The vortex dynamics in a stratified environment is of fundamental importance in various flow systems, however, the mechanism of successive vortex–interface interactions remains not fully understood. This study investigates synthetic jet vortex rings impinging on a water–oil interface by experiment and numerical simulation. Two cases in the laminar and transitional regimes are concerned with the Froude number (Fr) of 0.35 and 0.82, respectively. The vortex rings for the two cases follow a similar evolution with three distinct stages, including vortex free-travel, vortex–interface interaction and vortex stretching. As products of the vortex–interface interaction, the secondary vortex rings are baroclinically generated in both water and oil followed by the formation of hairpin vortices through azimuthal deformation. Distinguished from an isolated vortex–interface interaction, complex interactions occur between the primary vortex ring and hairpin vortices, which can enhance the vortex ring instability in existence of the stratification for the laminar case. However, the vortex ring instability for the transitional case can develop earlier due to nonlinear effects with increasing Reynolds number. The spatio-temporal properties of the interface deformation and interfacial waves are analysed. The maximum penetration height of vortex rings scales with Fr2 as that for the isolated situation. Particularly, the transitional case is found to produce destabilization of the interfacial waves at a further radial location. The mechanism is revealed by connecting the dynamics of the vortex and the interface, which can be attributed to the radial development of perturbances stemming from the vortex ring instability under strong vortex–interface interaction.

We report direct numerical simulations (DNS) of the Nusselt number $Nu$, the vertical profiles of mean temperature $\varTheta (z)$ and temperature variance $\varOmega (z)$ across the thermal boundary layer (BL) in closed turbulent Rayleigh–Bénard convection (RBC) with slippery conducting surfaces ($z$ is the vertical distance from the bottom surface). The DNS study was conducted in three RBC samples: a three-dimensional cuboid with length $L = H$ and width $W = H/4$ ($H$ is the sample height), and two-dimensional rectangles with aspect ratios $\varGamma \equiv L/H = 1$ and $10$. The slip length $b$ for top and bottom plates varied from $0$ to $\infty$. The Rayleigh numbers $Ra$ were in the range $10^{6} \leqslant Ra \leqslant 10^{10}$ and the Prandtl number $Pr$ was fixed at $4.3$. As $b$ increases, the normalised $Nu/Nu_0$ ($Nu_0$ is the global heat transport for $b = 0$) from the three samples for different $Ra$ and $\varGamma$ can be well described by the same function $Nu/Nu_0 = N_0 \tanh (b/\lambda _0) + 1$, with $N_0 = 0.8 \pm 0.03$. Here $\lambda _0 \equiv L/(2Nu_0)$ is the thermal boundary layer thickness for $b = 0$. Considering the BL fluctuations for $Pr>1$, one can derive solutions of temperature profiles $\varTheta (z)$ and $\varOmega (z)$ near the thermal BL for $b \geqslant 0$. When $b=0$, the solutions are equivalent to those reported by Shishkina et al. (Phys. Rev. Lett., vol. 114, 2015, 114302) and Wang et al. (Phys. Rev. Fluids, vol. 1, 2016, 082301(R)), respectively, for no-slip plates. For $b > 0$, the derived solutions are in excellent agreement with our DNS data for slippery plates.

Opposition control of artificially initiated turbulent spots in a laminar boundary layer was carried out in a low-turbulence wind tunnel with the aim to delay transition to turbulence by modifying the turbulent structure within the turbulent spots. The timing and duration of control, which was carried out using wall-normal jets from a spanwise slot, were pre-determined based on the baseline measurements of the transitional boundary layer. The results indicated that the high-speed region of the turbulent spots was cancelled by opposition control, which was replaced by a carpet of low-speed fluid. The application of the variable-interval time-averaging technique on the velocity fluctuation signals demonstrated a reduction in both the burst duration and intensity within the turbulent spots, but the burst frequency was increased.

Synchronization of turbulence in channel flow is investigated using continuous data assimilation. The flow is unknown within a region of the channel. Beyond this region the velocity field is provided, and is directly prescribed in the simulation, while the pressure is unknown throughout the entire domain. Synchronization takes place when the simulation recovers the full true state of the flow, or in other words when the missing region is accurately re-established, spontaneously. Successful synchronization depends on the orientation, location and size of the missing layer. For friction Reynolds numbers up to one thousand, wall-attached horizontal layers can synchronize as long as their thickness is less than approximately thirty wall units. When the horizontal layer is detached from the wall, the critical thickness increases with height and is proportional to the local wall-normal Taylor microscale. A flow-parallel, vertical layer that spans the height of the channel synchronizes when its spanwise width is of the order of the near-wall Taylor microscale, while the criterion for a crossflow vertical layer is set by the advection distance within a Lyapunov time scale. Finally, we demonstrate that synchronization is possible when only planar velocity data are available, rather than the full outer state, as long as the unknown region satisfies the condition for synchronization in one direction. These numerical experiments demonstrate the capacity of accurately reconstructing, or synchronizing, the missing scales of turbulence from observations, using continuous data assimilation.

A theoretical model is developed for the forced convection film boiling phenomenon over a heated sphere moving vertically downwards in the water. Unprecedented compared with the previous analytical studies, this model accounts for the buoyancy effects while solving the momentum and energy equations in the vapour phase to obtain the velocity and the temperature distribution in terms of the vapour boundary layer thickness. To calculate the vapour boundary layer thickness, an energy balance is applied at the vapour–liquid interface. The flow of liquid around the sphere is considered to be governed by potential theory, and the energy equation in liquid is then solved for the known velocity distribution. We find that the vapour boundary layer thickness increases with an increase in the sphere temperature, the bulk water temperature and a decrease in the free stream velocity. This further results in a decrease in the film boiling heat transfer coefficient. The present study concludes that at low free stream velocities (${<}0.5\, {\rm m}\,{\rm s}^{-1}$) buoyancy becomes significant in delaying the separation, and when the velocity is further reduced the separation angle approaches $180^{\circ}$.

This work is concerned with the laminar–turbulent transition in the boundary layer on an aircraft wing covered by a water film. We consider the initial stage of the transition process known as the receptivity of the boundary layer, namely, we study the generation of the interfacial instability waves by the unsteady free-stream acoustic noise interacting with a small roughness on the wing surface. For effective receptivity, the ‘forcing’ should obey the so-called ‘double-resonance’ principle. According to this principle, both the frequency and the wavenumber of the external perturbations should be in tune with the natural instability modes of the flow. Correspondingly, we choose the frequency of the acoustic wave to coincide with that of the interfacial instability wave. However, this makes the wavelength of the acoustic wave significantly larger than wavelength of the instability wave. Thus, the second resonance condition is not satisfied, which means that the acoustic wave alone cannot produce the instability waves in the boundary layer. Instead, the Stokes layer is created in the boundary layer just above the liquid film. As far as the film is concerned, it also experiences wave-like motion caused by the varying shear stress on the interface. The generation of the interfacial instability waves takes place when the Stokes layer encounters a wall roughness that is short enough for an appropriate scale conversion to take place. To describe the flow in the vicinity of the roughness, a suitably modified triple-deck theory is used.

In this paper, two-phase flow simulations of oscillatory sheet flow experimental configurations involving medium and fine sand using a turbulence-resolving two-fluid model are presented. The turbulence-resolving two-phase flow model reproduces the differences of behaviour observed between medium and fine sand whereas turbulence-averaged models require an almost systematic tuning of empirical model coefficients for turbulence–particle interactions. The two-fluid model explicitly resolves these interactions and can be used to study in detail the differences observed experimentally. Detailed analysis of concentration profiles, flow hydrodynamics, turbulent statistics and vertical mass balance allowed the confirmation that unsteady effects, namely phase-lag effect and enhanced boundary layer thickness, for fine sand are not only due to the small settling velocity of the particles relative to the wave period. The occurrence and intensity of unsteady effects are also affected by a complex interplay between flow instabilities, strong solid-phase Reynolds stress and turbulence attenuation caused by the presence of the particles.

Experiments on particle-free and particle-laden flows with the same incoming velocity were conducted in a horizontal wind tunnel. Three cases of particle-laden flows with different degrees of particle near-wall motions and similar particle volume fractions, including top-release particles, local-laying sand beds and global-laying sand beds, were designed to investigate the effects of collision bounces and impact splashing on turbulence statistics. The top-released particles accelerate the fluid during gravitational settling, but weaken the intensity and reduce the probability of ‘ejection’ and ‘sweep’ events. This leads to a weakened Reynolds stress and a decreased scale of the outer spectral peak at the centre of the logarithmic region, indicating a concentration of energy at small scales. In contrast, the collision bounce and impact splashing slow the fluid but promote the ‘ejection and sweep’ cycle with larger intensity, and thus enhance the Reynolds stress. Meanwhile, the bouncing and splashing generate ascending particles that transport the kinetic energy upwards, resulting in more energetic very-large-scale motions further from the wall. This study reveals the importance of particle motions to turbulence, and contributes to a further insight into the interactions between particles and turbulence in two-phase flows with erodible surfaces.

The transport coefficients of a dilute gas of inelastic hard spheres immersed in a gas of elastic hard spheres (molecular gas) are determined. We assume that the number density of the granular gas is much smaller than that of the surrounding molecular gas, so that the latter is not affected by the presence of the granular particles. In this situation, the molecular gas may be treated as a thermostat (or bath) of elastic hard spheres at a fixed temperature. The Boltzmann kinetic equation is the starting point of the present work. The first step is to characterise the reference state in the perturbation scheme, namely the homogeneous state. Theoretical results for the granular temperature and kurtosis obtained in the homogeneous steady state are compared against Monte Carlo simulations showing a good agreement. Then, the Chapman–Enskog method is employed to solve the Boltzmann equation to first order in spatial gradients. In dimensionless form, the Navier–Stokes–Fourier transport coefficients of the granular gas are given in terms of the mass ratio $m/m_g$ ($m$ and $m_g$ being the masses of a granular and a gas particle, respectively), the (reduced) bath temperature and the coefficient of restitution. Interestingly, previous results derived from a suspension model based on an effective fluid–solid interaction force are recovered in the Brownian limit ($m/m_g \to \infty$). Finally, as an application of the theory, a linear stability analysis of the homogeneous steady state is performed showing that this state is always linearly stable.

The buoyancy-driven dynamics of a pair of gas bubbles released in line is investigated numerically, focusing on highly inertial conditions under which isolated bubbles follow non-straight paths. In an early stage, the second bubble always drifts out of the wake of the leading one. Then, depending on the ratios of the buoyancy, viscous and capillary forces which define the Galilei ($Ga$) and Bond ($Bo$) numbers of the system, five distinct regimes specific to such conditions are identified, in which the two bubbles may rise independently or continue to interact and possibly collide in the end. In the former case, they usually perform large-amplitude planar zigzags within the same plane or within two distinct planes, depending on the oblateness of the leading bubble. However, for large enough $Ga$ and low enough $Bo$, they follow nearly vertical paths with small-amplitude erratic horizontal deviations. Increasing $Bo$ makes the wake-induced attraction toward the leading bubble stronger, forcing the two bubbles to realign vertically one or more times along their ascent. During such sequences, wake vortices may hit the trailing bubble, deflecting its path and, depending on the case, promoting or hindering further possibilities of interaction. In some regimes, varying the initial distance separating the two bubbles modifies their lateral separation beyond the initial stage. Similarly, minute initial angular deviations favour the selection of a single vertical plane of rise common to both bubbles. These changes may dramatically affect the fate of the tandem as, depending on $Bo$, they promote or prevent future vertical realignments.

Solvent exchange is a process involving mixing between a good solvent with dissolved solute and a poor solvent. The process creates local oversaturation which causes the nucleation of minute solute droplets. Such ternary systems on a macro-scale have remained unexplored in the turbulent regime. We experimentally study the solvent exchange process by injecting mixtures of ethanol and trans-anethole into water, forming a turbulent buoyant jet in the upward direction. Locally, turbulent mixing causes oversaturation of the trans-anethole following turbulent entrainment. We optically measure the concentration of the nucleated droplets using a light attenuation technique and find that the radial concentration profile has a sub-Gaussian kurtosis. In contrast to the entrainment-based models, the spatial evolution of the oversaturation reveals continuous droplet nucleation downstream and radially across the jet, which we attribute to the limited mixing capacity of the jet. Although we are far from a full quantitative understanding, this work extends the knowledge on solvent exchange into the turbulent regime, and brings in a novel type of flow, broadening the scope of multicomponent, multiphase turbulent jets with phase transition.

The influence of thermocapillary stresses on motion of a slowly evaporating single-component droplet in Stokes flow is investigated analytically for the situation where the environment does not have a temperature gradient in the far field. The conservation equations are solved in the liquid and gas phases and coupled at the gas–liquid interface by applying conditions for conservation of mass, species, momentum and energy. It is found that thermocapillary stresses may influence droplet motion by changing the the interface velocity, and that the gas-phase Lewis number of the evaporating component determines whether Marangoni effects increase or decrease droplet drag. If the Lewis number is less than unity, then thermal Marangoni effects increase droplet drag, while if the Lewis number is greater than unity, then thermal Marangoni effects decrease droplet drag. This is related to the sign of the temperature gradient along the droplet surface that is induced by convection. It is found that conditions may exist where a vaporizing droplet in a microgravity environment will exhibit continuous translational motion driven by thermocapillary effects.

Acoustic emission of a NACA 0012 aerofoil is investigated over a range of free-stream velocities. Acoustic spectra show a dominant tone and two sets of weaker side tones characterised by different frequency intervals. The frequency of the dominant tones in the acoustic spectra varies with velocity in a ladder-type structure. With increasing Reynolds number, the spectrum becomes progressively more broadband in nature. Through synchronised particle image velocimetry and acoustic measurements, the aeroacoustic noise generation mechanisms, resulting in different spectral characteristics and modulation types, are further investigated. A separation bubble and related significant velocity fluctuations are observed on the pressure side. Pressure side velocity spectra show characteristics similar to the acoustic ones, whereas velocity spectra on the suction side feature broadband characteristics. These findings confirm that noise emission is dominated by pressure side events for the Reynolds number range of this study, i.e. $2 \times 10^{5}$–$7 \times 10^{5}$. As the acoustic emission is defined by coherent flow structures, the proper orthogonal decomposition method is adopted to facilitate the understanding of the relation between the complex flow field and acoustic emission. Side tones in the acoustic spectra are attributed to two different modulation mechanisms in the aeroacoustic source region near the trailing edge. By aligning the sound pressure time history and the time coefficients of the dominant modes, the primary modulation of the dominant tone is found to be related to the amplitude modulation of the high-frequency velocity fluctuations associated with the acoustic feedback loop. A secondary modulation is attributed to periodic variation of the separation bubble and, therefore, variation in the roll-up of the shear layer, which results in a modulation of the amplitude of the velocity fluctuations associated with the convecting vortices at the trailing edge.

We explore wall-attached structures in a drag-reduced turbulent channel flow with the Navier slip boundary condition. Three-dimensional coherent structures of the streamwise velocity fluctuations (u) are examined in an effort to assess the influence of wall-attached u structures on drag reduction. We extract the u clusters from the direct numerical simulation (DNS) data; the DNS data for the no-slip condition are included for comparison. The wall-attached structures, which are physically adhered to the wall, in the logarithmic region are self-similar with their height and contribute to the presence of logarithmic behaviour. The influence of the streamwise slip on wall-attached structures is limited up to the lower bound of the logarithmic region. Although wall-attached self-similar structures (WASS) slide at the wall, the formation and hierarchy of WASS are sustained. Weakened mean shear by the streamwise slip results in a diminution in the population density of wall-attached structures within the buffer layer, leading to sparse population of WASS. In contrast, the space occupied by WASS in the fluid domain increases. The streamwise slip induces long tails in the near-wall part of WASS, reminiscent of the footprints of large-scale motions. Both a decrease in the population density of WASS and a reduction in the density of skin friction of WASS are responsible for the overall drag reduction.

Earthquakes are a great challenge for the safety of nuclear reactors. To address this challenge, we need to better understand how the reactor core responds to seismic forcing. The reactor core is made of fuel assemblies, which are themselves composed of flexible fuel rods immersed in a strong axial flow. This gives rise to strongly coupled fluid–structure interactions whose accurate modelling generally requires high computational costs. In this paper, we introduce a new model able to capture the mechanical response of the reactor core subjected to seismic forcing with low computational costs. This model is based on potential flow theory for the fluid part, and Euler–Bernoulli beam theory for the structural part, allowing us to predict the response to seismic forcing in presence of axial flow. The linear equations are solved in the Fourier space to decrease computational time. For validation purposes, first we use the proposed model to compute the response of a single cylinder in axial flow. We then implement a multiple-cylinder geometry made of four fuel assemblies, each made of $8\times 8$ cylinders, corresponding to an experimental facility available at CEA. The comparison between numerical results and experiments shows good agreement. The model can predict correctly the added mass. It can also capture qualitatively the coupling between assemblies and the effect of confinement. This shows that a potential flow approach can give insight into the complex fluid–structure interactions within a nuclear reactor and, in particular, be used to predict the response to seismic forcing at low computational cost.

The effects of a wavy wall on the stability of a hypersonic boundary layer on a flared cone are investigated by detailed experimental measurements and direct numerical simulations. The non-contact optical measurement method of focused laser differential interferometry is used to measure the disturbance development within the wavy region. The measurement results show that the second mode for the wavy wall is suppressed significantly compared with the smooth wall, and that multiple disturbances at low frequencies appear within the wavy region. Numerical corroboration against experimental measurements reveals good quantitative agreement. It is found that the disturbances at $f=360$ kHz on the wavy wall are suppressed appreciably, which are very significant on the smooth wall. And the disturbances at $f=140$ kHz and $f=260$ kHz develop within the wavy region, and increase considerably. Also, the disturbances achieve a significant increase over the first half of a wavy trough and become more stable over the second half of a wavy trough. The physical mechanism is found to be due to the change in wall geometry and is attributed to the spatially modulated mean flow. The disturbance growth rate is closely related to the level of the mean-flow distortion.

A scaling theory for the passive scalar transport in Couette flow, i.e. the flow between two parallel plates moving with different velocities, is proposed. This flow is determined by the bulk Reynolds number $Re_b$ and the Prandtl number $Pr$. In the turbulent regime, for moderate shear Reynolds number $Re_{\tau }$ and moderate $Pr$, we derive that the passive scalar transport characterised by the Nusselt number $Nu$ scales as $Nu \sim Pr^{1/2}Re_{\tau }^{2}Re_b^{-1}$. We then use the well-established scaling for the friction coefficient $C_f \sim Re_b^{-1/4}$ (corresponding to a shear Reynolds number $Re_{\tau } \sim Re_b^{7/8}$) which holds reasonably well within the range $3\times 10^{3} \leqslant Re_b \leqslant 10^{5}$, to obtain $Nu \sim Pr^{1/2}Re_b^{3/4}$ for the Nusselt number scaling. The theoretical results are tested against direct numerical simulations of Couette flows for the parameter ranges $81 \leqslant Re_b \leqslant 22361$ and $0.1 \leqslant Pr \leqslant 10$, finding good agreement. Analyses of the numerically obtained turbulent flow fields confirm logarithmic mean wall-parallel profiles of the velocity and the passive scalar in the inertial sublayer.

We perform a three-dimensional short-wavelength linear stability analysis of numerically simulated two-dimensional Kelvin–Helmholtz vortices in homogeneous and stratified environments at a fixed Reynolds number of $Re = 300$. For the homogeneous case, the elliptic instability at the vortex core dominates at early times, before being taken over by the hyperbolic instability at the vortex edge. For the stratified case of Richardson number $ Ri = 0.08$, the early-time instabilities comprise a dominant elliptic instability at the core and a hyperbolic instability influenced strongly by stratification at the vortex edge. At intermediate times, the local approach shows a new branch of (convective) instability that emerges at the vortex core and subsequently moves towards the vortex edge. A few more convective instability bands appear at the vortex core and move away, before coalescing to form the most unstable region inside the vortex periphery at large times. In addition, the stagnation point instability is also recovered outside the periphery of the vortex at intermediate times. The dominant instability characteristics from the local approach are shown to be in good qualitative agreement with the results based on global instability studies for both homogeneous and stratified cases. A systematic study of the dependence of the dominant instability characteristics on $ Ri $ is then presented. While $ Ri = 0.1$ is identified as most unstable (with convective instability being dominant), another growth rate maximum at $ Ri = 0.025$ is not far behind (with the hyperbolic instability influenced by stratification being dominant). Finally, the local stability approach is shown to predict the potential orientation of the flow structures that would result from hyperbolic and convective instabilities, which is found to be consistent with three-dimensional numerical simulations reported previously.

Debris flows are particle–fluid mixtures that pose a significant hazard to many communities throughout the world. Bouldery debris flows are often characterised by a deep dry granular flow front, which is followed by a progressively thinner and increasingly watery tail. The formation of highly destructive bouldery wave fronts is usually attributed to particle-size segregation. However, the moving-bed flume experiments of Davies (N. Z. J. Hydrol., vol. 29, 1990, pp. 18–46) show that discrete surges with dry fronts and watery tails also form in monodisperse particle–fluid mixtures. These observations motivate the development of a new depth-averaged mixture theory for debris flows, which explicitly takes account of the differing granular and phreatic surfaces, velocity shear, and relative motion between grains and fluid to explain these phenomena. The theory consists of four coupled conservation laws that describe the spatial and temporal evolution of the grain and water thicknesses and depth-averaged velocities. This system enables travelling wave solutions to be constructed that consist of (i) a large amplitude dry flow front that smoothly transitions to (ii) an undersaturated body, (iii) an oversaturated region and then (iv) a pure water tail. It is shown that these solutions are in good quantitative agreement with Davies’ experiments at high bed speeds and slope inclinations. At lower bed speeds and inclinations, the theory produces travelling wave solutions that connect to a steady-uniform upstream flow, and may or may not have a bulbous flow front, consistent with Davies’ observations.

The linear stability of thermal buoyant flow in a fluid-saturated vertical porous slab is studied under the assumption of weak and strong horizontal heterogeneities of the permeability. The two end vertical isothermal boundaries are impermeable and some paradigmatic cases of linear, quadratic and exponential heterogeneity models are deliberated. The stability/instability of the basic flow is examined by carrying out a numerical solution of the governing equations for the disturbances as Gill's proof (A.E. Gill, J. Fluid Mech, vol. 35, 1969, pp. 545–547) of linear stability is found to be ineffective. The possibilities of base flow becoming unstable due to heterogeneity in permeability are recognized, in contrast to Gill's stability problem. The neutral stability curves are presented and the critical Darcy–Rayleigh number for the onset of convective instability is computed for different values of the variable permeability constant. The similarities and differences between different heterogeneity models on the stability of fluid flow are clearly discerned.