This study utilises chromocapillary stresses induced by light-actuated photosurfactants to demonstrate theoretically that a stable uniform liquid layer wetting a substrate can be sculpted and stirred on the microscale. A mathematical model is presented for two photosurfactant species that can switch from trans to cis states. Switching takes place in the bulk and on the interface, and convection–diffusion–reaction equations describe the local concentrations there. Under uniform light illumination (e.g. blue light) the equilibrium concentrations of trans and cis are non-uniform with layer depth, and a quiescent state with a flat interface exists. A non-uniform light intensity along the layer is superimposed to drive the system out of equilibrium, and induce interfacial deformations and flow in the bulk. This is carried out asymptotically for small-intensity non-uniformities and the first-order non-uniform solutions are found in semi-analytic form. The solutions show that a local increase in intensity increases the surface tension locally by sweeping surfactant off the interface to generate an inward trapping flow (known as a ‘Marangoni tweezer’ in experiments). Light intensities with a sinusoidal variation along the interface are also considered to show that vortical mixing motions are set up. Additionally, the liquid sculpting problem is analysed and a class of inverse problems are solved to predict the distribution of the light intensity required to produce a desired target interfacial shape. Finally, a parametric study is carried out to evaluate the effect of Biot, Damköhler and Marangoni numbers on the maximum light-induced interfacial velocity.

Ensuring easy access to clean and safe drinking water using low-cost technology is essential to mitigate the rising water scarcity in emerging economies. Commercial large-scale desalination technologies need significant investment, making them unsuitable for off-grid and small-scale applications. However, this operation can be carried out using a low-cost desalination technology based on renewable energy, known as the solar still. In this research work, a modified basin solar still (basin solar still + internal mirrors + 8 kg gravel + black ink (400 ppm per litre)) was developed and experimentally tested in Visakhapatnam (17.68°N, 83.22°E), India, to determine its appropriateness for sustainable seawater desalination. It produced 14% to 23% more desalinated water than a conventional basin solar still. In addition, its thermal efficiency was between 41% and 42%, which was significantly greater than other basin solar stills reported in literature. In addition, high-quality desalinated water was generated at a cost that was around three times less than the drinking water offered at Indian Railways kiosks. Moreover, the ability to mitigate significant CO2 emissions while also addressing water scarcity demonstrated that the modified basin solar still continues to contribute effectively to the United Nations Sustainable Development Goal 6 (Clean Water and Sanitation).

Slender fibres, including textile-derived microplastics, are abundant in aquatic environments and often extend beyond the Kolmogorov length scale. While breakup at dissipative scales has been characterised by velocity-gradient statistics, no closure existed for inertial-range spans where eddy turnover sets the clock. Here we develop a turbulence-informed kinetic theory of fibre fragmentation bridging turbulence forcing and slender-beam mechanics. First, we derive a load-to-curvature mapping showing that spanwise forcing generates peak bending moments scaling as $\sim U_L L^2$, with $U_L$ the velocity increment across fibre length $L$. Second, we construct a breakup hazard $h(L)$ from curvature-threshold exceedances over eddy-time blocks, which identifies a turbulence-defined critical span $\ell _c$. For $L\gt \ell _c$, breakup is eddy-time-limited, $h(L)=O(\bar \varepsilon ^{1/3}L^{-2/3})$ with $\bar \varepsilon$ the mean turbulent energy dissipation rate, whereas for $L\lt \ell _c$, it is a rare-event process with $h(L)\propto L^{5/3+\alpha }$, $\alpha$ denoting the small correction from intermittency. Embedding this hazard in a self-similar binary kernel yields a closed population-balance equation for the fragment distribution $n(L,t)$ with sources and sinks. The framework produces explicit predictions: intermittency-corrected curvature scalings, critical spans set by material and flow parameters, start-up and halving times linked to surf-zone conditions and scaling profiles in the cascade. The steady-state bulk distribution on the subcritical branch, with vertical removal induced by horizontal convergence, follows $n(L)\propto L^{-8/3-\alpha }\simeq L^{-2.7}$, in striking agreement with the mean slope $\simeq -2.68$ observed for environmental microfibres in recent surveys. The reported variability of slopes is naturally explained in our framework by the coexistence of supercritical and subcritical branches together with $L$-dependent removal-driven sinks.

Turbulent flows, despite their apparent randomness, exhibit coherent structures that underpin their dynamics. Proper orthogonal decomposition (POD) has been widely used to extract these structures from experimental data. Periodic features such as vortex shedding can appear as POD mode pairs in strongly periodic flows, but detecting propagating structures in more complex flows is challenging. Hilbert proper orthogonal decomposition (HPOD) addresses this by applying POD to the analytic signal of the turbulent fluctuations, which yields complex modes with a $\pi /2$ phase shift between the real and imaginary components. These modes capture propagating structures effectively but introduce spectral leakage from the Hilbert transform used to derive the analytic signal. The current work investigates the relationship between the modes of the POD and those of the HPOD on the velocity fluctuations in the wake of a sphere. By comparing their outputs, POD mode pairs that correspond to the same propagating structures revealed by HPOD are identified. Furthermore, this study explores whether computing the analytic signal of the POD modes can replicate the HPOD modes, offering a more computationally efficient method for determining the pairs of POD modes that represent propagating structures. The results show that the pairs of POD modes identified by the HPOD can be determined more efficiently using the Hilbert transform directly on the POD modes. This method enhances the interpretive power of POD, enabling more detailed analysis of the turbulent dynamics without the need to compute the analytic signal of the entire turbulent fluctuation data.

A droplet impacting a deep fluid bath is as common as rain over the ocean. If the impact is sufficiently gentle, the mediating air layer remains intact, and the droplet may rebound completely from the interface. In this work, we experimentally investigate the role of translational bath motion on the bouncing to coalescence transition. Over a range of parameters, we find that the relative bath motion systematically decreases the normal Weber number required to transition from bouncing to merging. Direct numerical simulations demonstrate that the depression created during impact combined with the translational motion of the bath enhances the air-layer drainage on the upstream side of the droplet, ultimately favouring coalescence. A simple geometric argument is presented that rationalises the collapse of the experimental threshold data, extending what is known for the case of axisymmetric normal impacts to the more general three-dimensional scenario of interest herein.

In this paper, a two-component discrete Boltzmann method is used to investigate the influence of the relaxation time on the two-dimensional compressible Kelvin–Helmholtz instability under dual-mode perturbations. The evolution characteristics of density gradient, vorticity, mixing entropy, Knudsen number (Kn), and thermodynamic non-equilibrium (TNE) effects are analysed. The results reveal that increasing relaxation time enhances diffusive and dissipative effects, leading to smoother interfaces, weaker vortex structures and suppressed instability growth. The global density gradient and vorticity intensity decrease accordingly. Mixing entropy analysis shows that larger relaxation times promote early mixing through diffusion, while smaller ones enhance late-stage mixing via vortex-induced convection. The Kn and TNE counters exhibit similar spatial and temporal variations, both effectively capturing the interface dynamics and deviations from local equilibrium. Both their magnitudes and the area over which they are spatially distributed increase with relaxation time, reflecting enhanced non-equilibrium effects. Besides, the global Kn and average TNE intensity initially rise, then decline, increase again and finally decrease, increasing with the relaxation time. These are jointly driven by the competitive physical mechanisms of the interface stretching, vortex merging and diffusion mechanisms. The findings provide a theoretical foundation for further exploration of non-equilibrium processes in complex fluid systems.

We investigate the interaction between two equally signed neutral vortices, namely vortices with a vanishing area integral of vorticity in inviscid non–divergent two-dimensional flows or a vanishing volume integral of potential vorticity anomaly in three-dimensional quasi-geostrophic (QG) flows. The vortices have a continuous (potential) vorticity distribution, and are linear combinations of appropriately normalised cylindrical (or spherical) Bessel functions of order 0, truncated at a zero of the Bessel function of order 1. Some pairs of neutral vortices reach an oscillating near-equilibrium state, attracting and repelling each other as a result of the exchange of small amounts of vorticity in their peripheries. This vorticity exchange generates a dipolar moment within each vortex which separates the vortices slightly, whereas the subsequent radial redistribution of the vorticity causes the vortices to come back closer again. The interaction is slower and weaker in three-dimensional QG flows, as the potential vorticity exchange primarily takes place close to the horizontal mid-plane of the vortices. These results have been corroborated using two radically different numerical models, namely a pseudo-spectral model and a high-resolution contour-advection model, both in two and in three dimensions. The observed oscillation mechanism could explain the persistence of geophysical vortices under the influence of other vortices and their ability to form stable vortex structures without experiencing vortex merging.

This study explores the effect of friction Reynolds number ($\textit{Re}_\tau \approx 3000$–$13{\,}000$) on secondary flows in three-dimensional turbulent boundary layers induced by spanwise surface heterogeneity. Using a combination of floating-element drag balance and high-resolution hot-wire anemometry, we examine how varying spanwise spacing ($S/\delta$ where $\delta$ is the boundary layer thickness defined as the distance from the wall where streamwise mean velocity $U = 0.99U_\infty$) influences frictional drag, turbulence intensity, spectral energy distribution and the organisation of coherent structures. The results reveal that secondary flows modulate turbulence differently depending on $S/\delta$, with strong near-wall effects at $S/\delta \lt 1$ and outer-layer modulation at $S/\delta \gtrsim 1$. A robust spectral signature of secondary flows peaking at $\lambda _x \approx 3\delta$ and $y \approx 0.5\delta$ emerges across all cases. This peak coexists with, or suppresses, very large-scale motions (VLSMs), depending on flow region and spacing. While VLSMs are suppressed in low-momentum pathways, they gradually recover in high-momentum pathways at higher $S/\delta$ and $\textit{Re}_\tau$. These findings offer insights into the interplay between fluctuations caused by secondary motions and boundary layer structures at high Reynolds numbers.

The dynamics of turbulent Rayleigh–Taylor (RT) mixing layers is investigated across a broad range of Atwood and Reynolds numbers using the statistically stationary RT flow configuration – a computational framework that enables simulation of a minimal flow unit for RT flows at reduced cost. Normalizations are developed for all dominant non-transport terms in the continuity, mixed mass and turbulent kinetic energy budgets in terms of the input parameters: the mixing layer height $h$, gravitational acceleration $g$ and fluid densities $\rho _H$ and $\rho _L$. Most normalized quantities collapse well across the parameter space. In some cases, variations in the Atwood number $A$ (or the density ratio $R$) lead to consistent integral magnitudes but spatially shifted profiles. These shifts are primarily related to a division by density and are similarly observed in the analytical solution of the one-dimensional variable-density diffusion problem. The analysis introduces a reference density for the mixed mass, examines trends in Favre-averaged statistics and derives a scaling law for the growth rate of the mixing layer. For height definitions encompassing the full extent of the layer, the conventional growth parameter, $\alpha =\dot {h}^2/4Agh$, varies with Atwood number. Our analysis leads to an alternative formulation using an effective Atwood number, $A^*= (\ln R)/2$, that is consistent with the scaling proposed by Belen’kii & Fradkin (1965 Trudy FIAN 29, 207–238). Applying this $A^*$ scaling to existing RT data, the corresponding growth parameter, $\alpha ^*=\dot {h}^2/4A^*gh$, remains nearly constant across all Atwood numbers considered, offering a unified scaling for variable-density RT flows.

We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analysing time series of particle velocity increments at different scales, we show that their evolution is consistent with a Markov process across the inertial range. This Markovian character enables a coarse-grained description of particle dynamics through a Fokker–Planck equation, from which we can extract drift and diffusion coefficients directly from the data. The inferred coefficients reveal scale-dependent relaxation and noise amplitudes, indicative of inertial filtering and intermittency effects. Beyond the kinematic description, we analyse the thermodynamic properties of particle trajectories by computing the trajectory-dependent entropy production. We show that the statistics of entropy fluctuations satisfy both the integral fluctuation theorem and, under certain conditions, the detailed fluctuation theorem. These results establish a quantitative bridge between stochastic thermodynamics and particle-laden flows, and open the door to modelling turbulent transport using effective stochastic theories constrained by data and physical consistency.