When a water wave group encounters a floating body, it forces the body into motion; this motion radiates waves that modify the wave group. This study considers a floating body in the form of a two-dimensional (2-D) rectangular block constrained to heaving motion. The focus is on how the 2-D block modifies infragravity (IG) waves, a type of nonlinear low-frequency wave in the wave group. The IG waves transmitted beyond the block comprise two types: (i) bound IG waves generated by nonlinear interactions of first-order carrier waves, and (ii) free IG waves released due to discontinuities in flow potential created by the block. A systematic parameter sweep reveals that, when heaving motion is allowed, the transmitted IG waves differ significantly from those of stationary blocks. In some cases, heaving motion enables attenuation of the total transmitted IG waves, while stationary blocks cannot achieve similar effects. Only small-sized blocks are considered; they are ‘small’ compared with the IG wavelengths. The findings are relevant to dual-purpose wave energy converters designed for energy generation and coastal protection, floating breakwaters and other small-sized floating structures such as ships and some icebergs: the heaving motion of these objects may modify IG waves, thereby influencing harbour resonance, near-shore currents, beach erosion, wave forcing on ice shelves and coastal inundation.

In this paper, a phase-change model based on a geometric volume-of-fluid (VOF) framework is extended to simulate nucleate boiling with a resolved microlayer and conjugate heat transfer. Heat conduction in both the fluid and solid domains is simultaneously solved, with interfacial heat-transfer resistance (IHTR) imposed. The present model is implemented in the open-source software Basilisk with adaptive mesh refinement (AMR), which significantly improves computational efficiency. However, the approximate projection method required for AMR introduces strong oscillations within the microlayer due to intense heat and mass transfer. This issue is addressed using a ghost fluid method, allowing nucleate boiling experiments to be successfully replicated. Compared with previous literature studies, the computational cost is reduced by three orders of magnitude. We investigated the impact of contact angle on nucleate boiling through direct numerical simulation (DNS). The results show that the contact angle primarily influences the bubble growth by altering the hydrodynamic behaviour within the microlayer, rather than the thermal effect. An increase in contact angle enhances contact line mobility, resulting in a slower bubble growth, while maintaining an approximately constant total average mass flux. Furthermore, the sensitivity of bubble dynamics to the contact angle diminishes as the angle decreases. Finally, a complete bubble cycle from nucleation to detachment is simulated, which, to our knowledge, has not been reported in the open literature. Reasonable agreement with experimental data is achieved, enabling key factors affecting nucleate boiling simulations in the microlayer regime to be identified, which were previously obscured by limited simulation time.

In this work, we derive higher-order transport equations starting from the Boltzmann equation using a second-order accurate distribution function within the 13-moment framework. The equations are shown to be unconditionally linearly stable and consistent with Onsager’s symmetry principle. We also show that the equations comply with the second law of thermodynamics by establishing the non-negativity of the bulk entropy generation rate using the linearised form of the proposed equations. The force-driven Poiseuille flow problem, a standard benchmark problem, is selected to establish the validity of the equations. A complete analytical solution for this problem is proposed and compared against the Navier–Stokes, regularised 13, Grad 13 solutions and direct simulation Monte Carlo data. The proposed solution captures key rarefaction effects, including the Knudsen layer, non-uniform bimodal pressure profile, non-Fourier heat flux and the characteristic temperature dip at the centre. The analytical solution for the field variables indicates that the equations outperform the existing models in the slip- and transition-flow regimes for the problem considered. These satisfactory results point to the accuracy and applicability of the proposed equations, and the equations hold significant promise for rarefied gas dynamics at large Knudsen numbers.

This study considers the global instability of unidirectional flows through single, and double, bifurcation models using linear stability and direct numerical simulation (DNS). The motivation is respiratory flows, so we consider flow in both directions, through two geometries. We identify conditions (quantified by the Reynolds number, ${Re}=U^*D/\nu$, where $U^*$ is the peak centreline velocity, $D$ is the primary pipe diameter and $\nu$ is the kinematic viscosity) where temporal fluctuations occur using DNS. We calculate the linear stability of the steady flows, identifying the critical Reynolds number and leading unstable modes. For flows from single to double pipe, the critical Reynolds number is dependent on the number of bifurcations in the domain, but the mode structures are similar, with growth observed in regions dominated by longitudinal vortices formed by the centrifugal imbalance of flows passing through curved bifurcations. Flows in the opposite direction, from double to single pipe, also depend on the number of bifurcations in the domain. The flow through the double-bifurcation case undergoes two spatial symmetry-breaking bifurcations, altering the mode structure and critical Reynolds number. In all cases, the critical Reynolds number closely matches with temporal fluctuations observed from DNS, suggesting transition is the result of a linear instability, similar to other curved geometries like toroidal and helical pipes. We compare the frequencies of the modes with the frequencies observed from DNS, finding a close match during both initial and saturated flows. These results are important for understanding respiratory flows where turbulent mixing and streaming contribute to gas transport.

We developed a numerical method to investigate the effects of flow properties and phase transition between a gas and a liquid on sloshing-induced impact pressures acting on the walls of a partially filled tank. The conservation equations of mass, momentum and energy, as well as a transport equation for the volume fraction, were solved by considering flow compressibility, surface tension and phase transition. We modelled the phase transition by employing a mass transfer model, and validated our numerical method against experimental data. We investigated the effects of flow compressibility and density ratio between gas and liquid, representing a range similar to that of natural gas and hydrogen. We examined the effects of phase transition on sloshing-induced impact loads caused by a single-impact wave with gas pockets. Compressibility, density ratio and phase transition significantly affected the flow of the liquid–gas interface in the tank and, consequently, the impact pressure. The gas compressibility, caused by a single-wave impact with gas pockets, reduced the impact pressures significantly. Although the influence of density ratio on impact pressures is often emphasised, we demonstrated that, for impacts with gas pockets, the gas density was decisive and not the density ratio. With increasing gas density, the shape of the liquid–gas interface changed, and the pressure peak decreased. For the cases investigated, the viscosity of the liquid phase hardly influenced the impact pressures. Furthermore, the phase change during condensation considerably reduced the impact pressure peak. The pressure fluctuations after the first impact were strongly damped due to the vaporisation process.

We study the transport and deposition of inhaled aerosols in a mid-generation, mucus-lined lung airway, with the aim of understanding if and how airborne particles can avoid the mucus and deposit on the airway wall – an outcome that is harmful in case of allergens and pathogens, but beneficial in case of aerosolised drugs. We adopt the weighted-residual integral boundary-layer model of Dietze and Ruyer-Quil (J. Fluid Mech. 762, 2015, 68–109, to describe the dynamics of the mucus–air interface, as well as the flow in both phases. The transport of mucus induced by wall-attached cilia is also considered, via a coarse-grained boundary condition at the base of the mucus. We show that the capillary-driven Rayleigh–Plateau instability plays an important role in particle deposition by drawing the mucus into large annular humps and leaving substantial areas of the wall exposed to particles. We find, counter-intuitively, that these mucus-depleted zones enlarge on increasing the mucus volume fraction. Our simulations are eased by the fact that the effects of cilia and air turn out to be rather simple: the long-term interface profile is slowly translated by cilia and is unaffected by the laminar airflow. The streamlines of the airflow, though, are strongly modified by the non-uniform mucus film, and this has important implications for aerosol entrapment. Particles spanning a range of sizes (0.1–50 microns) are modelled using the Maxey–Riley equation, augmented with Brownian forces. We find a non-monotonic dependence of deposition on size. Small particles diffuse across streamlines due to Brownian motion, while large particles are thrown off streamlines by inertial forces – particularly when air flows past mucus humps. Intermediate-sized particles are tracer-like and deposit the least. Remarkably, increasing the mucus volume need not increase entrapment: the effect depends on particle size, because more mucus produces not only deeper humps that intercept inertial particles, but also larger depleted zones that enable diffusive particles to deposit on the wall.

Time-varying flow-induced forces on bodies immersed in fluid flows play a key role across a range of natural and engineered systems, from biological locomotion to propulsion and energy-harvesting devices. These transient forces often arise from complex, dynamic vortex interactions and can either enhance or degrade system performance. However, establishing a clear causal link between vortex structures and force transients remains challenging, especially in high-Reynolds-number nominally three-dimensional flows. In this study, we investigate the unsteady lift generation on a rotor blade that is impulsively started with a span-based Reynolds number of 25 500. The lift history from this direct-numerical simulation reveals distinct early-time extrema associated with rapidly evolving flow structures, including the formation, evolution and breakdown of leading-edge and tip vortices. To quantify the influence of these vortical structures on the lift transients, we apply the force partitioning method (FPM) that quantifies the surface pressure forces induced by vortex-associated effects. Two metrics – $Q$-strength and vortex proximity – are derived from FPM to provide a quantitative assessment of the influence of vortices on the lift force. This analysis confirms and extends qualitative insights from prior studies, and offers a simple-to-apply data-enabled framework for attributing unsteady forces to specific flow features, with potential applications in the design and control of systems where unsteady aerodynamic forces play a central role.

Tip leakage noise is one of the least understood noise sources in turbomachinery, arising from the interactions between the tip leakage flow, blade tips and casing boundary layer. This study employs experimental and parametric investigations to systematically identify three key non-dimensional parameters that govern tip leakage noise: the angle of attack $\alpha$, the ratio between the maximum aerofoil thickness and gap size $\tau _{\textit{max}}/e$ and between the gap size and boundary-layer thickness $e/\delta$. These parameters regulate two fluid-dynamic instabilities, vortex shedding and shear-layer roll-up, responsible for the two tip leakage noise sources. Specifically, the first noise source arises when $\tau _{\textit{max}}/e \lt 4$ and with the tip vortex positioned away from the aerofoil surface for $\alpha \geqslant 10^\circ$. The second noise source occurs whenever the tip flow separates at the pressure side edge, with its strength proportional to the lift coefficient, depending on $\alpha$, and diminishing as $e/\delta$ decreases and $\tau _{\textit{max}}/e$ increases. Additionally, a relationship between the first noise source and drag losses is established, demonstrating that these losses are governed by $\alpha$ and $\tau _{\textit{max}}/e$.

We investigate the shape of a tin sheet formed from a droplet struck by a nanosecond laser pulse. Specifically, we examine the dynamics of the process as a function of laser beam properties, focusing on the outstanding puzzle of curvature inversion: tin sheets produced in experiments and state-of-the-art extreme ultraviolet (EUV) nanolithography light sources curve in a direction opposite to previous theoretical predictions. We resolve this discrepancy by combining direct numerical simulations with experimental data, demonstrating that curvature inversion can be explained by an instantaneous pressure impulse with low kurtosis. Specifically, we parametrise a dimensionless pressure width, $ W$, using a raised cosine function and successfully reproduce the experimentally observed curvature over a wide range of laser-to-droplet diameter ratios, $ 0.3 \lt d/D_0 \lt 0.8$. The simulation process described in this work has applications in the EUV nanolithography industry, where a laser pulse deforms a droplet into a sheet, which is subsequently ionised by a second pulse to produce EUV-emitting plasma.

We study the two-dimensional steady-state creeping flow in a converging–diverging channel gap formed by two immobile rollers of identical radius. For this purpose, we analyse the Stokes equation in the streamfunction formulation, i.e. the biharmonic equation, which has homogeneous and particular solutions in the roll-adapted bipolar coordinate system. The analysis of existing works, investigating the particular solutions allowing arbitrary velocities at the two rollers, is extended by an investigation of homogeneous solutions. These can be reduced to an algebraic eigenvalue problem, whereby the associated discrete but infinite eigenvalue spectrum generates symmetric and asymmetric eigenfunctions with respect to the centre line between the rollers. These represent nested viscous vortex structures, which form a counter-rotating chain of vortices for the smallest unsymmetrical eigenvalue. With increasing eigenvalue, increasingly complex finger-like structures with more and more layered vortices are formed, which continuously form more free stagnation points. In the symmetrical case, all structures are mirror-symmetrical to the centre line and with increasing eigenvalues, finger-like nested vortex structures are also formed. As the gap height in the pressure gap decreases, the vortex density increases, i.e. the number of vortices per unit length increases, or the length scales of the vortices decrease. At the same time the rate of decay between subsequent vortices increases and reaches and asymptotic limit as the gap vanishes.

We analyse the process of convective mixing in two-dimensional, homogeneous and isotropic porous media with dispersion. We considered a Rayleigh–Taylor instability in which the presence of a solute produces density differences driving the flow. The effect of dispersion is modelled using an anisotropic Fickian dispersion tensor (Bear, J. Geophys. Res., vol. 66, 1961, pp. 1185–1197). In addition to molecular diffusion ($D_m^*$), the solute is redistributed by an additional spreading, in longitudinal and transverse flow directions, which is quantified by the coefficients $D_l^*$ and $D_t^*$, respectively, and it is produced by the presence of the pores. The flow is controlled by three dimensionless parameters: the Rayleigh–Darcy number $\textit{Ra}$, defining the relative strength of convection and diffusion, and the dispersion parameters $r=D_l^*/D_t^*$ and $\varDelta =D_m^*/D_t^*$. With the aid of numerical Darcy simulations, we investigate the mixing dynamics without and with dispersion. We find that in the absence of dispersion ($\varDelta \to \infty$) the dynamics is self-similar and independent of $\textit{Ra}$, and the flow evolves following several regimes, which we analyse. Then we analyse the effect of dispersion on the flow evolution for a fixed value of the Rayleigh–Darcy number ($\textit{Ra}=10^4$). A detailed analysis of the molecular and dispersive components of the mean scalar dissipation reveals a complex interplay between flow structures and solute mixing. We find that the dispersion parameters $r$ and $\varDelta$ affect the formation of fingers and their dynamics: the lower the value of $\varDelta$ (or the larger the value of $r$), the wider, more convoluted and diffused the fingers. We also find that for strong anisotropy, $r=O(10)$, the role of $\varDelta$ is crucial: except for the intermediate phases of the flow dynamics, dispersive flows show more efficient (or at least comparable) mixing than in non-dispersive systems. Finally, we look at the effect of the anisotropy ratio $r$, and we find that it produces only second-order effects, with relevant changes limited to the intermediate phase of the flow evolution, where it appears that the mixing is more efficient for small values of anisotropy. The proposed theoretical framework, in combination with pore-scale simulations and bead packs experiments, can be used to validate and improve current dispersion models to obtain more reliable estimates of solute transport and spreading in buoyancy-driven subsurface flows.