Layer formation can occur within stratified fluids, often associated with the effect of ‘double diffusion’ where the fluid buoyancy depends on two components with differing molecular diffusivities (e.g. heat and salt in seawater). However, since layering also occurs in one-component stratified fluids, the generation mechanism for layers is often unclear. In this paper, we present a framework that unifies multiple-layer generation mechanisms across both one- and two-component stratified fluids. We demonstrate how these mechanisms can be assessed using simulations of double-diffusive intrusions. Our simulations illustrate the importance of the negative turbulent diffusivity for buoyancy in contributing to layer formation.

To study the physics of small-scale properties of homogeneous isotropic turbulence at increasingly high Reynolds numbers, direct numerical simulation results have been obtained for forced isotropic turbulence at Taylor-scale Reynolds number $R_\lambda =2500$ on a $32\,768^3$ three-dimensional periodic domain using a GPU pseudo-spectral code on a 1.1 exaflop GPU supercomputer (Frontier). These simulations employ the multi-resolution independent simulation (MRIS) technique (Yeung & Ravikumar 2020, Phys. Rev. Fluids, vol. 5, 110517) where ensemble averaging is performed over multiple short segments initiated from velocity fields at modest resolution, and subsequently taken to higher resolution in both space and time. Reynolds numbers are increased by reducing the viscosity with the large-scale forcing parameters unchanged. Although MRIS segments at the highest resolution for each Reynolds number last for only a few Kolmogorov time scales, small-scale physics in the dissipation range is well captured – for instance, in the probability density functions and higher moments of the dissipation rate and enstrophy density, which appear to show monotonic trends persisting well beyond the Reynolds number range in prior works in the literature. Attainment of range of length and time scales consistent with classical scaling also reinforces the potential utility of the present high-resolution data for studies of short-time-scale turbulence physics at high Reynolds numbers where full-length simulations spanning many large-eddy time scales are still not accessible. A single snapshot of the $32\,768^3$ data is publicly available for further analyses via the Johns Hopkins Turbulence Database.

The present work brings to light the vibrations emerging when a circular cylinder, elastically mounted along a rectilinear path in quiescent fluid, is subjected to a forced rotation about its axis. These rotation-induced vibrations (RIV) are explored numerically for ranges of the four governing parameters. The Reynolds number and the reduced velocity (inverse of the non-dimensional natural frequency of the oscillator), based on the surface velocity of the rotating body and its diameter, are varied up to $100$ and $250$, respectively, and the structural damping ratio up to $50\,\%$. The structure to displaced fluid mass ratio ranges from $0.1$ to $1000$. Vibrations are found to occur over a vast region of the parameter space, including the four orders of magnitude of the mass ratio under study, and high levels of structural damping. The amplitude of RIV may exceed $30$ body diameters, while their frequency varies and deviates from the oscillator natural frequency, even though it is always lower. Despite its simplicity and the steady nature of the actuation, the system exhibits a considerable diversity of behaviours. Three distinct RIV regimes are encountered: two periodic regimes whose responses differ by their spectral contents, i.e. sinusoidal versus multi-harmonic, and an aperiodic regime. These regimes are all closely connected to flow unsteadiness, in particular via the interplay of the cylinder with previously formed vortices, which persist in the vicinity of the body.

Turbulent separating and reattaching flows are known to exhibit low-frequency fluctuations manifested in a large-scale contraction and expansion of the reverse-flow region. Previous experimental investigations have been restricted to planar measurements, while the computational cost to resolve the low-frequency spectrum with high-fidelity simulations currently appears to be unaffordable. In this article, we make use of volumetric measurements to reveal the low-frequency dynamics of a turbulent separation bubble (TSB) formed in the fully turbulent flow past a smooth backward-facing ramp. The volumetric velocity field measurements cover the entire separated flow region over a domain with a spanwise extent of $S=0.6\, {\textrm{m}}$. Spectral proper orthogonal decomposition (SPOD) of the velocity fluctuations reveals low-rank low-frequency behaviour at Strouhal numbers ${\textit{St}}\lt 0.05$, which was also observed in previous planar measurements. However, in contrast with the interpretation of a two-dimensional contraction/expansion motion, the low-frequency dynamics is shown to be inherently three-dimensional, and governed by large elongated structures with a spanwise wavelength of approximately $S/2$. A low-order model constructed with the leading SPOD mode confirms substantial changes of the TSB extent in the centre plane, linking it to the modal pattern that is strongly non-uniform in the spanwise direction. The findings presented in this study promote a more complete understanding of the low-frequency dynamics in turbulent separated flows, thereby enabling novel modelling and control approaches.

Cross-shelf transport in the inner continental shelf is governed by wind, wave and tidal interactions, but the role of Langmuir circulation (LC), induced by wave–current interaction and modulated by tides, has remained under-studied in this setting. We develop a Reynolds-averaged Navier–Stokes (RANS) model incorporating the Craik–Leibovich vortex force to resolve LC, coupled with a mass-conserving undertow and oscillating along-shelf tidal currents, and compare results against field data from the Martha’s Vineyard Coastal Observatory (MVCO). Under strong wave forcing (significant wave height $H_{\textit{sig}} = 2.12\,\mathrm{m}$ and significant wave period $T_w = 5.8\,\mathrm{s}$), LC persists throughout the tidal cycle, reducing vertical shear in the tidally averaged cross-shelf velocity profile compared with simulations excluding LC. During peak tidal velocity (reaching $25\,\mathrm{cm\,s^{-1}}$ with period of $ 12.42\,\mathrm{h}$), LC is temporarily suppressed but reforms rapidly as tidal energy declines, sustaining high vertical mixing. Conversely, under weak wave forcing ( $H_{\textit{sig}} = 0.837\,\mathrm{m}$, $T_w = 4.3\,\mathrm{s}$), tidal currents persistently suppress LC, resulting in a cross-shelf undertow profile with greater vertical shear compared with strong-wave conditions. Model–observation comparisons show that only simulations including both the Craik–Leibovich vortex force and tidal forcing reproduce the observed undertow structure at MVCO. These results demonstrate that accurate prediction of cross-shelf transport at tidal and subtidal time scales requires resolving both the generation and disruption of LC by tides.

Secondary fragmentation of an impulsively accelerated drop depends on fluid properties and velocity of the ambient flow. The critical Weber number $(\mathit{We}_{cr})$, the minimum Weber number at which a drop undergoes non-vibrational breakup, depends on the density ratio $(\rho )$, the drop $(\mathit{Oh}_d)$ and the ambient $(\mathit{Oh}_o)$ Ohnesorge numbers. The current study uses volume-of-fluid based interface-tracking multiphase flow simulations to quantify the effect of different non-dimensional groups on the threshold at which secondary fragmentation occurs. For $\mathit{Oh}_d \leqslant 0.1$, a decrease in $\mathit{Oh}_d$ was found to significantly influence the breakup morphology, plume formation and $\mathit{We}_{cr}$. The balance between the pressure difference between the poles and the periphery, and the shear stresses on the upstream surface, was found to be controlled by $\rho$ and $\mathit{Oh}_o$. These forces induce flow inside the initially spherical drop, resulting in deformation into pancakes and eventually the breakup morphology of a forward/backward bag. The evolution pathways of the drop morphology based on their non-dimensional groups have been charted. With inclusion of the data from the expanded parameter space, the traditional $\mathit{We}_{cr}-\mathit{Oh}_d$ diagram used to illustrate the dependence of the critical Weber number on $\mathit{Oh}_d$ was found to be inadequate in predicting the minimum initial $\mathit{We}$ required to undergo fragmentation. A new non-dimensional parameter $C_{\textit{breakup}}$ is derived based on the competition between the forces driving the drop deformation and the forces resisting the drop deformation. Tested using available experimental data and current simulations, $C_{\textit{breakup}}$ is found to be a robust predictor for the threshold of drop fragmentation.

In this paper we propose a novel control strategy for modulating nonlinear flapping and symmetry-breaking (S-B) bifurcations of a piezoelectric metamaterial beam behind a circular cylinder subjected to viscous flow. The beam incorporates distributed piezoelectric meta-cells connected via unidirectional circuits to enable self-sensing and adaptive control. A strongly coupled nonlinear fluid-structure-electro-control model within an arbitrary Lagrangian–Eulerian framework is developed for predicting the flapping dynamics of the large deformable piezoelectric metamaterial beam. The system exhibits multiple flow-induced modes, including limit-cycle oscillations, subharmonic responses and S-B deflections. These dynamic regimes arise from nonlinear bifurcations of the system, namely the period-doubling and spontaneous S-B bifurcations. Flapping control and wake topology transition of the system is achieved by suppressing the periodic-doubling bifurcation based on the vibration rebound effect through a self-sensing and adaptive-actuation mechanism of the beam. Floquet stability analysis confirms the effectiveness of control in delaying instability onset and suppressing chaotic transitions. Symmetry modulation of the beam is achieved via the localised perturbations induced from the piezoelectric meta-cells, which reshape the stability of the system. The transition from S-B mode to symmetry-recovery mode reflects a shift from a flow-separation-dominated to vibration-dominated vortex shedding pattern. This symmetry transition reorganises the energy exchange pathways between the flow and the beam. Quantitative analyses of the wake recovery and the energy harvesting efficiency confirm enhanced flow energy conversion under control. These results establish a framework for bifurcation control of slender structures in viscous flow, providing potential applications for underwater energy harvesting and flexible propulsion in unsteady environments.

Vapour-driven solutal Marangoni effects have been studied extensively due to their potential applications, including mixing, coating, and droplet transport. Recently, the absorption of highly volatile organic liquid molecules into water droplets, which drives Marangoni effects, has gained significant attention due to its intricate and dynamic physical behaviours. To date, steady-state scenarios have been considered mainly by assuming the rapid establishment of vapour–liquid equilibrium. However, recent studies show that the Marangoni flow arises even under uniform vapour concentration, and requires a considerable time to develop fully. It indicates that the vapour–liquid equilibrium takes longer to establish than was previously assumed, despite earlier studies reporting that vapour molecules instantly adsorb on the interface, highlighting the importance of observing transient flow patterns. Here, we experimentally and numerically investigate time-dependent flow structures throughout the entire lifetime of a droplet in ethanol vapour environments. Under two distinct vapour boundary conditions of uniform and localised vapour distributions, a significant flow structure change consistently occurs within the droplet. The time-varying ethanol vapour mass flux from numerical simulation reveals that the flow transition is caused by the high vapour absorption flux at the droplet contact line, due to the geometric singularity there. Based on the detailed analysis of the surface tension gradient along the droplet interface, we identify that the flow transition occurs before and after the vapour–liquid equilibrium is achieved at the droplet contact line, which induces the flow direction change near the contact line.

Based on the assumption of locally quasi-steady behaviour, Duran & Moreau (2013 J. Fluid Mech. 723, 190–231), assumed that, at a critical nozzle throat, the fluctuations of the Mach number vanish for linear perturbations of a quasi-one-dimensional isentropic flow. This appears to be valid only in the quasi-steady-flow limit. Based on the analytical model of Marble & Candel (1977 J. Sound Vib. 55, 225–243) an alternative boundary condition is obtained, which is valid for nozzle geometries with a finite limit of the second spatial derivative of the cross-section on the subsonic side of the throat. When the nozzle geometry does not satisfy this condition, the application of a quasi-one-dimensional theory becomes questionable. The consequences of this for the quasi-one-dimensional modelling of the acoustic response of choked nozzles are discussed for three specific nozzle geometries. Surprisingly, the relative error in the inlet nozzle admittance and acoustic wave transmission coefficient remains below a per cent, when the quasi-steady boundary condition is used at the throat. However, the prediction of the acoustic fluctuations assuming a quasi-steady critical-throat behaviour is incorrect, because the predicted acoustic field is singular at the throat.

Transient growth mechanisms operating on streaky shear flows are believed important for sustaining near-wall turbulence. Of the three individual mechanisms present – Orr, lift-up and ‘push over’ – Lozano-Duran et al. 2021 (J. Fluid Mech. 914, A8) have recently observed that both Orr and push over need to be present to sustain turbulent fluctuations given streaky (streamwise-independent) base fields whereas lift-up does not. We show here, using Kelvin’s model of unbounded constant shear augmented by spanwise-periodic streaks, that this is because the push-over mechanism can act in concert with a Orr mechanism based upon the streaks to produce much-enhanced transient growth. The model clarifies the transient growth mechanism originally found by Schoppa & Hussain (2002 J. Fluid Mech. 453, 57–108) and finds that this is one half of a linear instability mechanism centred at the spanwise inflexion points observed originally by Swearingen & Blackwelder (1987 J. Fluid Mech. 182, 255–290). The instability and even transient growth acting on its own are found to have the correct nonlinear feedback to generate streamwise rolls which can then re-energise the assumed streaks through lift-up indicating a sustaining cycle. Our results therefore support the view that, while lift-up is believed central for the roll-to-streak regenerative process, it is Orr and push-over mechanisms that are both key for the streak-to-roll regenerative process in near-wall turbulence.

Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and slowly varying bathymetry, we derive an analytical approximation to the wave ray curvature, which is validated by an open-source ray tracing framework. The approximation has the form of linear superposition of a current- and a depth-induced component, each depending on the gradients in the ambient fields. This separation enables quantification of their individual and combined contributions to refraction. Through analysis of a few limiting cases, we demonstrate how the sign and magnitude of these components influence the wave refraction, and identify conditions where they either amplify or counteract each other. We also identify which of the two plays a dominant role. These findings provide physically resolved insights into the influence of current and depth gradients on wave propagation, and are relevant for applications related to remote sensing and coastal wave forecasting services.

While flow confinement effects on a shear layer of an one-sided or submerged vegetation array’s interface have been widely studied, turbulent interactions between shear layers in channels with vegetation on both sides remain unclear. This study presents laboratory experiments investigating flow adjustments and turbulent interaction within a symmetrical vegetation–channel–vegetation system, considering varying array widths and densities. In the outer shear layer, the shear stress is primarily balanced by the pressure gradient. As the array extends laterally, the outer penetration of the shear layer reduces from a fully developed thickness to the half-width of the open region, resulting in flow confinement. Flow confinement enhances the pressure gradient, which increases the interior velocity and shear stress at the interface. Despite the time-averaged shear stress being zero at the centreline when the shear layer is confined, the shear instabilities from both sides interact, producing significant turbulent events at the centreline with equal contributions from each side. Furthermore, the two parallel vortex streets self-organised and created a wave response with a $\pi$-radian phase shift , where alternating vortex cores amplify the pressure gradient, intensifying coherent structures and facilitating momentum exchange across the channel centreline. Although the turbulent intensity is enhanced, the decreased residence time for turbulent flow events may limit transport distance. Overall, the shear layer that develops on one interface acts as an additional resistance to shear turbulence on the other interface, leading to a more rapid decline of shear stress in the open region, despite a higher peak at the interface.

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.

This paper presents an analytical method for modelling the acoustic field radiation from a semi-infinite elliptic duct in the presence of uniform subsonic flow. In contemporary aircraft design, elliptic ducts play crucial roles as inlets for advanced blended wing body configurations owing to their capacity to maximise the pre-compression effect of the fuselage and enhance the stealth performance of aircraft. The method uses Mathieu functions to describe the incident and scattered sound in the elliptic cylindrical coordinates. An analytical Wiener–Hopf technique is developed in this work to derive near- and far-field solutions. Numerical simulations based on a finite element method are conducted to validate the accuracy of the analytical method, revealing a strong correspondence with analytical predictions. A parametric study is conducted to explore the influence of the elliptic cross-section shape on noise directivity. Moreover, we investigate reflections within the duct via an extended derivation of the analytical model. The proposed method can be used to examine the acoustic characteristics of elliptic ducts with inflow mean flows, which holds relevance for noise control and optimisation of turbofan engine inlets and blended wing body applications.

The effect of uniform wall suction on compressible Görtler vortices excited by free stream vortical disturbances is studied via asymptotic and numerical methods. The flow is described by the boundary-region framework, written and solved herein for non-similar boundary layers. The suction, applied downstream of an impermeable region, reduces the amplitude of steady and unsteady Görtler vortices. The vortices are attenuated more when the boundary layer has reached the asymptotic-suction condition than when it is streamwise-dependent. The impact of suction weakens as the free stream Mach number increases. As the boundary layer becomes thinner, the exponential growth of the vortices is prevented because the disturbance spanwise pressure gradient and spanwise viscous diffusion are inhibited. The flow is described by the boundary-layer equations in this case, for which the wall-normal momentum equation is uninfluential at leading order and the curvature effects responsible for the inviscid pressure-centrifugal imbalance are therefore negligible. The influence of unsteadiness weakens as suction intensifies because, in the limit of a thin boundary layer, the boundary-region solution simplifies to a regular-perturbation series whose first terms are described by the steady boundary-layer equations. Suction broadens the stability regions and may favour the presence of oblique Tollmien–Schlichting waves at the expense of more energetic Görtler vortices for relatively high frequencies and moderate Mach numbers.

The presence of salt in seawater significantly affects the melt rate and morphological evolution of ice. This study investigates the melting process of a vertical cylinder in saline water using a combination of laboratory experiments and direct numerical simulations. The two-dimensional (2-D) direct numerical simulations and three-dimensional (3-D) experiments achieve thermal Rayleigh numbers up to $\textit{Ra}_{T}= \mathcal{O} (10^{9} )$ and saline Rayleigh numbers up to $\textit{Ra}_{S}=\mathcal{O} (10^{12} )$. Some 3-D simulations of the vertical ice cylinder are conducted at $\textit{Ra}_{T}= \mathcal{O} (10^{5} )$ to confirm that the results in 2-D simulations are qualitatively similar to those in 3-D simulations. The mean melt rate exhibits a non-monotonic relationship with ambient salinity. With increasing salinity, the mean melt rate initially decreases towards the point where thermal and saline effects balance, after which it increases again. Based on the ambient salinity, the flow can be categorised into three regimes: temperature-driven flow, salinity-driven flow and thermal-saline competing flow. In the temperature-driven and competing flow regimes, we find that the mean melt rate follows a $\textit{Ra}_{T_d}^{1/4}$ scaling, where the subscript $d$ denotes a response parameter. In contrast, in the salinity-driven flow regime, we see a transition from a $\textit{Ra}_{T_d}^{1/4}$ to a $\textit{Ra}_{T_d}^{1/3}$ scaling. Additionally, the mean melt rate follows a $\textit{Ra}_{S_d}^{1/3}$ scaling in this regime. The ice cylinder develops distinct morphologies in different flow regimes. In the thermal-saline competing flow regime, distinctive scallop (dimpled) patterns emerge along the ice cylinder due to the competition between thermal buoyancy and saline buoyancy. We observe these scallop patterns to migrate downwards over time, due to local differences in the melt rate, for which we provide a qualitative explanation.

Sink flow boundary layers on smooth and rough walls were studied experimentally. In all cases a turbulent, zero-pressure-gradient boundary layer was subject to acceleration with K = 3.2 × 10–6, which suppressed the turbulence in the outer region and produced conditions similar to those in turbulent sink flow cases with lower K. In the smooth-wall case, after the momentum thickness Reynolds number had dropped to about 600, the near-wall turbulence then dropped, resulting in relaminarisation. In the rough-wall cases, the near-wall turbulence was sustained in spite of the strong favourable pressure gradient, and relaminarisation did not occur. A temporary equilibrium appears to occur that is similar to that seen with lower K, in spite of the ratio of the boundary-layer thickness to the roughness height dropping to less than 5. Mean velocity and Reynolds stress profiles, quadrant analysis and turbulence spectra are used to show the development of the boundary layer in response to the pressure gradient and the differences between the rough- and smooth-wall cases. This is believed to be the first study to consider the spatial evolution of constant-K rough-wall boundary layers with K large enough to cause relaminarisation in the smooth-wall case.

In compressible turbulent boundary layers (CTBLs), the strong Reynolds analogy (SRA) refers to a set of quantitative relationships between temperature and velocity fluctuations. The essence of the SRA is the linear relationship between these fluctuations in large-scale motions. We investigate the transport processes of the second-order statistical moments associated with temperature and velocity fluctuations to reveal the physical mechanisms underlying this linear correlation. An important finding is that there exists a strong linear mechanism between the turbulent production of velocity and temperature fluctuations. Nonlinear mechanisms, such as the viscous-thermal dissipation, the work contribution, and particularly the pressure term, lead to the failure of the existing SRAs in the outer layer. Based on the above findings, a refined SRA (RSRA) is proposed, which better describes the quantitative relation between the temperature and velocity fluctuation intensities. An approximate expression for the turbulent Prandtl number under different Mach numbers and wall-cooling conditions is derived with the newly proposed RSRA. The relations proposed in this paper are validated through the direct numerical simulation data of flat-plate zero-pressure-gradient CTBLs at different Mach numbers and wall temperatures.

We analyse direct numerical simulations of homogeneous, forced, stably stratified turbulence to study how the pressure–strain and pressure scrambling terms are modified as stability is increased from near neutral to strongly stratified conditions. We decompose the pressure into nonlinear and buoyancy components, and find that the buoyancy part of the pressure–strain correlation changes sign to promote large-scale anisotropy at strong stability, unlike the nonlinear component, which always promotes large-scale isotropy. The buoyancy component of the pressure scrambling term is positive semidefinite and increases monotonically with stability. As its magnitude becomes greater than the nonlinear component (which is negative), the overall scrambling term generates buoyancy flux at very strong stability. We apply quadrant analysis (in the pressure-gradient space) to these correlations to study how contributions from the four quadrants change with stability. Furthermore, we derive exact relationships for the volume-averaged buoyancy components of these correlations which reveal (i) the buoyancy component of the pressure–strain correlation involves a weighted sum of the vertical buoyancy flux cospectrum, so counter-gradient buoyancy fluxes contribute to enhanced anisotropy by transferring vertical kinetic energy into horizontal kinetic energy; (ii) the buoyancy component of the pressure scrambling term involves a weighted sum of the potential energy spectrum; (iii) the weighting factor accentuates contributions from layered motions, which are a prominent feature of strongly stratified flows. These expressions apply generally to all homogeneous stratified flows independent of forcing and across all stability conditions, explaining why these effects have been observed for both forced and sheared stably stratified turbulence simulations.

The breakup of viscous liquid threads is governed by a complex interplay of inertial, viscous and capillary stresses. Theoretical predictions near the point of breakup suggest the emergence of a finite-time singularity, leading to universal power laws describing the breakup, characterised by a universal prefactor. Recent stability analyses indicate that, due to the presence of complex eigenvalues, achieving similarity may only be possible through time-damped oscillations, making it unclear when and how self-similar regimes are reached for both visco-inertial and viscous regimes. In this paper, we combine experiments with unprecedented spatio-temporal resolution and highly resolved numerical simulations to investigate the evolution of the liquid free surface during the pinching of a viscous capillary bridge. We experimentally show for the first time that, for viscous fluids the approach to the self-similar solution is composed of a large overshoot of the instantaneous shrinking speed before the system converges to the nonlinear pinch-off similarity solution. In the visco-inertial case, the convergence to the stable solution is oscillatory, whereas in the viscous case, the approach to singularity is monotonic. While our experimental and numerical results are in good agreement in the viscous regime, systematic differences emerge in the visco-inertial regime, potentially because of effects such as polymer polydispersity, which are not incorporated into our numerical model.