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.

By generating drag and turbulence away from the bed, aquatic vegetation shapes the mean and turbulent velocity profile. However, the near-bed velocity distribution in vegetated flows has received little theoretical or experimental attention. This study investigated the near-bed velocity profile and bed shear stress using a coupled particle image velocimetry and particle tracking velocimetry system, which enabled the acquisition of flow-field measurements at very high spatial and temporal resolution. A viscous sublayer with a linear velocity profile was present, but this sublayer thickness was much smaller in vegetated flows than in bare flows with the same channel velocity. However, the dimensionless viscous sublayer thickness was the same in vegetated and bare flows, $z_v^+ = z_v \langle u_*\rangle / \nu = 6.1 \pm 0.7$. In addition, in vegetated flow, the horizontally averaged velocity profile above the viscous sublayer did not follow the classic logarithmic law found for bare beds. This deviation was attributed to the violation of two key assumptions in the classic Prandtl mixing length theory. By modifying the mixing length theory for vegetated conditions, a new theoretical power law profile for near-bed velocity was derived and validated with velocity data from both the present and previous studies, with mean percent errors of 4.9 % and 7.8 %, respectively. Using the new velocity law, the spatially averaged bed shear stress (and friction velocity) can be predicted from channel-average velocity, vegetation density and stem diameter, all of which are conveniently measured in the field.

We present an experimental study of convection–evaporation of a pool of water evaporating into a quiescent atmosphere. The temperature difference between the bottom of the pool and the surrounding air, as well as the water layer’s aspect ratio $\varGamma$, are systematically varied. Compared with classical Rayleigh–Bénard convection (RBC), this configuration involves a free-surface mechanical upper boundary and a mixed thermal upper boundary in contact with a poorly conducting air layer: evaporation extracts latent heat from the liquid and injects lighter vapour into the air, while radiation adds further cooling. As a result, neither temperature nor heat flux is fixed at the water–air interface, but they are instead strongly coupled. To characterise the respective contributions of convection, evaporation and radiation, we perform three sets of experiments: convection–evaporation, evaporation without bottom heating and convection without evaporation. High-resolution infrared imaging reveals multiple scales of convection at the surface: small hot plumes, cold sheet-like plumes and a large-scale circulation. The latter is constrained by the tank geometry for $\varGamma \lesssim 12$, but several turbulent superstructures develop for larger $\varGamma$. This is reminiscent of RBC but with different temperature statistics, due to the mixed boundary condition. Scaling laws are derived for interfacial transfers and mean surface temperature. Evaporation dominates heat extraction, accounting for 60 %–70 % of the flux, while radiation contributes 15 %–20 %. The release of vapour further enhances coupling between the liquid and air layers. When evaporation is blocked, radiation becomes dominant (70 %–80 %).These results have important implications for industrial and natural systems.

A time-domain model of an ice shelf interacting with ocean water in a finite domain is developed, which combines Kirchhoff–Love plate theory with the shallow-water wave equations. In particular, the domain is divided into an open-water region and a region in which the ocean is covered by an ice shelf. Boundary conditions, together with continuity conditions at the ice–water interface, lead to a nonlinear matrix eigenvalue problem, which is solved numerically to obtain the natural modes and frequencies of the system. These form the basis for reconstructing the transient response to wave forcing using a spectral method. Simulations show how wave packets excite multiple modes and generate interference patterns through boundary reflections. Since the method solves the initial value problem in a geometry containing both an open-ocean region and an ice-shelf-covered region, it provides a foundation for simulating sequential break-up of ice shelves due to wave-induced mechanical stresses, and contributes to broader efforts to model ice shelf disintegration under ocean forcing.

Equilibrium shapes of hollow vortices with surface tension in a corner geometry are obtained by solving a free-boundary problem. Using the integral hodograph method, we derive the complex velocity potential in an auxiliary parameter plane, which includes the velocity magnitude along the free surface. A singular integral equation for the velocity magnitude is obtained by applying the dynamic boundary condition. Numerical solutions to this equation reveal a wave quantisation phenomenon on the boundary of the hollow vortex due to the surface tension. The number of waves allocated on the free surface is arbitrary, starting from some minimal value depending on the strain-to-circulation ratio, the corner angle and the surface tension. In the limiting case of zero surface tension, the solution is obtained analytically and shown to agree with previous studies based on alternative mathematical formulations. These findings provide the first known equilibrium configurations of hollow vortices with surface tension in the presence of solid boundaries.

We use direct numerical simulations to investigate fluid–solid interactions in suspensions of rigid fibres settling under gravity in a quiescent fluid. The solid-to-fluid density ratio is $\mathcal{O}(100)$, while the Galileo number ($ \textit{Ga}$) and fibre concentration ($n\ell_{\kern-1.5pt f}^3$) are varied over the ranges $ \textit{Ga} \in [180, 900]$ and $n\ell_{\kern-1.5pt f}^3 \in [0.36, 23.15]$; $\ell_{\kern-1.5pt f}$ denotes the fibre length and $n$ the number density. At high $ \textit{Ga}$ and/or low $n\ell_{\kern-1.5pt f}^3$, fibres cluster into gravity-aligned streamers with elevated concentrations and enhanced settling velocities, disrupting the flow homogeneity. As $ \textit{Ga}$ increases and/or $n\ell_{\kern-1.5pt f}^3$ decreases, the fluid-phase kinetic energy rises and the energy spectrum broadens, reflecting enhanced small-scale activity. The flow anisotropy is assessed by decomposing the energy spectrum into components aligned with and transverse to gravity. Vertical fluctuations are primarily driven by fluid–solid interactions, while transverse ones are maintained by pressure–strain effects that promote isotropy. With increasing $ \textit{Ga}$, nonlinear interactions become more prominent, producing a net forward energy cascade toward smaller scales, punctuated by localised backscatter events. Analysis of the local velocity gradient tensor reveals distinct flow topologies: at low $ \textit{Ga}$, the flow is dominated by axisymmetric compression and two-dimensional straining; at high $ \textit{Ga}$, regions of high fibre concentration are governed by two-dimensional strain, while voids are associated with axisymmetric extension. The fluid motion is predominantly extensional rather than rotational.

Low Reynolds number hydrodynamic interactions are generally considered both deterministic and reversible due to their linearity. However, the role of soft interactions in deformable suspensions drives nonlinear effects with ambiguous consequences. On the one hand, nonlinearities can be responsible for soft chaos, i.e. long-time apparent randomisation resulting from sensitivity to initial conditions. On the other hand, they can also drive steady streaming and/or drifting effects leading to alignment and ordering. Here, we conduct a comprehensive study on the binary interaction of elastic capsules positioned in different shear planes using high-fidelity particle-resolved simulations. The effects of alignment angle, inter-surface distance, capillary number and size ratio are systematically explored. Based on interaction stability, three regimes are identified: leapfrog, minuet and a novel capturing regime. Unlike leapfrog and minuet motions, where the satellite capsule ultimately escapes from the reference capsule, the capturing motion forms a stable doublet aligned along the vorticity direction. We reveal that capturing is a gentle interaction, which induces only minimal deformation and stress. The mechanism underlying the capturing regime is attributed to the interplay between periodic oscillations induced by the central capsule and steady drift along the vorticity direction. Harmonic analysis of interaction frequencies further underscores the nonlinearity inherent to this dynamics. Extending beyond binary systems, we show that this mechanism relays into ternary alignment, suggesting a generic route to chain formation, demonstrating that nonlinear hydrodynamic interactions alone can drive spontaneous ordering of deformable particles.