite programs, whose feasibility is tested. Over the streamwise lengths considered, the certified stability limit exceeds the classical energy bound. In particular, at the critical energy-stable streamwise length, where $\textit{Re}_E\approx 87.59$, the flow is found to be globally stable up to $\textit{Re} \approx 106.8$ (representing a $22\,\%$ improvement). Various modestly sized mode sets, capable of capturing sufficient features of the nonlinear dynamics of energy growth and subsequent decay, are proposed and found to be successful in producing improved bounds, with the simplest one involving only five modes.

This study investigates the genesis and temporal evolution of turbulent eddies in violent-sloshing flows using a fully meshless computational framework. A quasi-Lagrangian $\delta$-large-eddy simulation–smoothed particle hydrodynamics formulation is employed to solve the weakly compressible Navier–Stokes equations, together with a novel methodology to quantify slosh-induced energy dissipation, where $\delta$ denotes the density-diffusion operator introduced in the $\delta$-SPH formulation. Under violent periodic forcing, the flow exhibits a strongly nonlinear free-surface dynamics, characterised by recurrent wave breaking and energetic impacts against the tank walls. By decomposing the total viscous dissipation into enstrophy-related and deformation-related contributions, we find that the enstrophy fraction remains nearly constant, at around $30\,\%$, across the investigated regimes. Moreover, in the absence of surface tension, the enstrophy-related dissipation does not converge under grid refinement; the inclusion of surface tension regularises this behaviour and promotes a shift of the vortex population towards larger coherent structures. High-resolution two-dimensional simulations, spanning a wide range of spatial resolutions, are complemented by fully three-dimensional simulations and by reduced-width three-dimensional configurations, in which the spanwise direction is fully resolved over a limited extent. This combined analysis shows that, for this class of bounded violent free-surface flows, global loads and energy dissipation are primarily governed by free-surface fragmentation and reconnection, rather than by fully three-dimensional turbulent cascade mechanisms. As a result, two-dimensional simulations provide an accurate description of the dynamics controlling the integral quantities of interest. These findings offer new physical insight into the coupling between free-surface fragmentation, vortex dynamics and dissipation mechanisms in violent sloshing, and establish a reference framework for future studies of turbulence generation in confined free-surface flows.

A widely cited experimental dataset (Cleve et al., J. Fluid Mech., 2019, vol. 875, pp. 597–621) on non-spherical acoustic cavitation dynamics provides a valuable benchmark for model validation, yet its use is hindered by large uncertainties in the two key parameters: the equilibrium bubble radius and the acoustic pressure amplitude. This study introduces a robust parameter-identification framework to resolve these discrepancies and enable meaningful comparison with models. Using an in-house graphics processing unit-accelerated solver for solving the second-order perturbation model developed by Shaw (Phys. Fluids, 2006, vol. 18, issue 7, p. 072104), the dataset is systematically re-examined. A Fourier coefficient-based error metric is developed to quantify the pronounced mismatch between simulations and measurements. The proposed method reliably corrects the vast majority of the experimental parameters, yielding excellent agreement between numerical predictions and observations. The outcome is a validated dataset with accurately identified parameters that can serve as a reliable benchmark for validating advanced computational fluid dynamics simulations and theoretical models. In addition, the approach offers a general tool for future experiments where direct measurements of local acoustic pressure remain difficult.

Bulk permeability controls pore pressure build-up in a granular material and thereby the hydrological conditions under which it deforms. The resulting deformation, in turn, alters pore geometry and consequently the material’s permeability. When simulating deformation, models often update a material’s permeability using parametrisations developed for idealised materials consisting of approximately equisized grains. However, real Earth materials often have wide grain-size distributions with several distinct modes. Here, we derive a model to estimate bulk permeabilities for bidisperse granular materials based on their wide, bimodal grain-size distributions, making progress towards bridging the gap between idealised and Earth materials. By combining direct numerical simulations to simulate pore-scale Stokes flows with sequential homogenisation to exploit the scale-separation among many grain-size modes, we compute flow fields consistent with pore-scale physics with high computational efficiency. We identify when existing techniques for estimating permeability meet their limitations. We validate our model against laboratory measurements of permeability for a two-component mixture of idealised glass beads and sands with scale-separated grain sizes, producing estimates of permeability with quantified variability. We then test our model against laboratory measurements of permeability for subglacial sediments, achieving high accuracy without specific calibration. Our work provides a practical tool to estimate permeability in the presence of deformation for Earth materials using grain-size distributions as an invariant.

This paper presents a model for the full-range formation and propagation process of near- and far-field underwater explosion shock waves. The model combines coordinate mapping with the discontinuous Galerkin method so that fast-moving discontinuities, including the shock front and the bubble interface, remain on subdomain boundaries and do not require conventional shock-capturing treatment. In the near field, the computational domain is divided into interior and exterior regions, and the boundary conditions are supplied analytically through a two-medium Riemann solver and the Hugoniot jump conditions. In the far field, a new equation for the evolution of a finite-strength shock is derived by simplifying the inward characteristic with theoretical analysis. The resulting far-field equation is much less stiff than the full Euler or wave equation system and has a substantially smaller characteristic speed, allowing larger time steps and efficient propagation to long distances. Validation against experimental data shows that the model reproduces both the primary and secondary shocks with good accuracy, and that the far-field model predicts the decay of the shock peak in close agreement with the fully nonlinear near-field solution. Finally, we examine how internal waves repeatedly reflect inside the bubble and generate multiple pressure fluctuations in the emitted pressure history. Through scaling analysis and numerical validation, we identify when internal-wave effects become dynamically important and show that ambient pressure is the dominant controlling parameter.

Axisymmetric waves occur across a wide range of scales. This study analyses large-scale (with a jet height of up to 6 m) gravity-dominated axisymmetric waves (Bond number $ \textit{Bo}=\textit {O}(10^{5})$ and Weber number $\textit{We}=\textit {O}(10^{4}{-}10^{6})$), for which surface-tension effects are negligible. Our aim is to clarify the dynamics of highly nonlinear axisymmetric jet formation, cavity collapse and the consequent generation of secondary jets. The newly developed three-dimensional framework OceanSPHysics3D, combining unsteady potential flow with SPH, provides an integrated platform capable of handling multidirectional and axisymmetric waves, thereby enabling the full simulation of axisymmetric jet initiation and collapse. The computed free-surface elevations and jet evolution agree well with the experiments of McAllister et al. (2022 J. Fluid Mech. 935, A5) and an analytical jet-tip-angle formulation of Longuet-Higgins (1983 J. Fluid Mech. 127, 103–121). The simulations elucidate how the falling primary jet induces a secondary jet. The mechanisms forming the pre-jet trough and post-jet cavity are fundamentally different. The pre-jet trough arises geometrically from directional focusing of the constituent waves, yielding a self-similar shape when appropriately scaled. In contrast, the post-jet cavity is formed inertially by the falling continuous jet, and lacks both spatial and temporal self-similarity. Its collapse also differs: the cavity pinches off at the neck to generate upward and downward secondary jets, with local accelerations reaching $150g$. The primary-jet scale governs the ensuing secondary-jet dynamics, including vortex-ring formation and strong vertical mixing. These findings illustrate the complexity of axisymmetric jet dynamics, and demonstrate the ability of the present framework to reproduce the key coupled processes in such extreme free-surface events.

This study makes a twofold contribution regarding vorticity flux modulation by wall-pressure ‘footprints’. First, we present a continuous data assimilation (DA) framework for reconstructing flow fields from wall-pressure observations by embedding an adjoint-derived scalar source into the pressure Poisson equation. By leveraging elliptic pressure–velocity coupling, the method propagates wall-driven corrections across the domain, and avoids the costly global backward integration of four-dimensional variational DA while retaining phase-aware control of vorticity production and modal energy. Second, we validate the framework on a three-dimensional turbulent flow over a NACA0012 aerofoil at $12^{\circ}$, using synthetic wall-pressure data from high-fidelity large eddy simulations (LES). The DA strategy mitigates unresolved transition physics in coarse simulations by suppressing premature separation, restoring attachment, and recovering key flow metrics with near-LES fidelity. Spectral and wavelet analyses further demonstrate that the reconstruction captures both the scale-dependent energy distribution and the spatial coherence of the dominant structures. Two complementary mechanisms are identified: (i) an oscillator-like mechanism, where phase-locked tangential pressure gradients couple with normal vorticity gradients to modulate near-wall vorticity through linear and nonlinear interactions; and (ii) an amplifier-like mechanism, where trailing-edge inputs propagate upstream via scale-dependent elliptic coupling, exciting receptivity modes, and triggering transition cascades through Orr mechanisms and resolvent-matched instabilities. The sensor coverage study reveals scale-dependent sensitivity: streamwise-elongated motions remain robust under sparse arrays, whereas spanwise-dominated structures require near-wall sensing. These findings broaden the scope of continuous DA for wall-bounded flow reconstructions, offering a computationally efficient way to incorporate wall-pressure observations into existing solvers for enhanced accuracy.

Shallow flows partially obstructed by arrays of rigid elements develop a lateral shear layer that controls momentum exchange, turbulence production and scalar transport. We investigate this interfacial region through a tractable two-layer theoretical framework, laboratory measurements in an unusually wide (4 m) flume and graphics processing unit-accelerated weakly compressible smoothed particle hydrodynamics simulations. The depth-averaged velocity across the interface collapses onto a hyperbolic–tangent profile, enabling closed-form predictions for the mixing-layer thickness, outer-edge velocity and interfacial shear stress via a momentum balance that incorporates detrainment, pressure gradients and obstacle-induced dissipation. Coherent motions consist of quasi-periodic vortices that organise a sweep–ejection cycle and dominate the Reynolds shear stress; conditional statistics reveal a robust phase-locked structure, while Lagrangian trajectories exhibit ballistic, inertial and diffusive dispersion regimes whose anisotropies reflect the vortex scale and lifetime. Classical Rayleigh analysis shows that the depth-averaged velocity profiles are neutrally stable, indicating that the interfacial rollers do not arise from the inviscid Kelvin–Helmholtz instability. Instead, a reduced temporal model reproduces the characteristic instability window of drag-modified shallow shear layers, and the shallow-water modified Rayleigh equation shows that all configurations fall well within the unstable regime. The vortices therefore represent the nonlinear manifestation of a drag-induced lateral instability intrinsic to partially obstructed shallow flows. Together, these results provide a unified description of interfacial momentum balance, coherent-structure dynamics, Lagrangian dispersion and drag-modified stability, and offer physically grounded diagnostics for mixing in environmental and engineered porous-flow interfaces.

This study investigates the effect of a tangential electric field on the curvature singularity encountered by evolving vortex sheets. Weakly nonlinear models are derived by using asymptotic expansions based on the Dirichlet–Neumann operators. A fully nonlinear boundary integral method based on Cauchy’s integral formula and an angle –arclength derivative formulation in a Lagrangian framework is proposed. Linear stability analysis reveals a transition from the unstable regime to a neutrally stable regime at a critical electric field strength. However, both weakly nonlinear models and fully nonlinear simulations suggest that the curvature singularity persists regardless of the value of the electric field strength. The analysis demonstrates that the singularity time obeys two different asymptotic rules. For subcritical values of the tangential electric field and small initial amplitudes, the singularity time scales with the logarithm of the inverse of the amplitude, and monotonically increases with the electric field strength. For supercritical values of the tangential electric field the singular time is asymptotically larger, follows an inverse power law with respect to the initial amplitude and reaches local maxima as the electric field strength varies. Fully nonlinear simulations of the underlying electrodynamic Euler equations confirm that the curvature singularity can be significantly delayed when the electric field strength takes some special values. In the limit of large electric field strengths the numerical simulations indicate that the time to singularity formation is proportional to the inverse square root of the electric field strength.

Vertical-axis wind turbines (VAWTs) have emerged as natural complements to their horizontal counterparts but suffer from performance limitations associated with complex aerodynamics, in particular dynamic stall. To address this challenge, we employ deep reinforcement learning to identify optimal blade pitching policies. A framework based on the twin-delayed deep deterministic policy gradient algorithm is coupled with a validated numerical simulation of a two-bladed VAWT, aimed at maximising power generation. The agent receives only onboard measurements of blade pressure and position, rendering the problem partially observable. From these inputs, it learns policies for three distinct flow cases: one uniform flow and two shear flows. The resulting policies outperformed the optimum fixed-pitch setting within 100 turbine revolutions across all cases. Ultimately, the agent found cycle-averaged power coefficients that are 3.1–5.6 times larger than those of a blade fixed at zero degrees, while simultaneously reducing variations in blade loads. Improvements originate equally from both halves of turbine rotation, despite the latter-half’s low absolute power contribution and depleted flow energy. Through flow field analysis using the power partitioning method, the underlying mechanisms responsible for power production are revealed. The presence of a rotational flow around the airfoil leading edge dominates. Its net power contribution is determined by the rotational intensity and the blade’s kinematics. Kinematics also play a central role in mitigating dynamic stall. Flow separation is not intrinsically detrimental, as proper blade positioning can suppress its harmful effects.

In this study, we investigate the dynamics of a viscoplastic fluid placed above a Newtonian fluid in an inclined, long tube. The two fluids are miscible and have a density difference, with the viscoplastic fluid always denser. The experimental set-up allows varying inclination angles. Initially, the fluids are separated by a gate valve; upon opening it, distinct flow behaviours are observed, captured using cameras. The flow regimes depend on the interplay between buoyancy (due to the density difference), the yield stress of the viscoplastic fluid and the inclination angle. In tilted tubes, exchange flow with a slumping regime is observed, while in vertical configurations, a stable finger front forms at high values of the yield number ($Y$), representing the ratio of yield stress to buoyancy stress. As $Y$ decreases, helical, disconnected and slug finger regimes emerge. We investigate these flow regimes and quantify their transition boundaries, focusing on finger length and front velocity. Numerically, we develop a three-dimensional model based on the Herschel–Bulkley rheology, implementing the Papanastasiou regularisation and the volume-of-fluid method within the finite-volume framework of OpenFOAM. The simulations provide insights into velocity profiles, finger thickness and the distribution of yielded and unyielded regions. Numerical results indicate the finger tip becomes increasingly eccentric as the pipe is inclined, with a pronounced rise in eccentricity for inclinations exceeding $30^\circ$. These results are particularly relevant to industries like oil and gas, improving well integrity and protecting groundwater and the atmosphere by addressing cementing and sealing challenges.

We present a framework for large eddy simulations (LES) with immersed boundaries (IBs) to simulate high-Reynolds-number flows over complex walls. In this approach, which we call immersed boundary-modelled LES (IBMLES), we volume filter the Navier–Stokes equations to derive the IB bodyforce. This also gives rise to the subfilter-scale (SFS) stress and residual viscous stress tensors, the latter of which is closed, and we expect the SFS stress can be closed with existing models. We show that the IB bodyforce can be closed by modelling the wall-slip velocity and provide two such models. The first is an algebraic model based on volume filtering the Van Driest velocity profile, and the second is a slip-length model. We perform an a priori analysis by volume filtering direct numerical simulation (DNS) data of turbulent channel flow at friction Reynolds number $ \textit{Re}_{\tau }=5200$ to inform these models and investigate the behaviour of the other terms in this formulation. We find the streamwise wall-slip velocity is significant and both models show good agreement with volume-filtered DNS data on average. Slip velocity is non-uniform and retains a signature of inner or large-scale flow structures depending on filter size. The SFS terms are analogous to those in traditional LES and can likely be modelled with existing SFS models such the dynamic Smagorinsky model. Residual viscous stress is significant, so it must be considered in IBMLES. We perform filtering with multiple filter types and find there is little sensitivity to the choice of filter kernel so long as it abides by the assumptions given in this framework. Based on these results, we propose a dynamic procedure for determining the slip length that will be assessed in future studies.

We present a numerical study of three-dimensional gravity-capillary standing waves by using cubic and quintic truncated Hamiltonian formulations and the Craig–Sulem expansion of the Dirichlet–Neumann operator. The resulting models are treated as triply periodic boundary-value problems and solved via a spatio-temporal collocation method without executing initial-value calculations. This approach avoids the numerical stiffness associated with surface tension, and numerical instabilities arising from time integration. We reduce the number of unknowns significantly by exploiting the spatio-temporal symmetries for three types of symmetric standing waves. Comparisons with existing asymptotic and numerical results illustrate excellent agreement between the models and the full potential-flow formulation. We investigate typical bifurcations and standing waves that feature square, hexagonal and more complex flower-like patterns under the three-wave resonance. These solutions are generalisations of the classical Wilton ripples. Temporal simulations of the computed three-dimensional standing waves exhibit perfect periodicity and reveal an instability mechanism based on the previous reported oblique instability in two-dimensional standing waves.

Building upon the theoretical investigation of fully developed porous-channel flow by Nield et al. (J. Fluid Mech. vol. 322, 1996, 201–214), the present study examines hydrodynamically developing flow in anisotropic porous channels to better characterise realistic transport behaviour. A variational formulation for the steady incompressible Darcy–Brinkman–Forchheimer (DBF) equations is derived, where the Darcy, Brinkman and Forchheimer terms represent porous drag, viscous shear effects and nonlinear inertial resistance, respectively. The existence and uniqueness of solution are established using the Browder–Minty theorem together with the inf-sup condition to ensure the uniqueness of the pressure field. The porous medium is represented through a spatially varying anisotropic permeability tensor to account for directional resistance effects. A physics-informed neural network (PINN) framework using feed-forward deep neural networks (DNNs) is employed to solve the coupled nonlinear DBF equations solely from the governing equations and boundary conditions, without the need for external simulation or experimental data. Results indicate that lower anisotropic permeability ratios enhance both axial and transverse velocity components, whereas increasing the Darcy number substantially reduces pressure drop due to weakened porous resistance. The proposed framework provides an effective approach for modelling anisotropic porous-medium flows relevant to subsurface transport, filtration, biomedical devices and energy-storage systems.

We present a new kinetic model and its lattice Boltzmann realisation for the simulation of compressible, non-ideal fluid flows. The method employs first-neighbour lattices and introduces a consistent set of correction terms constructed via quasi-equilibrium attractors, ensuring positive-definite and Galilean-invariant Navier–Stokes dissipation rates. This construction circumvents the need for extended stencils or ad hoc regularisation, while maintaining numerical stability and thermodynamic consistency across a broad range of flow regimes. The resulting model accurately reproduces both the Euler and Navier–Stokes hydrodynamic limits. As a stringent validation, we demonstrate, for the first time within a lattice Boltzmann framework, quantitatively accurate simulations of shock–drop interactions at Mach numbers up to 1.47. The proposed approach thus extends the applicability of lattice Boltzmann methods to high-speed, non-ideal compressible flows with a minimal kinetic stencil.

Obtaining predictive low-order models is a central challenge in fluid dynamics. Data-driven frameworks have been widely used to obtain low-order models of aerodynamic systems; yet, resulting models tend to yield predictions that grow unbounded with time. Recently introduced stability-promoting methods can facilitate the identification of bounded models, but tend to require extensive brute-force tuning even in the context of simple academic systems. Here, we show how recent theoretical advances in the long-term boundedness of dynamical systems can be integrated into data-driven modelling frameworks to ensure that resulting models will yield bounded predictions of incompressible flows. Specifically, we propose to solve a particular set of convex semidefinite programming problems to (i) certify whether a system admits a globally attracting bounded set for the chosen modelling parameters, and (ii) compute a model with the optimal (tightest) bound on this globally attracting set. We demonstrate the approach via integration within the sparse identification of nonlinear dynamics (SINDy) modelling framework. Application on two low-order benchmark problems establishes the merits of the approach. We then apply our approach to obtain a low-order (six-mode) model of unsteady separation over a NACA-65(1)-412 aerofoil at ${\textit{Re}}=20\,000$ – a flow that has been notoriously difficult to model using data-driven methods. The resulting model is found to accurately predict the dynamics of unsteady separation, with model predictions remaining bounded indefinitely. We anticipate this work will benefit future efforts in modelling strongly nonlinear flows, especially in settings where physically viable long-term forecasts are paramount.