Previous studies show that at the small scales of stably stratified turbulence, the scale-dependent buoyancy flux reverses sign, corresponding to a conversion of turbulent potential energy (TPE) back into turbulent kinetic energy (TKE). Moreover, the magnitude of the reverse flux becomes stronger with increasing Prandtl number $\textit{Pr}$. Using a filtering analysis we demonstrate analytically how this flux reversal is connected to the mechanism identified in Bragg & de Bruyn Kops (2024 J. Fluid Mech. vol. 991, A10) that is responsible for the surprising observation that the TKE dissipation rate increases while the TPE dissipation rate decreases with increasing $\textit{Pr}$ in stratified turbulence. The mechanism identified by Bragg & de Bruyn Kops, which is connected to the formation of ramp–cliff structures in the density field, is shown to give the scale-local contribution to the buoyancy flux. At the smallest scales this local contribution dominates and explains the flux reversal, while at larger scales a non-local contribution is important. Direct numerical simulations of three-dimensional statistically stationary, strongly stably stratified turbulence confirm the theoretical analysis, and indicate that, while on average the local contribution only dominates the buoyancy flux at the smallest scales, it remains strongly correlated with the buoyancy flux at all scales. The results show that ramp cliffs are not only connected to the reversal of the local buoyancy flux but also the non-local part. At the small scales (approximately below the Ozmidov scale), ramp structures contribute exclusively to reverse buoyancy flux events, whereas cliff structures contribute to both forward and reverse buoyancy flux events.

A stakeholder structured engagement process at the Sustainable Water Infrastructure Management (SWIM) conference and workshop was held in December 2024. The participants identified critical current and future issues facing the water sector that are synthesized in this paper. In particular, they highlighted issues of water systems’ vulnerability and lack of resilience to hazards and stressors; inequities associated with water scarcity; and water quality problems – all affected by natural or man-made influences. The Smart One Water (S1W) vision was the baseline for the SWIM 2024 conference. This paper expands the S1W vision with a synthesis of the conference discussions about S1W-related fundamental concepts, practices and implementation barriers. It includes initial recommendations – based on a digital, data-focused, stakeholder-driven approach – with expert representatives of the public and private water supply sectors, academia, government and policymakers tasked to generate real-world adaptable ideas and practical solutions. Specifically, S1W envisions a future where water management and governance silos are eliminated to provide the necessary collaboration to enable efficient, resilient, affordable and equitable water access capable of adapting to a changing environment. This would be a future where communities govern collaboratively through integrated decision-making on policy, management and funding of natural and engineered water systems at the river basin scale.

This work uses large-eddy simulations to study the transition of a tulip flame stabilised by bubble vortex breakdown (BVB) mode towards a V flame stabilised by a conical vortex breakdown (CVB). The transition is triggered when the equivalence ratio is increased, resulting in a rise in temperature within the central recirculation zone (CRZ). Simultaneously, the pressure inside the CRZ bubble increases, while the average pressure inside the combustion chamber remains constant. This increase in pressure causes the CRZ bubble to open radially and expand, changing the vortex breakdown mode from BVB to CVB, and the flame shape from a tulip shape to a V shape. A criterion for a limit pressure inside the CRZ was then devised based on the radial momentum equation and the balance between centrifugal force and radial pressure gradient, found to control the radial motion of the CRZ. This criterion helped us to understand the main events of the transition, showing that, once the pressure inside the CRZ exceeds the limit given by the criterion, the flow topology changes from a BVB mode to a CVB mode. This transition highlights the differences between a BVB mode and a CVB mode, showing for the first time that there are characteristic pressure and velocity profiles for each mode in their swirling jets and CRZ. Finally, a significant achievement of this work is the identification of a novel mechanism for the controlled transition of vortex breakdown mode, a combustion-driven transition of vortex breakdown mode.

The modal and non-modal stability of laminar flow in a rectangular microchannel is investigated by incorporating the effects of Coriolis forces due to rotation, cross-sectional aspect ratio and superhydrophobic wall slip. The full Navier–Stokes equations are linearised into modified Orr–Sommerfeld and Squire equations, which are then formulated as an eigenvalue problem using small disturbances of the Tollmien–Schlichting type. These equations are subsequently solved by the spectral collocation method. The transition to instability in rotating microchannel flows, influenced by aspect ratio and slip conditions, is analysed through eigenvalue spectra and neutral stability curves. For non-modal analysis, we express the solution in matrix exponential form and then, using the singular value decomposition method, calculate the maximum energy growth. The study reveals that the flow becomes unstable in the presence of rotation at a critical Reynolds number of $ Re_c \approx 40$ for a low aspect ratio and $ Re_c \approx 50.4$ for a high aspect ratio. We find that instability is more pronounced in spanwise-rotating flows at higher aspect ratios compared with those at lower aspect ratios. Rotation induces disturbances from both walls along the spanwise direction, forming secondary flow structures near the centreline. Furthermore, we examine the influence of anisotropic slip by separately considering streamwise and spanwise slip as limiting cases. The numerical results demonstrate that while streamwise slip has a stabilising effect on rotating flows at small scales, a sufficiently large spanwise slip length can trigger instability at Reynolds numbers lower than those observed in the no-slip case. Rotation has the potential to enhance non-modal transient energy growth, while streamwise slip can effectively suppress this instability. These findings suggest that the onset of instability and transient energy growth can be effectively regulated by adjusting the aspect ratio and spanwise slip of the channel walls.

The dual-tone transition phenomenon and its formation mechanism in the flow around a heptagonal cylinder (side number $N= 7$) are experimentally investigated in depth over a range of free-stream velocities corresponding to Reynolds numbers of the order of $10^4$–$10^5$. Dual tone in this context refers to the emergence of two dominant peaks in the far-field acoustic spectrum when a flow in transition regime passes over a polygonal cylinder in principal orientations. The dual-tone phenomenon is also observed in an $N = 9$ cylinder in the face orientation and an $N = 11$ in the corner orientation, which contrasts with all the other polygonal cylinders of $N\in {\mathbb{Z}}[3,12]$ systematically investigated in the present study, where only a single tonal peak dominates the spectrum, similar to the Aeolian tone observed in the circular cylinder in the subcritical regime. The emergence of the dual tone is found to be responsible for the reduction of far-field noise. Continuous wavelet transform analysis reveals that the occurrence of the two competing tones in the time domain can be empirically modelled by Gaussian distributions. Additional proper orthogonal decomposition based phase averaging using time-resolved planar particle image velocimetry enables coherent vortex structure identification for the two quasi-stable shedding modes, which are responsible for the formation of the two tones. Near-wall flow and pressure fluctuation analysis further confirms that the two tones originate from stochastic shear-layer separation–reattachment switching, thereby generating two patterns of dipole sound sources through distinct vortex formation pathways.

This study presents an active flow control framework for fluid–structure interaction (FSI) systems involving a flexible plate in the wake of a cylinder, by integrating Koopman-based reduced-order models (ROMs) with model predictive control (MPC). Specifically, a novel switched-system control strategy is developed, wherein kernel dynamic mode decomposition (DMD) and residual DMD are jointly employed to construct accurate ROMs capable of capturing strongly nonlinear FSI dynamics. This approach ensures accurate low-order representations across multiple control inputs, while suppressing spurious modes. The resulting Koopman ROMs provide fast state predictions over a receding horizon, enabling an MPC optimiser to determine real-time actuation. To improve control performance, resolvent analysis is utilised to optimise the actuator–probe placement. Remarkably, only three strategically placed structural probes are sufficient to capture dominant Koopman modes and enable effective closed-loop control. The proposed framework is then applied to regulate synthetic jets on the cylinder to suppress the plate’s flapping. It successfully stabilises large-amplitude (LAF), small-deflection (SDF) and small-amplitude (SAF) flapping regimes within a unified control strategy. By combining Koopman modal decomposition with an analysis of system energy evolution, we elucidate distinct control mechanisms across these regimes. For LAF and SAF cases, control is achieved primarily through local modulation of existing saturated modes, which requires relatively low actuation energy. In contrast, stabilisation of the SDF case involves the emergence of entirely new Koopman modes that disrupt the original symmetry-breaking dynamics, resulting in increased control input. The framework matches the control performance of reinforcement learning while markedly reducing computational cost.

Aeroacoustic noise generated by wings under the wing-in-ground (WIG) effect is prevalent in various industrial applications, such as WIG vehicles, tower–blade interactions, and slat device noise issues. At chord-based Reynolds number 50 000 and freestream Mach number 0.3, the introduction of an engine jet transforms the separated stall noise of an NACA 4412 aerofoil under the influence of the WIG effect into laminar boundary layer vortex shedding (LBL-VS) noise. This study investigates the underlying mechanisms of this LBL-VS noise. Instead of relying on acoustic analogy, the unapproximated acoustic field is captured with high fidelity using direct numerical simulations. We identify the vorticity transfer process around the trailing edge as a key mechanism in the generation of LBL-VS noise. The results show that as the ground clearance decreases, the overall noise intensity is reduced. When the clearance becomes sufficiently small (10 % chord length), the well-organised vortex structures above the aerofoil break down under high adverse pressure, transitioning into a turbulent state that disrupts the vorticity transfer process. At this clearance, the dominant noise frequency drops from the vortex shedding frequency to an intermittent bursting frequency. This intermittent behaviour arises because only when certain vortices are amplified by acoustic feedback can they shed from the trailing edge, triggering the vorticity transfer process and generating pressure fluctuations. These findings provide new insights into the LBL-VS noise mechanisms under WIG conditions, and can inform strategies for noise reduction in relevant applications.

We integrate a discrete vortex method (DVM) with complex network analysis to strategise dynamic stall mitigation over aerofoils with active flow control. The objective is to inform the actuator placement and the timing to introduce control inputs during the highly transient process of dynamic stall. To this end, we treat a massively separated flow as a network of discrete vortical elements and quantify the interactions among the vortical nodes by tracking the spread of displacement perturbations between each pair of vortical elements using a DVM. This allows us to perform network broadcast mode analysis to identify an optimal set of discrete vortices, the critical timing and the direction to seed perturbations as control inputs. Motivated by the objective of dynamic stall mitigation, the optimality is defined as maximising the reduction of total circulation of the free vortices generated from the leading edge over a prescribed time horizon. We demonstrate the use of the analysis on a two-dimensional flow over a flat plate aerofoil and a three-dimensional turbulent flow over an SD$7003$ aerofoil. The results from the network analysis reveal that the optimal timing for introducing disturbances occurs slightly after the onset of flow separation, before the shear layer rolls up and forms the core of the dynamic stall vortex. The broadcast modes also show that the vortical nodes along the shear layer are optimal for introducing disturbances, hence providing guidance to actuator placement. Leveraging these insights, we perform nonlinear simulations of controlled flows by introducing flow actuation that targets the shear layer slightly after the separation onset. We observe that the network-guided control results in a $21 \,\%$ and $14\,\%$ reduction in peak lift for flows over the flat plate and SD$7003$ aerofoil, respectively. A corresponding decrease in vorticity injection from the aerofoil surface under the influence of control is observed from simulations, which aligns with the objective of the network broadcast analysis. The study highlights the potential of integrating the DVMs with the network analysis to design an effective active flow control strategy for unsteady aerodynamics.

This direct numerical simulation study analyses the transition-to-turbulence in plane Couette flow (PCF) with three-dimensional (3-D) roughness. Square ribs of height $k=0.2h$ (where $h$ is the half-channel height) and a streamwise pitch separation of $\lambda =10k$, classified as k-type roughness, are mounted on the stationary wall. This configuration features alternating rough and smooth zones in the spanwise direction and is referred to as 3-D k-type roughness. We compare the behaviour of 3-D k-type roughness in the transitional regime with that of two-dimensional (2-D) k-type roughness (Gokul & Narasimhamurthy 2024 J. Fluid Mech. vol. 1000, p. A40). The route-to-transition in 3-D k-type roughness confirms the formation of laminar–turbulent patterns, which exist in the transitional Reynolds number range $\textit{Re} \in [325, 350]$. This range interestingly overlaps with those for smooth PCF ($\textit{Re} \in [325, 400]$) and 2-D k-type roughness ($\textit{Re} \in [300, 325]$), thereby indicating that 3-D k-type roughness amalgamates the characteristics of both the rough and smooth zones. In striking contrast to the 2-D k-type roughness, the laminar–turbulent bands in the 3-D k-type configuration are of non-uniform bandwidth. The 3-D k-type roughness surprisingly introduces continuous competition among bands of opposite orientations, a characteristic unique in this case. Due to this competition, the large-scale flow associated with the oblique bands is never fully aligned with the diagonal direction. The smooth zones in the 3-D k-type roughness exhibit complex interactions, evident from oscillatory velocity signals and multiple high-energy peaks in the frequency spectra, which likely contribute to the competing patterns with opposite orientations.

Pulsed gravity currents are generated by the sequential release of dense material into a lighter ambient. We investigate the dynamics of pulsed gravity currents using physical scale experiments, two-dimensional depth-averaged shallow water equation (SWE) based models and three-dimensional lattice Boltzmann method (LBM) simulations. Integrating these results we show for the first time that short duration pulsed releases generate intrusive layers, which accelerate front propagation relative to an instantaneously released current of the same total volume. Conversely, a long delay time between pulses produces a current that propagates slower than an equivalent instantaneous release. This finding is supported by physical experiments and depth-resolving LBM simulations. The depth-resolving simulations show that intrusions in pulsed flows experience less drag resistance than those generated by instantaneous releases. The depth-averaged model considered in the present study does not accurately capture the intrusive flow dynamics of pulsed currents. However, the limitations of the finite-depth SWE model may be mitigated by extensions to incorporate entrainment and density stratification. The results also motivate further research into the impact of buoyancy Reynolds number and channel slope on the propagation of pulsed currents.

We investigate the role of slippery boundaries, quantified by the Navier boundary friction coefficient $\beta$, in regulating heat transport and flow structures in rotating Rayleigh–Bénard convection. Owing to the Ekman pumping effect arising from viscous boundary layers that is intensified with increasing boundary friction, it is found that the properties of global heat transport exhibit two distinct parameter regimes separated by a transitional Rayleigh number ($ \textit{Ra}_t$). In the rotation-dominated regime ($ \textit{Ra} \lt \textit{Ra}_t$), enhanced viscous friction increases the efficiency of Ekman pumping, significantly elevating the Nusselt number and lowering the convection onset threshold. Conversely, in the buoyancy-dominated regime ($ \textit{Ra} \gt \textit{Ra}_t$), boundary-induced viscous dissipation suppresses convective motions, thereby reducing heat transport. Large-scale vortices (LSVs), prevalent under free-slip conditions, progressively dissipate as $\beta$ increases, revealing that viscous friction disrupts the inverse energy cascade from baroclinic to barotropic modes. Through kinetic energy partitioning analysis, the transition between quasi-two-dimensional and three-dimensional turbulent states is identified, with the parameter $\beta _{\textit{cr}}$ following a generic scaling relation on the Prandtl (Pr) and Ekman (Ek) numbers $\beta _{\textit{cr}}\sim \textit{Pr}^{-0.67}\textit{Ek}^{-1.18}$. This relation enables us to predict LSV emergence across different parameter spaces. Furthermore, it is reported that the heat-transport scaling exponent, the convection onset and the partitioning of kinetic energy between barotropic and baroclinic components undergo a smooth flow transition at $\beta _{\textit{cr}}$. These results also indicate a direct correlation between Ekman pumping efficacy and the friction coefficient $\beta$, demonstrating that controlling boundary friction can modulate global transport properties and reshape flow structures.

To advance understanding of the influence hill-slope and hill-shape have on neutrally stratified turbulent air flow over isolated forested hills, we interrogate four turbulence-resolving simulations. A spectrally friendly fringe technique enables the use of periodic boundary conditions to simulate flow over isolated two-dimensional (2D) and three-dimensional (3D) hills of cosine shape. The simulations target recently conducted wind tunnel (WT) experiments that are configured to fall outside the regimes for which current theory applies. Simulation skill for flow over isolated 3D hills is demonstrated through matching the canopy and hill configuration with the recently conducted WT experiments and comparing results. The response of the mean and turbulent flow components to 2D versus 3D hills along the hill-centreline are discussed. The phase and amplitude of spatially varying flow perturbations over forested hills are evaluated for flows outside the regime valid for current theory. Flow over isolated 2D forested hills produces larger amplitude vertical motions on a hill’s windward and leeward faces and the speed-up of the mean wind compared with that over isolated 3D forested hills at the hill-centreline. The 3D hills generate surface pressure minima over hill-crests that are only half the magnitude of those over 2D hills. The spatial region over which hill-induced negative pressure drag acts increases with increasing hill steepness. Assumptions in partitioning the flow into an upper layer with an inviscid response to the hill’s pressure field are robust and lead to solid predictions of hill-induced perturbations to the mean flow; however, applying those assumptions to predict the evolution of the turbulent moments only provides approximate explanations at best.

Submesoscale processes, typically shaped by intricate interactions between frontal dynamics and turbulence, have significant impacts on the transport of momentum, heat and biogeochemical tracers in the ocean. This study employs large-eddy simulations to investigate submesoscale frontogenesis and arrest in the ocean surface boundary layer. We compare a single-sided front with a dense filament, which can be viewed as a two-sided front. Both cases exhibit a similar life cycle, including frontogenesis driven by secondary circulation, frontal arrest due to the growth of instability and turbulence, and eventual frontal decay. One major difference is that the filament remains stationary throughout its life cycle, while the front propagates towards the denser side. Another distinction lies in the relative contributions of horizontal and vertical turbulent fluxes. In the filament case, horizontal (cross-front) turbulent flux dominates and effectively counteracts the frontogenetic tendency induced by secondary circulation, leading to frontal arrest. In contrast, both vertical and horizontal turbulent fluxes are crucial for the arrest of the single-sided front. Horizontal shear production is the primary source of turbulence in the filament, associated with the emergence of horizontal coherent eddies and consistent with the characteristics of horizontal shear instability. For the front, the development of horizontal eddies is less pronounced, and vertical shear production plays a more important role. This study reveals the similarities and differences between the dynamics of submesoscale fronts and filaments, as well as the role of turbulence in their evolution, providing insights for improved representation of these processes in ocean models.

Interfacial interactions between gas bubbles and the free surface are a hallmark of flows involving aqueous foams. In practice, bubble foams commonly arise from processes such as breaking waves at the ocean–atmosphere interface, plunging liquid jets and the effervescence of carbonated liquids. Once generated, bubbles within foam layers remain afloat at the free surface for finite durations before finally bursting into a fine spray of droplets. While the birth and bursting of bubble foams have received considerable attention, the understanding of floating bubbles is limited mainly to a single bubble. To build on this, in this article, we undertake numerical simulations of two or more floating bubbles in various canonical settings to examine their geometry and self-organising nature, with implications for real-world phenomena such as ocean spray production. Under lateral confinement, floating bubbles are prone to form vertically stacked layers. To this end, we analyse the geometry of coaxial pairs of floating bubbles and link geometrical differences between single and coaxial bubbles to various aspects of the ensuing bursting stage. Furthermore, we extend the existing theory of isolated floating bubbles to obtain unified analytical expressions for the shape parameters of single and coaxial bubbles of small sizes. Next, we investigate a pair of side-by-side floating bubbles, which serves as a minimal configuration to understand the formation of bubble rafts through self-organisation. We discover that Bond numbers in the range $10\leqslant \textit{Bo}\leqslant 50$ are more favourable for raft formation due to pronounced capillary attraction. The time required for two floating bubbles to assemble through capillary attraction grows exponentially with their initial separation. We also develop a linear model to capture the evolution of bubble spacing during capillary migration at low Bond numbers. Lastly, we extend the two-bubble configuration and showcase the emergent dynamics of a swarm of floating bubbles in mono- and bilayer configurations.

This work presents wavepacket models for supersonic round twin jets operating at perfectly expanded conditions, computed via plane-marching parabolised stability equations based on mean flows obtained from the compressible Reynolds-averaged Navier–Stokes (RANS) equations. High-speed schlieren visualisations and non-time-resolved PIV measurements are performed to obtain experimental datasets for validating the modelling strategy. The RANS solutions are found to be in good quantitative agreement with the particle image velocimetry (PIV) mean-flow measurements, confirming the ability of the approach to capture the interaction between jets at the mean-flow level. The obtained wavepackets consist of toroidal and flapping fluctuations of the twin-jet system, and show similarities with those of single axisymmetric jets. However, for the case of closely spaced jets, they exhibit deviations in the phase speed of structures travelling in the outer mixing layer and those travelling in the inner one, leading to different non-axisymmetric behaviours. In particular, toroidal twin-jet wavepackets feature tilted ring-like structures with respect to the jet axis, while flapping twin-jet wavepackets are distorted and lose the clean chequerboard pattern typically observed in $m = 1$ modes in axisymmetric jets. A quantitative comparison of the modelled wavepackets with experimentally educed coherent structures is performed in terms of their structural agreement measured through an alignment coefficient, providing a first validation of the modelling strategy. Alignment coefficients are found to be particularly high in the intermediate range of studied frequencies.