Nonlinear dynamical systems often allow for multiple statistically stationary states for the same values of the control parameters. Herein, we introduce a framework that selectively eliminates specific nonlinear triad interactions, thereby suppressing emergence of a particular state, and enabling the emergence of another. The methodology is applied to yield the multiple convection-roll states in two-dimensional planar Rayleigh–Bénard convection (e.g. Wang et al., 2020, Phys. Rev. Lett., vol. 125, 074501) in the turbulent regime. The intrusive framework presented here is based on the observation that the characteristic wavenumber associated with the mean horizontal size of the convection rolls mediates triadic scale interactions resulting in both kinetic energy and temperature variance cascades that are dominant energy transfer processes in a statistically stationary state. Suppression of these cascades mediated by a candidate wavenumber hinders the formation of the convection rolls at that wavenumber. Consequently, convection rolls are formed at another candidate wavenumber which is allowed to mediate energy to establish the cascade processes. In case no stable convection-roll states are possible, this technique does not tend to yield any convection rolls, making it a suitable method for discovering multiple states. Whereas in previous investigations the signature of different states in the initial condition in simulations yielded the multiple states, the present method alleviates such dependence of the emergence of multiple states on initial conditions. It is also demonstrated that accurate predictions of statistical quantities, such as Nusselt number and volume-averaged Reynolds numbers, can also be obtained using this method. The convection-roll states yielded using this technique may be used as initial conditions for direct simulations quickly converging to the target roll state without taking long convergence routes involving state transitions. Additionally, because only one state can possibly emerge in each simulation, this technique can empirically designate each of the multiple states with respect to their stability.

The transient dynamics of a wake vortex, modelled as a strong swirling $q$-vortex, is investigated with a focus on optimal transient growth driven by continuous eigenmodes associated with continuous spectra. The pivotal contribution of viscous critical-layer eigenmodes (Lee and Marcus, J. Fluid Mech. vol. 967, 2023, p. A2) amongst the entire eigenmode families to optimal perturbations is numerically confirmed, using a spectral collocation method for a radially unbounded domain that ensures correct analyticity and far-field behaviour. The consistency of the numerical method across different sensitivity tests supports the reliability of the results and provides flexibility for tuning. Both axisymmetric and helical perturbations with axial wavenumbers of order unity or less are examined through linearised theory and nonlinear simulations, yielding results that align with existing literature on energy growth curves and optimal perturbation structures. The initiation process of transient growth is also explored, highlighting its practical relevance. Inspired by ice crystals in contrails, the backward influence of inertial particles on the vortex flow, particularly through particle drag, is emphasised. In the pursuit of optimal transient growth, particles are initially distributed at the periphery of the vortex core to disturb the flow. Two-way coupled vortex–particle simulations reveal clear evidence of optimal transient growth during ongoing vortex–particle interactions, reinforcing the robustness and significance of transient growth in the original nonlinear vortex system over finite time periods.

Supersonic free jets are extensively employed across a range of applications, especially in high-tech industries such as semiconductor processing and aerospace propulsion. Due to the difficulties involved in flow measurement, previous research on supersonic free jets has primarily focused on investigating near-field shockwave structures, with quantitative experimental analysis of the far-field zone being relatively scarce. However, physical understanding of the far-field flow, particularly post-shockwave energy dissipation, holds significant importance for the application and utilisation of these jets in vacuum environments. Therefore, this study aims to provide a robust experimental foundation for a rarefied supersonic free jet through the analysis of the flow field in both the near- and far-field zones. Nanometre-sized tracer particles and molecules were utilised to measure the rarefied supersonic jet flow field using particle image velocimetry and acetone molecular tagging velocimetry, respectively. The experiments revealed that in rarefied conditions, the supersonic jet exhibits a one-barrel shockwave structure in the near field, and after passing the Mach disk, a long annular viscous layer develops downstream. Experimental data on the jet velocity profile and width demonstrated a transition to a laminar flow regime in the far-field zone. This transition aligns with the theoretically inferred flow regimes based on the complex Reynolds number. The velocity profile and potential core length of the laminar flow regime could be modelled using a bi-modal distribution, which represents the summation of symmetric Gaussian distributions.

Ventilated cavities in the wake of a two-dimensional bluff body are studied experimentally via time-resolved X-ray densitometry. With a systematic variation of flow velocity and gas injection rate, expressed as Froude number ($\textit{Fr}$) and ventilation coefficient ($C_{qs}$), four cavities with different closure types are identified. A regime map governed by $\textit{Fr}$ and $C_{qs}$ is constructed to estimate flow conditions associated with each cavity closure type. Each closure exhibits a different gas ejection mechanism, which in turn dictates the cavity geometry and the pressure in the cavity. Three-dimensional cavity closure is seen to exist for the supercavities at low $\textit{Fr}$. However, closure is nominally two-dimensional for supercavities at higher $\textit{Fr}$. At low $C_{qs}$, cavity closure is seen to be wake-dominated, while supercavities are seen to have interfacial perturbation near the closure at higher $C_{qs}$, irrespective of $\textit{Fr}$. With the measured gas fraction, a gas balance analysis is performed to quantify the gas ejection rate at the transitional cavity closure during its formation. For a range of $\textit{Fr}$, the transitional cavity closure is seen to be characterised by re-entrant flow, whose intensity depends on the flow inertia, dictating the gas ejection rates. Two different ventilation strategies were employed to systematically investigate the formation and maintenance gas fluxes. The interaction of wake and gas injection is suspected to dominate the cavity formation process and not the maintenance, resulting in ventilation hysteresis. Consequently, the ventilation gas flux required to maintain the supercavity is significantly less than the gas flux required to form the supercavity.

Ultra-thin liquid sheets generated by impinging two liquid jets are crucial high-repetition-rate targets for laser ion acceleration and ultra-fast physics, and serve widely as barrier-free samples for structural biochemistry. The impact of liquid viscosity on sheet thickness should be comprehended fully to exploit its potential. Here, we demonstrate experimentally that viscosity significantly influences thickness distribution, while surface tension primarily governs shape. We propose a thickness model based on momentum exchange and mass transport within the radial flow, which agrees well with the experiments. These results provide deeper insights into the behaviour of liquid sheets and enable accurate thickness control for various applications, including atomization nozzles and laser-driven particle sources.

Cavitation bubble pulsation and liquid jet loads are the main causes of hydraulic machinery erosion. Methods to weaken the load influences have always been hot topics of related research. In this work, a method of attaching a viscous layer to a rigid wall is investigated in order to reduce cavitation pulsations and liquid jet loads, using both numerical simulations and experiments. A multiphase flow model incorporating viscous effects has been developed using the Eulerian finite element method (EFEM), and experimental methods of a laser-induced bubble near the viscous layer attached on a rigid wall have been carefully designed. The effects of the initial bubble–wall distance, the thickness of the viscous layer, and the viscosity on bubble pulsation, migration and wall pressure load are investigated. The results show that the bubble migration distance, the normalised thickness of the oil layer and the wall load generally decrease with the initial bubble–wall distance or the oil-layer parameters. Quantitative analysis reveals that when the initial bubble–wall distance remains unchanged, there exists a demarcation line for the comparison of the bubble period and the reference period (the bubble period without viscous layer under the same initial bubble–wall distance), and a logarithmic relationship is observed that $\delta \propto \log_{10} \mu ^*$, where $\delta =h/R_{max}$ is the thickness of the viscous layer h normalised by the maximum bubble radius $R_{max}$, $\mu ^* = \mu /({R_{max }}\sqrt {{\rho }{{\mathop {P}\nolimits } _{{atm}}}})$ is the dynamic viscosity $\mu$ normalised by water density $ \rho $ and atmospheric pressure $P_{atm}$. The results of this paper can provide technical support for related studies of hydraulic cavitation erosion.

The escalating presence of microplastics (<5 mm) in drinking water presents urgent environmental and health challenges, yet the United Nations Environment Programme’s (UNEP) Global Plastics Treaty draft texts, including UNEP/PP/INC.5/4 and the Chair’s Text, lack robust provisions to address this issue. This Letter to the Editor analyzes deficiencies in the treaty’s approach, identifying critical gaps in standardized terminology, globally consistent monitoring methodologies, comprehensive source control and enforceable international regulations. Leveraging insights from California’s innovative microplastics monitoring framework, which employs spectroscopy-based detection and provisional health thresholds, we highlight scalable solutions for global policy. Key obstacles include technological disparities, economic reliance on plastic production, limited toxicological data and geopolitical barriers to unified action. We propose targeted strategies for the Intergovernmental Negotiating Committee (INC-5.2), including adopting precise microplastics definitions, establishing universal detection protocols, regulating both primary and secondary microplastic sources and supporting research and capacity-building in low-resource regions. These measures aim to enhance the treaty’s ability to mitigate microplastic pollution in drinking water, fostering science-driven global cooperation to protect ecosystems and public health.

The long-term development of coral reef frameworks and the net vertical accretion of reefs fundamentally underpins the provisioning of most reef-related ecosystem services. One area of particular concern at present is how rates of reef accretion are changing under ecological decline and what the consequences of this may be for the capacity of reefs to keep pace with near-future sea-level rise (SLR). This may have major implications for the capacity of reefs to maintain their coastal protective functions and to support reef island stability. Both are issues relevant to understanding future tropical coastal risk. Long-term (millennial timescale) rates of reef accretion are relatively well constrained, including through past periods of sea-level fluctuations. However, widespread and persistent ecological degradation of coral communities has caused many reefs to diverge significantly from their past accretion trajectories. This renders historical analogues increasingly unreliable for projecting future accretion potential. Addressing this necessitates a reorientation towards considering reef accretion rates across shorter (ecological to geomorphic) timescales, i.e., over years to multi-decades. This is essential if we are to better constrain contemporary reef accretion rate and SLR interactions at timescales relevant to predicting emerging coastal risks and understanding future implications for reef-derived benefits. Here, we review existing approaches for quantifying vertical reef accretion rates of modern reefs. These methods span data recovered from fossil outcrops or core-derived records, the conversion of carbonate budget data, direct in situ measurements and emerging remote sensing and image-based techniques. The review explores the advantages and limitations of these different approaches and outlines options for developing an integrated framework to link past, present and future reef accretion potential.

We study the dispersion of bubble swarms rising in initially quiescent water using three-dimensional Lagrangian tracking of deformable bubbles and tracer particles in an octagonal bubble column. Two different bubble sizes (3.5 mm and 4.4 mm) and moderate gas volume fractions ($0.52\,\%{-}1.20\,\%$) are considered. First, we compare the dispersion inside bubble swarms with that for single-bubble cases, and find that the horizontal mean squared displacement (MSD) in the swarm cases exhibits oscillations around the asymptotic scaling predicted for a diffusive regime. This occurs due to wake-induced bubble motion; however, the oscillatory behaviour is heavily damped compared to the single-bubble cases due to the presence of bubble-induced turbulence (BIT) and bubble–bubble interactions in the swarm. The vertical MSD in bubble swarms is nearly an order of magnitude faster than in the single-bubble cases, due to the much higher vertical fluctuating bubble velocities in the swarms. We also investigate tracer dispersion in BIT, and find that concerning the time to transition away from the ballistic regime, larger bubbles with a higher gas void fraction transition earlier than tracers, consistent with Mathai et al. (2018, Phys. Rev. Lett., vol. 121, 054501). However, for bubble swarms with smaller bubbles and a lower gas void fraction, they transition at the same time. This differing behaviour is due to the turbulence being more well-mixed for the larger bubble case, whereas for the smaller bubble case, the tracer dispersion is highly dependent on the wake fluctuations generated by the oscillating motion of nearby bubbles.