The basic question of whether a hybrid method for turbulence simulation can plausibly capture laminar-to-turbulent transition is addressed. The $\ell ^2$–$\omega$ adaptive detached eddy simulation model (Yin & Durbin, Intl J. Heat Fluid Flow, vol. 62, 2016, pp. 499–509) does so. It dynamically adjusts a model constant, based on local mesh resolution and instantaneous flow features. In a laminar flow, the adaptive procedure returns zero subgrid viscosity, and large-scale low-frequency perturbations are resolved on the grid. However, rather than fully simulating transition, the hybrid model switches on at transition; small-scale turbulence is not resolved. It is found that the correct transitional behaviour is captured because the adaptive formulation responds to the initiation of small-scale components in the field of velocity gradient. The current work addresses flat-plate transition under the influence of free-stream turbulence and pressure gradient, encompassing bypass and separation-induced transition. First, the transition prediction mechanism of the adaptive model is explained. Then, the ability to predict transition statistically is evaluated, along with sensitivity studies of boundary conditions and mesh resolution.

We investigate the dynamics of a self-rewetting drop placed on a substrate with a constant temperature gradient via three-dimensional numerical simulations using a conservative level-set approach to track the interface of the drop. The surface tension of a so-called self-rewetting fluid exhibits a parabolic dependence on temperature with a well-defined minimum. Two distinct drop behaviours, namely deformation and elongation, are observed when it is placed at the location of the minimum surface tension. The drop spreads slightly and reaches a pseudo-steady state in the deformation regime, while it continuously spreads until breakup in the elongation regime. Theoretical models based on the forces exerted on the drop have been developed to predict the critical condition at which the drop undergoes the transition between the two regimes, and the predictions are in good agreement with the numerical results. We also investigate the effect of the initial position of the drop with respect to the location of the minimum surface tension on the spreading and migration dynamics. It is found that, at early times, the migration of the drop obeys an exponential function with time, but it diverges at the later stage due to an increase in the drop deformation.

Near-critical fluids subject to simultaneous thermal quench and an imposed external acceleration field are reported to develop ‘sink zones’, where the temperature in the bulk falls below the imposed boundary value. This anomalous cooling effect persists for a long period of time corresponding to the diffusive elimination of the cold boundary layer. The sink-zone phenomenon has been captured previously in numerical simulations (Zappoli et al., J. Fluid Mech, vol. 316, 1996, pp. 53–72; Sharma et al., Phys. Rev E, vol. 96, 2017, 063102; Sharma et al., Phys. Fluids, vol. 29, 2017, 126103) and was observed experimentally (Beysens et al., Phys. Rev. E, vol. 84, 2011, 051201). The present work provides a detailed and thorough theoretical analysis and interpretation based on matched asymptotic expansions. By examining the one-dimensional transient flow and temperature with a mean-field approach, we provide further insight into this striking phenomenon, showing that the behaviour involved is unique to highly compressible near-critical van der Waals gases. We also show that the sub-cooling phenomenon cannot be predicted in perfect gases unless very extreme conditions are applied.

Our understanding of animal locomotion in air and water has progressed considerably, based on studies of their wakes. Wake vortices are the hallmarks of momentum transfer and enable an inverse inference of the forces applied by animals. Such approach has recently been extended to locomotion at the air–water interface, focusing on the familiar water striders and their dual hallmarks, surface capillary waves and bulk water vortices, produced by their paddling legs. However, the principal mechanisms of propulsion used in this type of locomotion remain a matter of debate. We confirm that the main force driving propulsion is the capillary force resulting from surface tension, and that interface relaxation makes a major contribution to the increase in vorticity of the water bulk. There is therefore no one-to-one mapping between forces and hallmarks in the fluid. Locomotion at the air–water interface for animals with virtual oars much larger than the size of their legs thus requires specific treatment outside the existing framework based on immersed propulsive appendices.

The motion of a rigid sphere in ambient simple shear flow of a Newtonian fluid between infinite parallel walls is calculated via the lattice Boltzmann method for various particle Reynolds numbers, ${\textit {Re}}_p=Ga^2/\nu$, where $G$ is the velocity gradient of the shear; $a$ is the particle radius; and $\nu$ is the kinematic viscosity of the fluid. For a neutrally buoyant sphere, there exists a critical ${\textit {Re}}_p$ below which the hydrodynamic lift force has a single zero crossing, driving the particle to an equilibrium position at the centre of the channel. Above the critical ${\textit {Re}}_p$, the equilibrium position of the sphere undergoes a supercritical pitchfork bifurcation; inertial lift creates three equilibrium positions: an unstable equilibrium position at the centre and two stable equilibria equidistant from the centre. The critical ${\textit {Re}}_p$ occurs below the transition to unsteady flow, and increases with increasing particle confinement ratio, $\kappa =a/H$, where $H$ is the channel height. The equilibrium position of a non-neutrally buoyant sphere shifts toward a confining wall of the channel, in a manner that is dependent on the orientation, i.e. horizontal or vertical, of the channel. In both channel alignments, the gravitational force breaks the symmetry of the particle dynamics about the centreline of the channel, resulting in an imperfect bifurcation above a critical ${\textit {Re}}_p$. However, a sufficiently strong gravitational force will break the bifurcation and produce a single off-centre equilibrium position. We finally consider a neutrally buoyant sphere under the cessation or reversal of shear flow.

Motivated by design challenges related to aerospace propulsive jets, an experimental investigation has been conducted of the high Mach number jet plume flow field from a round convergent nozzle at under-expanded shock-containing conditions. Hot jets up to a total temperature ratio of 3 were considered. Laser doppler anemometry (LDA) measurements in the jet near field (first 15 nozzle exit diameters) captured the turbulent mixing process in detail, enabling the separate effects of compressibility and static temperature ratio (t) on the development of the velocity and turbulence profiles to be identified. Compressibility dominated in the initial shear layer region, whereas temperature effects controlled the downstream jet merging zone. Analysis of shear layer development demonstrated that, at all temperature ratios, a similar, but significantly stronger, damping effect was observed as in planar shear layers (correlated well by convective Mach number Mc). Consideration of the interaction of compressibility and temperature ratio – which reduce/enhance turbulent mixing respectively – provided for the first time a rational explanation of the observation that increasing jet temperature influenced flow development only up to a static temperature ratio t ~ 1.5, after which further increase has little effect. Measurements of the potential core length (Lp) were analysed to produce an empirical correlation that also illustrated the diminishing effects of heat addition at all jet Mach numbers. The data provide the improved understanding and empirical design techniques essential for developing technologies for jet noise and infra red (IR) signature reduction and represent an important validation test case for computational fluid dynamics (CFD) modelling.

We consider three-dimensional turbulence from which vortex stretching is removed. The resulting system conserves enstrophy, but does not conserve kinetic energy. Using spectral closure, it is shown that enstrophy is transferred to small scales by a direct cascade. The inviscid truncated system tends to an equipartition of enstrophy over wave vectors. No inverse cascade is observed once the scales larger than the forcing scale are in equipartition.

The critical dynamics of supersonic combustion waves is studied in the context of the direct initiation of detonation in a spherical geometry. The study is performed by an asymptotic analysis in the limit of small heat release, including unsteadiness, curvature and the gradient of the burnt-gas flow. Derivation of analytical expressions for the rarefaction wave in the burnt-gas flow, combined with numerical studies, provides the basis of the analysis. The critical trajectories ‘detonation velocity vs front radius’ $\mathcal {D}(r_f)$ are characterized by a decay well below the Chapman–Jouguet (CJ) velocity at a small radius (however, larger than the detonation thickness), followed by a re-acceleration process back to a CJ detonation. The phenomenon is explained by the dynamics of the sonic point inside the inert rarefaction wave behind the reaction zone. The key mechanism is a critical slowdown as soon as the sonic condition (relative to the lead shock) approaches the reaction zone from behind, leading to an increase of the time delay in the nonlinear response of the combustion wave to the rarefaction-wave-induced decay. Detonation fails if the rate of decay is strong enough to prevent the sonic point catching the reaction zone. Concerning successful initiation, the link between the trajectories $\mathcal {D}(r_f)$ of the fully unsteady problem and of the self-similar CJ solution of the discontinuous model is deciphered in the long-time limit.

Flow in sidewall cerebral aneurysms can be ideally modelled as the combination of flow over a spherical cavity and flow in a curved circular pipe, two canonical flows. Flow in a curved pipe is known to depend on the Dean number $De$, combining the effects of Reynolds number $\textit {Re}$ and of the curvature along the pipe centreline, $\kappa$. Pulsatility in the flow introduces a dependence on the Womersley number $Wo$. Using stereo particle image velocimetry measurements, this study investigated the effect of these three key non-dimensional parameters, by modifying pipe curvature ($De$), flow rate ($Re$) and pulsatility frequency ($Wo$), on the flow patterns in a spherical cavity. A single counter-rotating vortex was observed in the cavity for all values of pipe curvature $\kappa$ and Reynolds number $\textit {Re}$, for both steady and pulsatile inflow conditions. Increasing the pipe curvature impacted the flow patterns in both the pipe and the cavity, by shifting the velocity profile towards the cavity opening and increasing the flow rate in to the cavity. The circulation in the cavity was found to collapse well with only the Dean number, for both steady and pulsatile inflows. For pulsatile inflow, the counter-rotating vortex was unstable and the location of its centre over time was impacted by the curvature of the pipe, as well as $\textit {Re}$ and $Wo$ in the free stream. The circulation in the cavity was higher for steady inflow than for the equivalent average Reynolds number and Dean number pulsatile inflow, with very limited impact of the Womersley number in the range studied. A second part of this study, that focuses on the changes in fluid dynamics when the intracranial aneurysm is treated with a flow-diverting stent, can be found in this issue (Barbour et al., J. Fluid Mech., vol. 915, 2021, A124).

The flow in a spherical cavity on a curved round pipe is a canonical flow that describes well the flow inside a sidewall aneurysm on an intracranial artery. Intracranial aneurysms are often treated with a flow-diverting stent (FDS), a low-porosity metal mesh that covers the entrance to the cavity, to reduce blood flow into the aneurysm sac and exclude it from mechanical stresses imposed by the blood flow. Successful treatment is highly dependent on the degree of reduction of flow inside the cavity, and the resulting altered fluid mechanics inside the aneurysm following treatment. Using stereoscopic particle image velocimetry, we characterize the fluid mechanics in a canonical configuration representative of an intracranial aneurysm treated with a FDS: a spherical cavity on the side of a curved round pipe covered with a metal mesh formed by an actual medical FDS. This porous mesh coverage is the focus of Part 2 of the paper, characterizing the effects of parent vessel $Re$, $De$ and pulsatility, $Wo$, on the fluid dynamics, compared with the canonical configuration with no impediments to flow into the cavity that is described in Part 1 (Chassagne et al., J. Fluid Mech., vol. 915, 2021, A123). Coverage with a FDS markedly reduces the flow $Re$ in the aneurysmal cavity, creating a viscous-dominated flow environment despite the parent vessel $Re>100$. Under steady flow conditions, the topology that forms inside the cavity is shown to be a function of the parent vessel $De$. At low values of $De$, flow enters the cavity at the leading edge and remains attached to the wall before exiting at the trailing edge, a novel behaviour that was not found under any conditions of the high-$Re$, unimpeded cavity flow described in Part 1. Under these conditions, flow in the cavity co-rotates with the direction of the free-stream flow, similar to Stokes flow in a cavity. As $De$ increases, the flow along the leading edge begins to separate, and the recirculation zone grows with increasing $De$, until, above $De \approx 180$, the flow inside the cavity is fully recirculating, counter-rotating with respect to the free-stream flow. Under pulsatile flow conditions, the vortex inside the cavity progresses through the same cycle – switching from attached and co-rotating with the free-stream flow at the beginning of the cycle (low velocity and positive acceleration) to separated and counter-rotating as $De$ reaches a critical value. The location of separation within the harmonic cycle is shown to be a function of both $De$ and $Wo$. The values of aneurysmal cavity $Re$ based on both the average velocity and the circulation inside the cavity are shown to increase with increasing values of $De$, while $Wo$ is shown to have little influence on the time-averaged metrics. As $De$ increases, the strength of the secondary flow in the parent vessel grows, due to the inertial instability in the curved pipe, and the flow rate entering the cavity increases. Thus, the effectiveness of FDS treatment to exclude the aneurysmal cavity from the haemodynamic stresses is compromised for aneurysms located on high-curvature arteries, i.e. vessels with high $De$, and this can be a fluid mechanics criterion to guide treatment selection.

In this paper, we study wave transmission in a rotating fluid with multiple alternating convectively stable and unstable layers. We have discussed wave transmissions in two different circumstances: cases where the wave is propagative in each layer and cases where wave tunnelling occurs. We find that efficient wave transmission can be achieved by ‘resonant propagation’ or ‘resonant tunnelling’, even when stable layers are strongly stratified, and we call this phenomenon ‘enhanced wave transmission’. Enhanced wave transmission only occurs when the total number of layers is odd (embedding stable layers are alternatingly embedded within clamping convective layers, or vice versa). For wave propagation, the occurrence of enhanced wave transmission requires that the clamping layers have similar properties, the thickness of each clamping layer is close to a multiple of the half-wavelength of the corresponding propagative wave and the total thickness of the embedded layers is close to a multiple of the half-wavelength of the corresponding propagating wave (resonant propagation). For wave tunnelling, we have considered two cases: tunnelling of gravity waves and tunnelling of inertial waves. In both cases, efficient tunnelling requires that the clamping layers have similar properties, the thickness of each embedded layer is much smaller than the corresponding e-folding decay distance and the thickness of each clamping layer is close to a multiple-and-a-half of the half-wavelength (resonant tunnelling).

The surface gravity wave pattern that forms behind a steadily moving disturbance is well known to comprise divergent waves and transverse waves, contained within a distinctive $V$-shaped wake. In this paper, we are concerned with a theoretical study of the limit of a slow-moving disturbance (small Froude numbers) in the absence of surface tension, for which the wake is dominated by transverse waves. Three configurations are considered: flow past a submerged source singularity, a submerged doublet and a pressure distribution applied to the surface. We treat the linearised version of these problems and use the method of stationary phase and exponential asymptotics to demonstrate that the apparent wake angle is less than the classical Kelvin angle and to quantify the decrease in apparent wake angle as the Froude number decreases. These results complement a number of recent studies for sufficiently fast-moving disturbances (large Froude numbers) where the apparent wake angle has been also shown to be less than the classical Kelvin angle. As well as shedding light on the issue of apparent wake angle, we also study the fully nonlinear problems for our three configurations under various limits to demonstrate the unique and interesting features of Kelvin wake patterns at small Froude numbers.

This study identifies and explains the formation mechanisms (FMs) of the secondary vortex street in the far wake of a circular cylinder. Direct numerical simulation and transient growth analysis are performed for a Reynolds number (Re) in the range of 100–200. Unlike most of the earlier studies, which have attributed the formation of the secondary vortices to either the hydrodynamic instability of the mean flow (FM1) or a merging of the two-layered vortices (FM2), the present study demonstrates that both FM1 and FM2 are at play. Specifically, FM1 is observed for Re = 150–160, whereas FM2 is observed for Re = 200. Interestingly, both FM1 and FM2 exist (in an alternate manner) for Re = 170 and 180. The underlying physical mechanism controlling the manifestation of either FM1 or FM2 is explored. In short, secondary vortices that emerge after and before the annihilation of the two-layered vortices are formed from FM1 and FM2, respectively. The variation in the streamwise locations for the emergence of the secondary vortices with Re is quantified and physically explained. Fundamentally, the emergence of the secondary vortices through either FM1 or FM2 is induced by the convective instability of the shear layers in the intermediate wake, which is further induced by an obvious increase in the shear rate of the shear layers as the wake gradually transitions from a primary vortex street to a two-layered vortex street. The general conclusions drawn from a circular cylinder are expected to be applicable to other bluff bodies.

This study explores thermal convection in suspensions of neutrally buoyant, non-colloidal suspensions confined between horizontal plates. A constitutive diffusion equation is used to model the dynamics of the particles suspended in a viscous fluid and it is coupled with the flow equations. We employ a simple model that was proposed by Metzger, Rahli & Yin (J. Fluid Mech., vol. 724, 2013, pp. 527–552) for the effective thermal diffusivity of suspensions. This model considers the effect of shear-induced diffusion and gives the thermal diffusivity increasing linearly with the thermal Péclet number (Pe) and the particle volume fraction (ϕ). Both linear stability analysis and numerical simulation based on the mathematical models are performed for various bulk particle volume fractions $({\phi _b})$ ranging from 0 to 0.3. The critical Rayleigh number $(R{a_c})$ grows gradually by increasing ${\phi _b}$ from the critical value $(R{a_c} = 1708)$ for a pure Newtonian fluid, while the critical wavenumber $({k_c})$ remains constant at 3.12. The transition from the conduction state of suspensions is subcritical, whereas it is supercritical for the convection in a pure Newtonian fluid $({\phi _b} = 0)$. The heat transfer in moderately dense suspensions $({\phi _b} = 0.2\text{--}0.3)$ is significantly enhanced by convection rolls for small Rayleigh number (Ra) close to $R{a_c}$. We also found a power-law increase of the Nusselt number (Nu) with Ra, namely, $Nu\sim R{a^b}$ for relatively large values of Ra where the scaling exponent b decreases with ${\phi _b}$. Finally, it turns out that the shear-induced migration of particles can modify the heat transfer.

We analyse analytically and numerically the scale-invariant stationary solution to the internal-wave kinetic equation. Our analysis of the resonant energy transfers shows that the leading-order contributions are given (i) by triads with extreme scale separation and (ii) by triads of waves that are quasi-collinear in the horizontal plane. The contributions from other types of triads is found to be subleading. We use the modified scale-invariant limit of the Garrett and Munk spectrum of internal waves to calculate the magnitude of the energy flux towards high wavenumbers in both the vertical and the horizontal directions. Our results compare favourably with the finescale parametrization of ocean mixing that was proposed in Polzin et al. (J. Phys. Oceanogr., vol. 25, issue 3, 1995, pp. 306–328).

High-resolution direct numerical simulations are performed to study the turbulent shear flow of liquid metal in a cylindrical container. The flow is driven by an azimuthal Lorentz force induced by the interaction between the radial electric currents injected through electrodes placed at the bottom wall and a magnetic field imposed in the axial direction. All physical parameters, are aligned with the experiment by Messadek & Moreau (J. Fluid Mech. vol. 456, 2002, pp. 137–159). The simulations recover the variations of angular momentum, velocity profiles, boundary layer thickness and turbulent spectra found experimentally to a very good precision. They further reveal a transition to small scale turbulence in the wall side layer when the Reynolds number based on Hartmann layer thickness $R$ exceeds 121, and a separation of this layer for $R \geq 145.2$. Ekman recirculations significantly influence these quantities and determine global dissipation. This phenomenology well captured by the 2-D PSM model (Pothérat, Sommeria & Moreau, J. Fluid Mech. vol. 424, 2000, pp. 75–100) until small-scale turbulence appears and incurs significant extra dissipation only captured by 3-D simulations. Secondly, we recover the theoretical law for the cutoff scale separating large quasi-two-dimensional (Q2-D) scales from small three-dimensional ones (Sommeria & Moreau, J. Fluid Mech. vol. 118, 1982, pp. 507–518), and thus establish its validity in sheared magnetohydrodynamics (MHD) turbulence. We further find that three-componentality and three-dimensionality appear concurrently and that both the frequency corresponding to the Q2-D cutoff scale and the mean energy associated with he axial component of velocity scale with the true interaction parameter $N_t$, respectively, as $0.063 N_t^{0.37}$ and $0.126N_t^{-0.92}$.

We conduct numerical investigations on the early-stage agglomeration of identically charged microparticles in homogeneous isotropic turbulence. The turbulent flow field is evolved by direct numerical simulation, and the adhesive discrete element method is employed to simulate particle transport and agglomerate formation. Through extensive simulations, the effect of Coulomb repulsion on collision frequency is examined. As the particle charge increases, the collision kernel, when plotted as a function of the Stokes number St, is found to change from the increasing trend to the decreasing trend. From decomposition analysis, it turns out that this monotonicity inversion is caused by the shifting of the dominant collision mechanism from preferential concentration to the sling effect. Besides, once particles contact with each other, the sticking probability is shown to solely depend on the dimensionless adhesion parameter, $A{d_n}$, revealing the major role of interparticle adhesion in the collision process. When the effects of Coulomb repulsion and adhesion both exist, particles with moderate collision velocities are more likely to contribute to the formation of agglomerates. The structure of the agglomerates is then measured using the fractal dimension. It is found that, due to its isotropic feature, Coulomb repulsion effectively reduces the agglomeration rate but has a negligible effect on the structure of agglomerates.

Cylinder stubs of finite length, mounted in a wall-normal manner on a flat plate, exert considerable control on their wake when rotating around their central axis. The present paper investigates these effects with linear stability theory and a direct numerical simulation. Three configurations are considered: evenly spaced corotating roughness elements, as well as positive and negative counter-rotating roughness pairs. Here, ‘positive’ and ‘negative’ are defined in accordance with the induced high- and low-speed streaks, respectively. A primary feature of the rotating-cylinder-induced wake is a ‘dominating inner vortex’ (DIV), which intensifies the lift-up effect and creates high-amplitude streaks. Linear stability analysis shows that the modified streaky flow is capable of effectively stabilizing Tollmien–Schlichting (TS) modes. The mechanism of TS mode stabilization, as found by a perturbation kinetic energy analysis, is attributed to the reduction of the wall-normal perturbation production. On the other hand, an inviscid inflectional instability mode related to the presence of the roughness appears which destabilizes the boundary-layer flow, primarily due to an increase in wall-normal perturbation energy production, but also due to increasing spanwise energy production, depending on the case. The inflectional instability roughness mode is more amplified with thicker cylinders since the induced DIV tends to support longer-living inflection points. Regarding an imaginable laminar–turbulent transition delay, positive rotating thinner roughness pairs would be preferable.

We consider a free-surface thin film placed on a thermally conductive substrate and exposed to an external heat source in a set-up where the heat absorption depends on the local film thickness. Our focus is on modelling film evolution while the film is molten. The evolution of the film modifies local heat flow, which in turn may influence the film surface evolution through thermal variation of the film's material properties. Thermal conductivity of the substrate plays an important role in determining the heat flow and the temperature field in the evolving film and in the substrate itself. In order to reach a tractable formulation, we use asymptotic analysis to develop a novel thermal model that is accurate, computationally efficient, and that accounts for the heat flow in both the in-plane and out-of-plane directions. We apply this model to metal films of nanoscale thickness exposed to heating and melting by laser pulses, a set-up commonly used for self and directed assembly of various metal geometries via dewetting while the films are in the liquid phase. We find that thermal effects play an important role, and in particular that the inclusion of temperature dependence in the metal viscosity modifies the time scale of the evolution significantly. On the other hand, in the considered set-up the Marangoni (thermocapillary) effect turns out to be insignificant.

The interaction of zero-mean-shear turbulence (generated using an oscillating grid) with solid and permeable boundaries is studied experimentally. The influence of wall permeability is characterised using the permeability Reynolds number, $Re_K$, which represents the ratio of the typical pore size in the permeable medium to a viscous length scale. Instantaneous velocity measurements, obtained using two-dimensional particle imaging velocimetry, are used to study the effect boundary permeability has on the root mean square of fluctuating velocity components, the vertical flux of turbulent kinetic energy (TKE) and conditional turbulent statistics associated with events in which intercomponent energy transfer is concentrated. When $Re_K \lesssim 0.2$ the boundary acts as if it were impermeable; results indicate the interaction is dominated by the kinematic blocking effect of the boundary on the boundary-normal TKE flux, with additional mechanisms acting through intercomponent energy transfer. The results show these mechanisms are inhibited as $Re_K$ increases, due to the transportation of turbulent energy into the porous medium as the macroscopic blocking condition is relaxed, thereby reducing TKE within the boundary-affected region and inhibiting the formation of high-pressure stagnation events that are responsible for intercomponent energy transfer. The results illustrate how the turbulence structure above a permeable boundary is sensitive to the blocking effect on the boundary-normal turbulent velocity. In light of these results, we propose that further analysis is required to establish the validity of a commonly used model of the boundary conditions enforced at the boundary of porous media, in which a no-penetration boundary condition on the boundary-normal velocity component is proposed.