This paper presents an experimental and analytical investigation of the turbulent transport and flame geometric characteristics of free turbulent buoyant diffusion flames under different fuel mass fluxes and burner boundary conditions (i.e. with/without a flush floor). The stereo particle image velocimetry technique was utilised to measure the three-dimensional instantaneous velocity fields of the free methane buoyant flames with a burner diameter (d) of 0.30 m and dimensionless heat release rates ($\dot{Q}^{*}$) of 0.50–0.90. The results showed that, compared with the configuration without a floor, the time-averaged axial velocity fluctuations squared and the time-averaged radial velocity fluctuations squared decreased, and the peak values of the time-averaged radial velocity, the time-averaged radial velocity fluctuations squared and the time-averaged axial and radial fluctuation product shifted towards the burner centreline in the configuration with a flush floor. Based on the dimensional analysis and the gradient transport assumption, the mean turbulent viscosity within the mean flame height ($\nu _{t}^{=}$) was scaled. Compared with the configuration without a floor of under equal $\dot{Q}^{*}$, the turbulent viscosity decreased in the configuration with a flush floor, resulting in an increase in mean flame height and a reduction in mean flame width. Based on the concepts of turbulent mixing and equal axial convection and radial diffusion times, semi-physical models were derived for the mean flame height and the mean flame width, respectively. The two correlations agreed well with the experimental data of this work for the two burner configurations with and without a flush floor.

Stress–velocity cross-spectra provide critical insights into the wall turbulence dynamics, where second-order cross-spectra have been used to characterise the amplitude modulation of large-scale motions on smaller scales. Here, we investigate the higher-order stress–velocity cross-spectra. Through theoretical analysis, we derive an exact relationship demonstrating that the difference in convection velocity between streamwise Reynolds normal stress fluctuations ($r$) and streamwise velocity fluctuations ($u$) – termed the $r{-}u$ convection velocity difference – is governed jointly by the second- and fourth-order cross-spectra. A new ‘coherence similarity’ (CS) model is proposed, which reveals an approximate similarity between higher-order and second-order cross-spectra. As a result, the $r{-}u$ convection velocity difference can be explained in terms of second-order cross-spectral properties. Numerical validation confirms that the CS model predicts higher-order cross-spectra and the convection velocity difference accurately. Furthermore, the contours of stress–velocity cross-spectra undergo a structural transition from single-lobe to triple-lobe patterns with increasing wall distance, suggesting the presence of complex space–time coupling between $r$ and $u$.

This study uses a coupled lattice Boltzmann and discrete element method to perform interface-resolved simulations of turbulent channel flow laden with finite-size cylindrical particles. The aim is to investigate interactions between wall-bounded turbulence and non-spherical particles with sharp edges. The particle-to-fluid density ratio is unity and gravity is neglected. Comparative analyses are conducted among long (length-to-diameter aspect ratio 2), unit (1) and short ($ 1/2 $) cylinders, along with spheres and literature data for spheroids. Results reveal both shared and distinct dynamic behaviours of cylinders and their effects on turbulence modulation. Notably, disk-like short cylinders can remain trapped near the wall due to their flat faces aligning closely with it – a behaviour unique to particles with sharp edges. Long and unit cylinders, as well as spheres, preferentially accumulate in high-speed streaks, while short cylinders cluster in low-speed streaks, demonstrating a strong aspect-ratio effect. Near the wall, long cylinders align their axis with the streamwise direction, while short cylinders orient perpendicular to the wall. Rotationally, long cylinders primarily spin, whereas short ones predominantly tumble. These trends arise from orientation preferences and differences in axial and spanwise moments of inertia. Cylindrical particles increase wall drag compared with the single-phase case, with short cylinders causing the greatest enhancement due to strong near-wall accumulation. Overall, the influence of aspect ratio on particle dynamics and turbulence modulation is more pronounced for cylindrical particles than for spheroidal ones.

The fast-changing nature of sustainable mobility and the exponential growth of electric vehicles (EVs) have now placed battery supply chains (SCs) at the forefront of environmental concern. This review article examines 84 peer-reviewed studies published between 2008 and 2025, highlighting that 78% of the studies were published from 2020 to 2025, reflecting the rapid acceleration of EV battery sustainability research in recent years. Following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses method, the review has identified significant environmental hotspots and trade-off issues across six phases of the battery SC, as well as inconsistencies regarding methodology, such as functional units of measurement, and missing data in relation to the Global South. Hotspots are most prominent in South America and Central Africa (extraction), China and South Korea (manufacturing) and Southeast Asia (end-of-life). New contributions include a comparison of the life cycle assessment approaches, using new data from 2023 to 2025, adding updated insights on policy evolution, improved recycling efficiencies and digital traceability technologies that enhance supply-chain transparency. Furthermore, this review highlights ignored areas, such as informal recycling of batteries and unfair regulations across borders, and it provides recommendations, which are relevant to policymakers, industry and academia, to improve transparency in the SC, better compliance with environmental, social and governance requirements and sustainability initiatives.

In this work we propose a neural operator-based coloured-in-time forcing model to predict space–time characteristics of large-scale turbulent structures in channel flows. The resolvent-based method has emerged as a powerful tool to capture dominant dynamics and associated spatial structures of turbulent flows. However, the method faces the difficulty in modelling the coloured-in-time nonlinear forcing, which often leads to large predictive discrepancies in the frequency spectra of velocity fluctuations. Although the eddy viscosity has been introduced to enhance the resolvent-based method by partially accounting for the forcing colour, it is still not able to accurately capture the decay rate of the time-correlation function. Also, the uncertainty in the modelled eddy viscosity can significantly limit the predictive reliability of the method. In view of these difficulties, we propose using the neural operator based on the DeepONet architecture to model the stochastic forcing as a function of mean velocity and eddy viscosity. Specifically, the DeepONet-based model is constructed to map an arbitrary eddy-viscosity profile and corresponding mean velocity to stochastic forcing spectra based on the direct numerical simulation data at $Re_\tau =180$. Furthermore, the learned forcing model is integrated with the resolvent operator, which enables predicting the space–time flow statistics based on the eddy viscosity and mean velocity from the Reynolds-averaged Navier–Stokes (RANS) method. Our results show that the proposed forcing model can accurately predict the frequency spectra of velocity in channel flows at different characteristic scales. Moreover, the model remains robust across different RANS-provided eddy viscosities and generalises well to $Re_\tau =550$.

The path followed since Faraday’s first observations of acoustic streaming has led to a modern picture of this field as split into separate panels of a tryptic: standing acoustic waves in a channel with uniform background density, known as Rayleigh–Schlichting streaming, with stratified background density, known as baroclinic streaming, and acoustic waves progressing far from the walls under the shape of an attenuated beam, known as Eckart streaming. In their theoretical work, Mushthaq et al. (2025 J. Fluid Mech. 1017, A32) describe in a single continuous parameter space both Rayleigh–Schlichting and baroclinic streaming, thus making a decisive step forward in the frontier between two of these panels. Dealing with a stratification of thermal origin, they identify the level of heating above which baroclinic streaming becomes of the same order of magnitude or greater than Rayleigh–Schlichting streaming. They also depict the major part played by the channel size to wavelength ratio in this problem. This work will be of great help in designing the next generation of experiments concerning acoustic streaming and acoustic management of heat transfer. It is of interest for engineering fields like microfluidics, electronics cooling and biomedical applications. It can also serve as an inspiring basis for academic works in which waves are crossed with stratification.

Direct numerical simulations of two-phase, free-surface flow past a fully submerged, fixed circular cylinder are conducted for transitional Reynolds numbers $400 \leqslant {\textit{Re}} \leqslant 2000$, with Weber number ${\textit{We}} = 1000$, Froude number ${\textit{Fr}} = 1$ and a fixed gap ratio $G = 0.5$. This parameter combination corresponds to the gas entrainment regime characterised by the production of multiscale gas bubbles through interface breakup in the wake, which is of particular interest for its implications in enhancing gas transfer and mixing in environmental and engineering flows, such as air–water gas exchange processes in rivers and oceans, and the design and performance of naval and offshore structures. For ${\textit{Re}}= 400$, the jet forced through the $0.5D$ gap where $D$ is the diameter of the cylinder, efficiently convects opposite-signed vorticity downstream, suppressing the classical von Kármán instability and yielding a quasisteady recirculation bubble. The jet’s stabilising influence, however, breaks down once ${\textit{Re}} \approx 500$: periodic vortex shedding re-emerges and the wake becomes unsteady in spite of the continuing jet. The corresponding dimensionless shedding frequency Strouhal number $St$ grows with ${\textit{Re}}$ as $0.52-72.7{\textit{Re}}^{-1}$. The onset of unsteadiness first shortens the mean separation length but then drives it towards a saturation plateau for higher ${\textit{Re}}$ values. Surface rupture in the turbulent wake fragments entrained air into a multiscale bubble population whose number density follows $S_b(R_{\textit{eff}}) \propto R_{\textit{eff}}^{-6}$, consistent with gravity–capillary breakup in breaking waves, where $R_{\textit{eff}}$ represents the effective radii of the bubbles. Intermittency in entrainment corresponding to vortex shedding contrasts sharply with the finger-like structures observed under laminar conditions, underscoring the role of turbulent mixing. The coupled analysis of vorticity transport, shear-layer instability and bubble statistics elucidates how momentum exchange and air entrainment over a submerged body are governed under non-turbulent and turbulent conditions.

Future water demand modeling is of crucial importance for stakeholders, particularly in the era of rapidly changing climate and socioeconomic conditions. The modeling results can be applied to develop effective adaptation strategies that ensure equitable and sustainable allocation of water to various economic sectors, including institutional, commercial, industrial (ICI), residential and agricultural. However, a comprehensive review of existing future water demand modeling methods that consider both climatic and socioeconomic factors as well as the major economic sectors is currently lacking. This review article contributes to fill this knowledge gap while introducing a more streamlined and comprehensive methodological approach for conducting literature reviews in the environmental sciences domain. At the core of this method is a new framework designed to support research questions formulation and literature search strategies named STAR (Systems, Trouble/Treatment, Alternative, Response). In addition, it presents a data-requirement-based metric as well as a new nomenclature for classification of surveyed methods and approaches to guide the selection process of future water demand modeling methods. Furthermore, it proposes a hybrid modeling approach made up of three components (computational intelligence, dynamic systems and probabilistic scenarios) in the form of a theoretical workflow for future water demand modeling. The proposed workflow ensures broad applicability, making it adaptable not only to water demand management but also to a wide range of challenges across the environmental sciences.

Statistical structure and the underlying energy budget of wall-shear-stress fluctuations are studied in both Poiseuille and Couette flows with emphasis on its streamwise component. Using a dimensional analysis and direct numerical simulation data, it is shown that the spectra of streamwise wall dissipation for $\lambda \lesssim 1000 \delta _\nu$ are asymptotically invariant with the Reynolds number (${\textit{Re}}$), whereas those for $\lambda \gtrsim \delta$ decay with ${\textit{Re}}$ (here, $\lambda$ is a nominal wall-parallel wavelength, and $\delta _\nu$ and $\delta$ are the viscous inner and outer length scales, respectively). The wall dissipation increases with ${\textit{Re}}$ due to the increasing contribution of the spectra at $1000 \delta _\nu \lesssim \lambda \lesssim \delta$. The subsequent analysis of the energy budget shows that the near-wall motions associated with these wall-dissipation spectra are driven mainly by turbulent transport and are ‘inactive’ in the sense that they contain very little Reynolds shear stress (or turbulence production). As such, turbulent-transport spectra near the wall are also found to share the same ${\textit{Re}}$-scaling behaviour with wall dissipation, and this is observed in the spectra of both the wall-normal and inter-scale turbulent transports. The turbulent transport underpinning the increase of wall dissipation with ${\textit{Re}}$ is characterised by energy fluxes towards the wall, together with inverse energy transfer from small to large length scales along the wall-parallel directions.

We highlight the complete transition from liquid-wall-film instability of an annular gas–liquid flow inside a nozzle to spray formation at the trailing edge, aiming to identify two distinct flow regimes of ripple waves and disturbance waves and to clarify their distinct fragmentation mechanisms. Experiments conducted under strictly controlled boundary conditions support our theoretical analysis, revealing that the onset of disturbance waves coincides with the liquid-film Weber number (${\textit{We}}$) of unity, marking a significant change in following fragmentation dynamics. For ${\textit{We}}\lt 0.5$, the liquid wall film forms three-dimensional ripple waves driven by the superposition of Kelvin–Helmholtz and Rayleigh–Taylor (RT) instabilities, with no disturbance waves present. At the trailing edge, the liquid film temporarily accumulates, extends into isolated ligaments along the axial direction via RT instability, and subsequently fragments into droplets through Plateau–Rayleigh instability, displaying a weak coupling between ripple wave dynamics and fragmentation. In contrast, for ${\textit{We}}\gt 0.5$, disturbance waves with long wavelengths and large amplitudes become prominent, superimposed on the base ripple waves. As these disturbance waves reach the trailing edge, they are spontaneously ejected as liquid sheets at the same frequency, forming transverse rims through RT instability and rapidly disintegrating into fine droplets. This regime demonstrates a direct coupling between disturbance-wave dynamics and fragmentation.

This work presents a comprehensive analysis of steady cone-jet electrospray (SCJ-ES) that captures the full range of its steady jet scales within the Taylor-cone electric field. We identify three fundamental regions, each governed by distinct scaling laws and dominant physical mechanisms: (i) the transition region, characterised by the balances that fix the emitted current; (ii) the charge convection-dominated region, where surface charge transport dominates total charge transport and the Taylor field drives jet acceleration; and (iii) the ballistic region, where the jet attains a fixed cylindrical scale before undergoing Rayleigh breakup into charged droplets. This refined theoretical framework harmonises existing models, particularly those using the Taylor–Melcher leaky dielectric model as an electrokinetic approximation for SCJ-ES. Notably, our newly proposed spatial scales achieve a remarkable collapse of published experimental SCJ-ES jet profiles. We also apply this framework to study the charge of resulting droplets using extensive literature data, observing significant differences between weak and strong electrolytes, consistent with recent findings.

We investigate the effectiveness of linear optimal perturbation (LOP) for the flow past a finite span wing in reducing the lifespan of its trailing vortex system. Two approaches, referred to as local and model analysis, are introduced and used for our investigation. Both analyses assume that the baseflow is parallel. Local analysis is suited for intermediate distance from the wing where both tip vortices (TVs) and trailing edge wake (TEW) are present. Its results suggest that the unperturbed baseflow is stable. The separation between TVs and TEW increases downstream and their dynamics appear to be uncoupled at large distance from the wing. When perturbation corresponding to LOP is added to the baseflow, the vortices are displaced forming a helical twist. With time, the maximum displacement initially increases and then saturates. The perturbation retains its compact wavepacket-like structure, and perturbation energy within the tip vortex remains nearly constant. In the model analysis, the far wake is modelled as a pair of counter-rotating $q$-vortices. For low Reynolds number, the flow is stable. However, for higher Reynolds number, the trailing vortices develop Crow instability. Its growth rate is found to be in good agreement with earlier studies. Instability leads to contact of vortices, resulting in the formation of vortex rings. The time for vortex contact decreases with increase in the strength of the initial perturbation. The results suggest that LOP is effective in reducing the lifespan of trailing vortices.

Surfactants are usually added in droplet-based systems to stabilise them. When their concentration exceeds the critical micelle concentration (CMC), they self-assemble into micelles, which act as reservoirs regulating the availability of monomers in the continuous phase, thereby promoting interfacial remobilisation. The monomers get adsorbed onto a drop’s interface to alter its surface tension, and thus, governs how the drop moves within the suspending phase. Indeed, fine tuning droplet trajectories remain crucial in many classical as well as modern applications. Yet, the role of soluble surfactants in modulating droplet movement, especially at high concentrations, hitherto remains poorly understood. To address this, here we investigate the motion and cross-stream migration of a non-deforming drop in an unbounded Poiseuille flow, in the presence of bulk-soluble surfactants at concentrations above the CMC. We build a mixed semi-analytical-cum-numerical framework using spherical harmonics to determine the ensuing velocity and concentration fields. Our results suggest that the drop migrates towards the flow centreline, the extent of which depends on the interplay between the bulk concentration and the sensitivity of the interfacial tension to the surfactant molecules. This propensity for migration plateaus in the presence of micelles, although changing their specific properties seems to have relatively little impact. We further establish that adsorption–desorption between the interface and the bulk tends to suppress migration, while a relatively stronger coupling between bulk and interfacial transport facilitates the same. These findings highlight the crucial role of micelles in droplet motion, with implications in microfluidic control strategies and surfactant-driven flow manipulation.

Flow regimes arising in a T-shaped cell filled with liquid metal under the action of oppositely directed azimuthal electromagnetic forces were investigated. A flow regime map was produced, and the key characteristics of each observed flow type were described. Among the identified flow regimes, funnel rotation, jet flows, tornado-like vortex and their combinations can be distinguished. A flow topologically similar to a magnetohydrodynamic tornado, as well as vertical jet streams, were obtained for the first time without through-flow pumping, using fundamentally planar forces. The study includes experimental observation of flow structures on the free surface of a liquid metal and on the main cell axis, as well as three-dimensional numerical modelling to reconstruct the flow structure in the bulk. A low-melting-point gallium alloy was used as the working fluid. Surface velocity measurements were performed using particle image velocimetry with bubble tracers. Numerical simulations were conducted in a simplified formulation, neglecting free surface deformation.