We study flows generated within a two-dimensional corner by the chemical activity of the confining boundaries. Catalytic reactions at the surfaces induce diffusio-osmotic motion of the viscous fluid throughout the domain. The presence of chemically active sectors can give rise to steady eddies reminiscent of classical Moffatt vortices, which are mechanically induced in similar confined geometries. In our approach, an exact analytical solution of the diffusion problem in a wedge geometry is derived and coupled to the diffusio-osmotic slip-velocity formulation, yielding the stream function of associated Stokes flow. In selected limiting cases, simple closed-form expressions provide clear physical insight into the underlying mechanisms. Our results open new perspectives for the design of microscale mixing strategies in dead-end pores and cornered microfluidic channels, and offer benchmarks for numerical simulations of confined (diffusio-)osmotic systems.

We consider the problem of a cylindrical (quasi-two-dimensional) droplet impacting on a hard surface. Cylindrical droplet impact can be engineered in the laboratory, and a theoretical model of the system can also be used to shed light on various complex experiments involving the impact of liquid sheets. We formulate a rim-lamella model for the droplet-impact problem. Using Gronwall’s inequality applied to the model, we establish theoretical bounds for the maximum spreading radius $\mathcal{R}_{\textit{max}}$ in droplet impact, specifically $k_1 {\textit{Re}}^{1/3}-k_2(1-\cos \vartheta _a)^{1/2}({\textit{Re}}/{\textit{We}})^{1/2}\leq \mathcal{R}_{\textit{max}}/R_0\leq k_1{\textit{Re}}^{1/3}$, valid for ${\textit{Re}}$ and ${\textit{We}}$ sufficiently large. Here, ${\textit{Re}}$ and ${\textit{We}}$ are the Reynolds and Weber number based on the droplet’s pre-impact velocity and radius $R_0$, $\vartheta _a$ is the advancing contact angle (assumed constant in our simplified analysis) and $k_1$ and $k_2$ are constants. We perform several campaigns of simulations using the volume of fluid method to model the droplet impact, and we find that the simulation results fall within the theoretical bounds.

Extreme weather events, combined with human-induced factors, such as expanding impervious surfaces and inadequate drainage infrastructure, are driving escalating urban flood risks worldwide. In this study, we present a novel spatiotemporal Long Short-Term Memory (LSTM)-based surrogate of the U.S. Environmental Protection Agency (EPA)’s Storm Water Management Model (SWMM) to predict maximum water depth and inflow at the asset level within urban drainage networks. The high-resolution SWMM model, encompassing the full network of conduits and manholes, was first calibrated and validated using U.S. Geological Survey (USGS) observations. The LSTM surrogate was then trained on data from 5,000 rainfall events across seven Annual Recurrence Intervals (ARIs) ranging from 1 to 100 years. The SWMM-LSTM surrogate model consistently achieves high predictive performance for both water depth and inflow, highlighting its robustness across diverse storm scenarios and ARI conditions. Hyperparameter optimization via grid search revealed task-specific configurations: larger hidden layers with moderate dropout improved water depth predictions, while deeper network architectures with minimal dropout optimized inflow forecasts. By providing rapid, computationally efficient predictions without compromising accuracy, the SWMM-LSTM surrogate offers a practical tool for real-time flood risk assessment, scenario evaluation and actionable decision-making in complex urban drainage systems.

This paper extends the two-layer high-level Green–Naghdi (HLGN) internal-wave model to study boundary time-varying problems, involving moving bottom or surface disturbances. The equations for the two-layer HLGN model with time-varying boundaries are presented, accompanied by a time-domain algorithm for solving these equations. The wave profiles predicted by the HLGN model for internal waves generated by boundary disturbances, whether occurring at the bottom or at the surface, show excellent agreement with results obtained by the fully nonlinear potential-flow (FNPF) solution. For internal waves generated by a surface moving disturbance, the results obtained by the HLGN model show good agreement with the experimental observations and the FNPF solution, including the relationships between the disturbance speed and the resulting wave amplitude and phase speed. Furthermore, the HLGN model is applied to analyse the evolution of the wave profiles and speed generated by the surface disturbance with different moving speeds. In addition, the extended HLGN model incorporates background linear shear currents to examine internal waves generated by a moving bottom disturbance with a linear shear current. The results reveal that background vorticity exerts a pronounced modulation effect on the wave profile and velocity field. Counter-flow narrows the waves and increases their phase speed, whereas co-flow broadens the waves and enhances their amplitude.

The effects of wall temperature on hypersonic boundary layer transition are investigated by analysing the kinematics (acoustic ray trajectories) and mechanics (fluctuation energy production and transport) of second-mode instabilities. The disturbance energy formulation is taken from Roy & Scalo (J. Fluid Mech. 2025, vol. 1007, A49). Flow conditions are taken from a Mach 6 boundary layer over a $3^\circ$ cone, with varying degrees of wall-to-adiabatic temperature ratios, $\varTheta =T_w/T_{\textit{ad}}=0.25{-}1.75$. Boundary layer-resolved axisymmetric direct numerical simulations with companion Laguerre polynomials-based linear stability theory provide the supporting numerical datasets. It was found that second-mode instabilities comprise two decks, separated by the pressure node location $(y=y_\pi )$. The upper deck ($y\gt y_\pi$) is characterised by temperature ($T^{\prime}$) and density ($\rho'$) fluctuations working with in-phase wall-normal velocity fluctuations ($v'$) to sustain the total disturbance energy production term, $-(\rho _0 v'T'\partial T_0/\partial y+\rho ' u_0 v' \partial u_0/\partial y$), which peaks at the generalised inflection point $y=y_i$. The downward-oriented energy flux peaks below the critical layer, $y\lt y_c$, and sustains acoustic energy accumulation in the lower deck. Effective energy transfer requires the streamwise and wall-normal fluxes to maintain a $90^\circ$ phase difference. This is satisfied especially for colder walls, whereas heated walls yield out-of-phase $v'$–$T'$ and in-phase pressure ($p'$) – streamwise velocity ($u'$) fluctuations, reducing the disturbance energy production and discouraging the coupling between the two decks. Ray tracing reveals the trajectory of purely acoustic wave paths emanating from the wall, as trapping occurs below the generalised inflection line $(y_i)$, governed by the mean flow velocity gradients $(\partial u_0/\partial y)$.

We studied the reconstruction of turbulent flow fields from trajectory data recorded by actively migrating Lagrangian agents. We propose a deep-learning model, track-to-flow (T2F), which employs a vision transformer as the encoder to capture the spatiotemporal features of a single agent trajectory, and a convolutional neural network as the decoder to reconstruct the flow field. To enhance the physical consistency of the T2F model, we further incorporate a physics-informed loss function inspired by the framework of physics-informed neural network (PINN), yielding a variant model referred to as T2F+PINN. We first evaluate both models in a laminar cylinder wake flow at a Reynolds number of $\textit{Re} = 800$ as a proof of concept. The results show that the T2F model achieves velocity reconstruction accuracy comparable to that of existing flow reconstruction methods, while the T2F+PINN model reduces the normalised error in vorticity reconstruction relative to the T2F model. We then apply the models in turbulent Rayleigh–Bénard convection at a Rayleigh number of $Ra = 10^{8}$ and a Prandtl number of $\textit{Pr} = 0.71$. The results show that the T2F model accurately reconstructs both the velocity and temperature fields, whereas the T2F+PINN model further improves the reconstruction accuracy of gradient-related physical quantities, such as temperature gradients, vorticity and the $Q$ value, with a maximum improvement of approximately 60 % compared to the T2F model. Overall, the T2F model is better suited for reconstructing primitive flow variables, while the T2F+PINN model provides advantages in reconstructing gradient-related quantities. Our models open a promising avenue for accurate flow reconstruction from a single Lagrangian trajectory.

We present a linear stability analysis of two-dimensional magnetoconvection considering the effects of spatial confinement (characterised by the aspect ratio $\varGamma$) and magnetic field (characterised by the Hartmann number $\textit{Ha}_{i=x,y,z}$ with subscript representing its direction). It is found that when the magnetic field is perpendicular to the convection domain ($y$-direction), it does not affect the onset of convection due to zero Lorentz force. With a magnetic field in the $z$ (vertical) or $x$ (horizontal) directions, the onset of convection is delayed, resulting in a larger critical Rayleigh number $Ra_c$ for the onset of convection. We outline phase diagrams showing the dominating factors determining $Ra_c$. When $\varGamma \leqslant 0.83\textit{Ha}_z^{-0.5}$ for vertical and $\varGamma \leqslant 0.66\textit{Ha}_x^{-1.01}$ for horizontal magnetic field, $Ra_c$ is mainly determined by the geometrical confinement with $Ra_c=502\varGamma ^{-4.0}$. When $\varGamma \geqslant 2^{1/6}\pi ^{1/3}\textit{Ha}_z^{-1/3}$ for vertical and $\varGamma \geqslant 5$ for the horizontal magnetic field, $Ra_c$ is mainly determined by the magnetic field with $Ra_c=\pi ^2\textit{Ha}^2$. In the intermediate regime, both the magnetic field and spatial confinement determine $Ra_c$, and a horizontal magnetic field is found to suppress convection more than a vertical magnetic field. In addition, under a horizontal magnetic field, there exists a subregime characterised by $Ra_c = 9.9\,\varGamma ^{-2.0} \textit{Ha}_x^2$, which is explained by a theoretical model. The magnetic field also modifies the length scale $\ell$. For a vertical magnetic field, $\ell$ decreases with increasing $\textit{Ha}_z$, following $\ell =2^{1/6}\pi ^{1/3}\textit{Ha}^{-1/3}$. For a horizontal magnetic field, when $\varGamma \lt 0.62\textit{Ha}_x^{0.47}$, the flow is a single-roll structure with $\ell$ being the width of the domain. The study thus shed new light on the interplay between magnetic field and spatial confinement.

We present a study on the melting dynamics of neighbouring ice bodies by means of idealised simulations, focusing on collective effects, with the goal of obtaining fundamental insight into how collective interactions influence the melting of ice. Two neighbouring (vertically or horizontally aligned), square-shaped and equally sized ice objects (size of the order of centimetres) are immersed in quiescent fresh water at a temperature of ${20}\,^\circ \textrm {C}$. By performing two-dimensional direct numerical simulations, and using the phase-field method to model the phase change, the collective melting of these objects is studied. When the objects are horizontally aligned, no significant influence of the neighbouring object on the melting time is observed. On the other hand, when vertically aligned, although the melting of the upper object is mostly unaffected, the melting time and the morphology of the lower ice body strongly depends on the initial inter-object distance. We report that the melting of the bottom object can be enhanced by more than 10 %, or delayed more than 20 %, displaying a non-monotonic dependence on the initial object size. We show that this behaviour results from a non-trivial competition between layering of cold fluid, which lowers the heat transfer, and convective flows, which favour mixing and heat transfer. For this melting in mixed convection, we were able to collapse our data onto a single curve.

Particle-laden supersonic jets are often encountered in advanced engineering applications where a comprehensive control of particle dispersion is crucial. Although particle dispersion has been extensively studied in the past, the local mechanisms that cause the radial particle transport, such that particles leave the jet core, remain unclear in supersonic jets. To this end, we conduct a direct numerical simulation of a confined low Reynolds number, perfectly expanded supersonic jet carrying four different-sized particles. Here, particles and gas are simulated with Lagrangian and Eulerian approaches, and the fluid–particle energy and momentum exchange is modelled with two-way coupling. The initial Stokes number of these particles ranges between $1.5$ and $6.0$. We found that each particle size has a specific axial location, $x_r$, where they start travelling radially. This location is defined by a local Stokes number of approximately ${\textit{St}}^* \approx 0.6$; the delay in particles’ response to the local eddies in a supersonic flow causes their ${\textit{St}}^*$ to drop below unity. The local turbulent structures formed by the jet promote the radial transport of the particles that have similar characteristic time scales. Despite two-way momentum coupling, particles and gas influence each other via different mechanisms. For the considered range of ${\textit{St}}$, particles dominantly influence the fluctuating velocity component of the gas, while gas mainly affects the mean velocity component of the particles. Moreover, the particles’ reaction to the compressibility effects is a direct function of particle inertia, where the probability of finding larger particles in a high-density gradient and dilatation region is higher.

This work proposes a data-driven explicit algebraic stress-based detached-eddy simulation (DES) method. Despite the widespread use of data-driven methods in model development for both Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulations (LES), their applications to DES remain limited. The challenge mainly lies in the absence of modelled stress data, the requirement for proper length scales in RANS and LES branches, and the maintenance of a reasonable switching behaviour. The data-driven DES method is constructed based on the algebraic stress equation. The control of RANS/LES switching is achieved through the eddy viscosity in the linear part of the modelled stress, under the $\ell ^2-\omega$ DES framework. Three model coefficients associated with the pressure–strain terms and the LES length scale are represented by a neural network as functions of scalar invariants of velocity gradient. The neural network is trained using velocity data with the ensemble Kalman method, thereby circumventing the requirement for modelled stress data. Moreover, the baseline coefficient values are incorporated as additional reference data to ensure reasonable switching behaviour. The proposed approach is evaluated on two challenging turbulent flows, i.e. the secondary flow in a square duct and the separated flow over a bump. The trained model achieves significant improvements in predicting mean flow statistics compared with the baseline model. This is attributed to improved predictions of the modelled stress. The trained model also exhibits reasonable switching behaviour, enlarging the LES region to resolve more turbulent structures. Furthermore, the model shows satisfactory generalization capabilities for both cases in similar flow configurations.