Breaking wave impacts on rigid structures have been extensively studied, yet the role of structural elasticity in shaping the impact and response remains insufficiently understood. In this study, we experimentally investigate the hydroelastic behaviour of a vertical cantilever plate subjected to multimodal solitary breaking wave impacts. The plate is mounted near the still water level on a 1 : 10 sloping beach, and the wave height-to-depth ratio ($H/h$) is varied from 0.15 to 0.40 to systematically control the impact type from non-breaking to highly aerated wave impacts. We show that aeration significantly affects hydroelastic impacts. The spatio-temporal extent of the impact pressure on the elastic plate increases with air entrapment, while the peak pressure becomes highly sensitive as the wave approaches the flip-through regime. Pressure oscillations associated with bubble formation induce high-frequency structural vibrations, particularly under low-aeration conditions. Furthermore, we find that the elasticity has a limited effect on the peak pressure, impact duration and impulse, but increases the maximum quasi-hydrostatic force on the plate for the scenarios investigated. Following the impact, two distinct free-top deflections are identified, i.e. a deflection $\Delta x_{\textit{imp}}$ with high acceleration induced by the impact pressure and a deflection $\Delta x_{{hp}}$ with high magnitude caused by the maximum quasi-hydrostatic pressure. These deflections scale with the Cauchy number as $\Delta x_{\textit{imp}}/l \sim Ca_{\textit{imp}}/6$ and $\Delta x_{{hp}}/l \sim Ca_{{hp}}/12$ (where l is the plate length), exhibiting parabolic and linear trends with $H/h$, respectively. This work presents a benchmark dataset and introduces a predictive law for structural deflection, providing practical insights into hydroelastic effects across various impact regimes.

Understanding particle motion in narrow channels can guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of fluid-filled channel walls can slow down or increase the dispersion of tracer particles via entropic trapping in the wall bulges or hydrodynamic flows induced by wall fluctuations, respectively. Previous studies concentrated primarily on the case of a single Brownian tracer. Here, we address what happens when there is a large ensemble of interacting Brownian tracers – a common situation in applications. Introducing repulsive interactions between tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon reminiscent of that seen for single tracers in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of tracers numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Interactions between the fluctuating wall and the now-nearby particles then drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, our perturbation theory quantifies dispersion in generic advection–diffusion systems.

In this study, changes in the mean flow of a compressible turbulent boundary layer spatially evolving from low to ‘moderate’ Reynolds numbers are examined. All discussions are based on literature data and a direct numerical simulation (DNS) of a supersonic boundary layer specifically designed to be effectively free of spurious inflow effects in the range $4000 \lessapprox Re_\theta \lessapprox 5000$, which enables discussion of sensitive properties such as the turbulent wake. Most noticeably, the DNS data show the formation of a distinct ‘bend’ in the friction coefficient distribution reflected in sudden deviation from established low-Reynolds-number correlations. As will be shown, the bend is related to the surprisingly abrupt saturation of the turbulent wake, marking the change from low- to moderate-Reynolds-number behaviour; in previous studies, this trend was potentially obscured by data scatter in experiments and/or insufficient domain length in DNS. Moreover, the influence of the wake saturation on the formation of the early logarithmic overlap layer is assessed, which, if fully developed, leads to the onset of high-Reynolds-number behaviour further downstream.

It has been commonly observed on open waters that ducklings/goslings follow their mothers in a highly organized formation. The questions arise: (1) why are they swimming in formation? (2) what is the best swimming formation? (3) how much energy can be preserved by each individual in formation swimming? To address these questions, we established a simplified mathematical and numerical model and calculated the wave drag on a group of waterfowl in a swimming formation. We observed two new and interesting findings: wave-riding and wave-passing. By riding the waves generated by a mother duck, a trailing duckling can obtain a significant wave-drag reduction. When a duckling swims at the ‘sweet point’ behind its mother, a destructive wave interference phenomenon occurs and the wave drag of the duckling turns positive, pushing the duckling forward. More interestingly, this wave-riding benefit could be sustained by the rest of the ducklings in a single-file line formation. Starting from the third one in a queue, the wave drag of individuals gradually tended towards zero, and a delicate dynamic equilibrium was achieved. Each individual under that equilibrium acted as a wave passer, passing the waves’ energy to its trailing one without any energy losses. Wave-riding and wave-passing are probably the principal reasons for the evolution of swimming formation by waterfowl. This study is the first to reveal the reasons why the formation movement of waterfowl can preserve individuals’ energy expenditure. Our calculations provide new insights into the mechanisms of formation swimming.

Suspensions of microswimmers exhibit distinct characteristics as compared with those of passive particles because the internal particles are in a state of spontaneous motion. Although there have been many studies of microswimmer suspensions, not many have carefully considered the hydrodynamics. Hydrodynamics becomes particularly important when discussing non-dilute suspensions, because the lubrication flow generates a large force when the swimmers are in close proximity. This paper focuses on hydrodynamics and describes the transport phenomena of microswimmer suspensions, such as migration, collective motion, diffusion and rheology. The paper is structured to progressively scale up from a single microswimmer to collective motion to a macroscale continuum. At each scale, the discussion also evolves from dilute to concentrated suspensions. We first introduce natural swimming microorganisms, artificial microswimmers and mathematical models, as well as the fundamentals of fluid mechanics relevant to microswimmers. We then describe the migration of microswimmers by taxis, where microswimmers respond passively or actively to their hydrodynamic environment. Microswimmers exhibit collective motions, the mechanism of which is discussed in terms of hydrodynamics. The spreading of microswimmers is often diffusive, and the diffusion coefficient is much larger than for passive particles. Similarly, the mass diffusivity in microswimmer suspensions is higher due to their swimming activity. We explain these macroscopic diffusion properties. The viscosity of microswimmer suspensions can be higher or lower depending on the characteristics and orientation of the microswimmers. We describe the rheological properties of microswimmer suspensions in shear flow and Poiseuille flow. Finally, current issues and future research perspectives are discussed.

Convection in planetary environments is often modelled using stress-free boundary conditions, with diffusion-free geostrophic turbulence scalings frequently assumed. However, key questions remain about whether rotating convection with stress-free boundary conditions truly achieves the diffusion-free geostrophic turbulence regime. Here, we investigated the scaling behaviours of the Nusselt number ($Nu$), Reynolds number (${Re}$) and dimensionless convective length scale ($\ell /H$, where $H$ is the height of the domain) in rotating Rayleigh–Bénard convection under stress-free boundary conditions within a Boussinesq framework. Using direct numerical simulation data for Ekman number $Ek$ down to $5\times 10^{-8}$, Rayleigh number $Ra$ up to $5\times 10^{12}$, and Prandtl number $Pr = 1$, we show that the diffusion-free scaling of the heat transfer $Nu - 1 \sim Ra^{3/2}\, Pr^{-1/2}\, Ek^2$ alone does not necessarily imply that the flow is in a geostrophic turbulence regime. Under the stress-free conditions, ${Re}$ and $\ell /H$ deviate from the diffusion-free scalings, indicating a dependence on molecular diffusivity. We propose new non-diffusion-free scaling relations for this diffusion-free heat transfer regime with stress-free boundary conditions: $\ell /H \sim Ra^{1/8}\, Pr^{-1/8}\, Ek^{1/2}$ and ${Re} \sim Ra^{11/8}\, Pr^{-11/8}\, Ek^{3/2}$. Our findings highlight the need to assess both thermal and dynamic characteristics to confirm geostrophic turbulence.

We introduce a novel approach to derive compressibility corrections for Reynolds-averaged Navier–Stokes (RANS) models. Using this approach, we derive variable-property corrections for wall-bounded flows that take into account the distinct scaling characteristics of the inner and outer layers, extending the earlier work of Otero Rodriguez et al. (Intl J. Heat Fluid Flow, 73, 2018, 114–123). We also propose modifying the eddy viscosity to account for changes in the near-wall damping of turbulence due to intrinsic compressibility effects. The resulting corrections are consistent with our recently proposed velocity transformation (Hasan et al. Phys. Rev. Fluids, 8, 2023, L112601) in the inner layer and the Van Driest velocity transformation in the outer layer. Furthermore, we address some important aspects related to the modelling of the energy equation, primarily focusing on the turbulent Prandtl number and the modelling of the source terms. Compared with the existing state-of-the-art compressibility corrections, the present corrections, combined with accurate modelling of the energy equation, lead to a significant improvement in the results for a wide range of turbulent boundary layers and channel flows. The proposed corrections have the potential to enhance modelling across a range of applications, involving low-speed flows with strong heat transfer, fluids at supercritical pressures, and supersonic and hypersonic flows.

Turbulence–chemistry interaction in a Mach-7 hypersonic boundary layer with significant production of radical species is characterised using direct numerical simulation. Overriding a non-catalytic surface maintained as isothermal at 3000 K, the boundary layer is subject to finite-rate chemical effects, comprising both dissociation/recombination processes as well as the production of nitric oxide as mediated by the Zel’dovich mechanism. With kinetic-energy dissipation giving rise to temperatures exceeding 5300 K, molecular oxygen is almost entirely depleted within the aerodynamic heating layer, producing significant densities of atomic oxygen and nitric oxide. Owing to the coupling between turbulence-induced thermodynamic fluctuations and the chemical-kinetic processes, the Reynolds-averaged production rates ultimately depart significantly from their mean-field approximations. To better characterise this turbulence–chemistry interaction, which arises primarily from the exchange reactions in the Zel’dovich mechanism, a decomposition for the mean distortion of finite-rate chemical processes with respect to thermodynamic fluctuations is presented. Both thermal and partial-density fluctuations, as well as the impact of their statistical co-moments, are shown to contribute significantly to the net chemical production rate of each species. Dissociation/recombination processes are confirmed to be primarily affected by temperature fluctuations alone, which yield an augmentation of the molecular dissociation rates and reduction of the recombination layer’s off-wall extent. While the effect of pressure perturbations proves largely negligible for the mean chemical production rates, fluctuations in the species mass fractions are shown to be the primary source of turbulence–chemistry interaction for the second Zel’dovich reaction, significantly modulating the production of all major species apart from molecular nitrogen.

A novel data-driven modal analysis method, reduced-order variational mode decomposition (RVMD), is proposed, inspired by the Hilbert–Huang transform and variational mode decomposition (VMD), to resolve transient or statistically non-stationary flow dynamics. First, the form of RVMD modes (referred to as an ‘elementary low-order dynamic process’, ELD) is constructed by combining low-order representation and the idea of intrinsic mode function, which enables the computed modes to characterize the non-stationary properties of space–time fluid flows. Then, the RVMD algorithm is designed based on VMD to achieve a low-redundant adaptive extraction of ELDs in flow data, with the modes computed by solving an elaborate optimization problem. Further, a combination of RVMD and Hilbert spectral analysis leads to a modal-based time-frequency analysis framework in the Hilbert view, providing a potentially powerful tool to discover, quantify and analyse the transient and non-stationary dynamics in complex flow problems. To provide a comprehensive evaluation, the computational cost and parameter dependence of RVMD are discussed, as well as the relations between RVMD and some classic modal decomposition methods. Finally, the virtues and utility of RVMD and the modal-based time-frequency analysis framework are well demonstrated via two canonical problems: the transient cylinder wake and the planar supersonic screeching jet.

We experimentally and theoretically examine the maximum spreading of viscous droplets impacting ultra-smooth solid surfaces, where viscosity plays a dominant role in governing droplet spreading. For low-viscosity droplets, viscous dissipation occurs mainly in a thin boundary layer near the liquid–solid interface, whereas for high-viscosity droplets, dissipation is expected to extend throughout the droplet bulk. Incorporating these dissipation mechanisms with energy conservation principles, two distinct theoretical scaling laws for the maximum spreading factor ($\beta _m$) are derived: $\beta _m \sim ({\textit{We}}/ {\textit{Oh}})^{1/6}$ for low-viscosity regimes (${\textit{Oh}} \lesssim 0.1$) and $\beta _m \sim \textit{Re}^{1/5}$ for high-viscosity regimes (${\textit{Oh}} \gt 1$), where $\textit{We}$, $\textit{Re}$ and $\textit{Oh}$ are the Weber, Reynolds and Ohnesorge numbers, respectively. Both scaling laws show good agreement with the experimental data for their respective validity ranges of $\textit{Oh}$. Furthermore, to better model experimental data at vanishing $\textit{Re}$, we introduce a semi-empirical scaling law, $\beta _m \sim (A + {\textit{We}}/ {\textit{Oh}})^{1/6}$, where $A$ is a fitting parameter accounting for finite spreading ($\beta _m \approx 1$) at negligible impact velocities. This semi-empirical law provides an effective description of $\beta _m$ for a broad experimental range of $10^{-3} \leqslant {\textit{Oh}} \leqslant 10^0$ and $10^1 \leqslant {\textit{We}} \leqslant 10^3$.