The flow inside a circular pipe is known to support localised patches of turbulence travelling downstream. When the diameter of the pipe is slowly increasing, seemingly analogous but motionless patches can congest the flow and lead to disastrous energetic performance. Until now, no theory has predicted quantitatively the flow rates at which such a steady turbulent puff could be expected. The recent large-scale numerical study by Selvam et al. (J. Fluid Mech., vol. 771, 2015, R2) offers the first realistic simulation of this phenomenon, with a detailed analysis of the bifurcation sequence leading from the laminar flow to the localised turbulence regime. Similarities and differences between straight and divergent cases are also discussed.

It is often observed that small drops or bubbles detach from the interface separating two co-flowing immiscible fluids. The size of these drops or bubbles can be orders of magnitude smaller than the length scales of the parent fluid mass. Examples are tip-streaming from drops or coaxial jets in microfluidics, selective withdrawal, ‘skirt’ formation around bubbles or drops, and others. It is argued that these phenomena are all reducible to a common instability that can occur due to a local convergence of streamlines in the neighbourhood of a zero-vorticity point or line on the interface. When surfactants are present, this converging flow tends to concentrate them in these regions weakening the effect of surface tension, which is the only mechanism opposing the instability. Several analytical and numerical calculations are presented to substantiate this interpretation of the phenomenon. In addition to some idealized cases, the results of two-dimensional simulations of co-flowing jets and a rising drop are presented.

When a vertical rigid plate is uniformly accelerated horizontally from rest into an initially stationary layer of inviscid incompressible fluid, the free surface will undergo a deformation in the locality of the contact point. This deformation of the free surface will, in the early stages, cause a jet to rise up the plate. An understanding of the local structure of the free surface in the early stages of motion is vital in many situations, and has been developed in detail by King & Needham (J. Fluid Mech., vol. 268, 1994, pp. 89–101). In this work we consider the effects of introducing weak surface tension, characterized by the inverse Weber number $\mathscr{W}$, into the problem considered by King & Needham. Our approach is based upon matched asymptotic expansions as $\mathscr{W}\rightarrow 0$. It is found that four asymptotic regions are needed to describe the problem. The three largest regions have analytical solutions, whilst a numerical method based on finite differences is used to solve the time-dependent harmonic boundary value problem in the last region. Our results identify the local structure of the jet near the vicinity of the contact point, and we highlight a number of key features, including the height of this jet as well as its thickness and strength. We also present some preliminary experimental results that capture the spatial structure near the contact point, and we then show promising comparisons with the theoretical results obtained within this paper.

Axisymmetric non-isothermal spreading/dewetting of droplets on a substrate is studied, wherein the surface tension is a function of temperature, resulting in Marangoni stresses. A lubrication theory is first extended to determine the drop shape for spreading/dewetting limited by slip. It is demonstrated that an apparent angle inferred from a fitted spherical cap shape does not relate to the contact-line speed as it would under isothermal conditions. Also, a power law for the thermocapillary spreading rate versus time is derived. Results obtained with direct numerical simulations (DNS), using a slip length down to $O(10^{-4})$ times the drop diameter, confirm predictions from lubrication theory. The DNS results further show that the behaviour predicted by the lubrication theory – that a cold wall promotes spreading, and a hot wall promotes dewetting – is reversed at sufficiently large contact angles and/or viscosity of the surrounding fluid. This behaviour is summarized in a phase diagram, and a simple model that supports this finding is presented. Although the key results are found to be robust when accounting for heat conduction in the substrate, a critical thickness of the substrate is identified above which wall conduction significantly modifies wetting behaviour.

Large-scale patterns, which are well-known from the spiral defect chaos (SDC) regime of thermal convection at Rayleigh numbers $\mathit{Ra}<10^{4}$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh–Bénard convection in extended cylindrical cells with an aspect ratio ${\it\Gamma}=50$ and $\mathit{Ra}>10^{5}$. They are revealed when the turbulent fields are averaged in time and turbulent fluctuations are thus removed. We apply the Boussinesq closure to estimate turbulent viscosities and diffusivities, respectively. The resulting turbulent Rayleigh number $\mathit{Ra}_{\ast }$, that describes the convection of the mean patterns, is indeed in the SDC range. The turbulent Prandtl numbers are smaller than one, with $0.2\leqslant \mathit{Pr}_{\ast }\leqslant 0.4$ for Prandtl numbers $0.7\leqslant \mathit{Pr}\leqslant 10$. Finally, we demonstrate that these mean flow patterns are robust to an additional finite-amplitude sidewall forcing when the level of turbulent fluctuations in the flow is sufficiently high.

For a stratified incompressible Euler fluid under gravity confined by rigid boundaries, sources of vorticity are classified with the aim of isolating those which are sensitive to the topological configurations of density isopycnals, for both layered and continuous density variations. The simplest case of a two-layer fluid is studied first. This shows explicitly that topological sources of vorticity are present whenever the interface intersects horizontal boundaries. Accordingly, the topological separation of the fluid domain due to the interface–boundary intersections can contribute additional terms to the vorticity balance equation. This phenomenon is reminiscent of Klein’s ‘Kaffeelöffel’ thought-experiment for a homogeneous fluid (Klein, Z. Math. Phys., vol. 59, 1910, pp. 259–262), and it is essentially independent of the vorticity generation induced by the baroclinic term in the bulk of the fluid. In fact, the two-layer case is generalized to show that for the continuously stratified case topological vorticity sources are generically present whenever density varies along horizontal boundaries. The topological sources are expressed explicitly in terms of local contour integrals of the pressure along the intersection curves of isopycnals with domain boundaries, and their effects on vorticity evolution are encoded by an appropriate vector, termed here the ‘topological vorticity’.

This paper is concerned with the dynamics of large bubbles subject to various strengths of buoyancy effects, which are associated with applications for underwater explosion. The bubble is produced by electric discharge in a low-pressure tank to enhance the buoyancy effects. Experiments are carried out for a bubble in an infinite field, below a free surface and above a rigid boundary. The effects of buoyancy are reflected by the dimensionless parameter ${\it\delta}=\sqrt{{\it\rho}gR_{m}/(p_{amb}-p_{v})}$, where $R_{m}$, $p_{amb}$, $p_{v}$, ${\it\rho}$ and $g$ are the maximum bubble radius, ambient pressure, saturated vapour pressure, density of water and the acceleration of gravity respectively. A systematic study of buoyancy effects is carried out for a wide range of ${\it\delta}$ from 0.034 to 0.95. A series of new phenomena and new features is observed. The bubbles recorded are transparent, and thus we are able to display and study the jet formation, development and impact on the opposite bubble surface as well as the subsequent collapsing and rebounding of the ring bubble. Qualitative analyses are carried out for the bubble migration, jet velocity and jet initiation time, etc. for different values of ${\it\delta}$. When a bubble oscillates below a free surface or above a rigid boundary, the Bjerknes force due to the free surface (or rigid boundary) and the buoyancy are in opposite directions. Three situations are studied for each of the two configurations: (i) the Bjerknes force being dominant, (ii) the buoyancy force being dominant and (iii) the two forces being approximately balanced. For case (iii), we further consider two subcases, where both the balanced Bjerknes and buoyancy forces are weak or strong. When the Bjerknes and buoyancy forces are approximately balanced over the pulsation, some representative bubble behaviours are observed: the bubble near free surface is found to split into two parts jetting away from each other for small ${\it\delta}$, or involutes from both top and bottom for large ${\it\delta}$. A bubble above a rigid wall is found to be subject to contraction from the lateral part leading to bubble splitting. New criteria are established based on experimental results for neutral collapses where there is no dominant jetting along one direction, which correlate well with the criteria of Blake et al. (J. Fluid Mech., vol. 170, 1986, pp. 479–497; J. Fluid Mech., vol. 181, 1987, pp. 197–212) but agree better with the experimental and computational results.

This numerical study investigates flow and turbulence structure through and around a circular array of solid circular cylinders of diameter $d$. The region containing the array of rigid cylinders resembles a porous circular cylinder of diameter $D$. The porous cylinder Reynolds number defined with the steady incoming flow velocity is $\mathit{Re}_{D}=10\,000$. Fully three-dimensional (3D) large eddy simulations (LES) are conducted to study the effects of the volume fraction of solids of the porous cylinder ($0.023<\text{SVF}<0.2$) and $d/D$ on the temporal variation and mean values of the drag/lift forces acting on the solid cylinders and on the porous cylinder. The effects of the bleeding flow through the circular porous cylinder on the wake structure and the influence of the SVF and $d/D$ on the onset of flow three-dimensionality within or downstream of the porous cylinder and transition to turbulence are discussed. Results are compared with experimental data, predictions of theoretical models available in the literature and also with the canonical case of a solid cylinder ($\text{SVF}=1,d/D=1$). Three-dimensional LES predict that large-scale wake billows are shed in the wake of the porous cylinder for $\text{SVF}>0.05$, similar to the von Karman vortex street observed for solid cylinders. As the SVF decreases, the length of the separated shear layers (SSLs) of the porous cylinder and the distance from the back of the porous cylinder at which wake billows form increase. For sufficiently low volume fractions of solids (e.g. $\text{SVF}=0.05$, 0.023), no wake billows are shed and the interactions among the wakes of the solid cylinders are weak. Even for $\text{SVF}=0.023$, SSLs containing large-scale turbulent eddies form on the two sides of the porous cylinder, but their ends cannot interact to generate wake billows. In both regimes, the force acting on some of the solid cylinders within the array is highly unsteady. As opposed to results obtained based on 2D simulations, no intermediate regime in which the force acting on the solid cylinders is close to steady is present. Interestingly, an energetic low frequency corresponding to a Strouhal number defined with the diameter of the porous cylinder of approximately 0.2 is present within the porous cylinder and near-wake regions not only for cases where wake billows are generated but also for cases where no wake billows form. In the latter cases, this frequency is due to an instability acting on the SSLs which induces in-phase large-scale undulatory deformations of the two SSLs. A combined drag parameter for the porous cylinder ${\it\Gamma}_{D}=\overline{C}_{d}\,aD/(1-\text{SVF})$ is introduced, where $aD$ is the non-dimensional frontal area per unit volume of the porous cylinder. This parameter characterizes by how much the velocity of the bleeding flow at the back of the porous cylinder is reduced compared with the incoming flow velocity for a given total drag force acting on the porous cylinder. Results from simulations conducted with different values of the SVF, $d/D$ and mean time-averaged solid cylinder streamwise drag parameter, $\overline{C}_{d}$, show that ${\it\Gamma}_{D}$ increases monotonically with increasing $aD$. Several ways of defining the spatial extent of the wake region in a less ambiguous way are proposed.

The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two- and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria. We found that at a critical deflection angle across the incident shock wave, the perturbations related to the turbulent boundary layer cause bi-directional transition processes between regular and irregular shock patterns for a free-stream Mach number of $\mathit{Ma}_{0}=2$. Computational results show that the mean deflection angle across the separation shock is decoupled from the incident shock wave and can be accurately modelled by the generalised free interaction theory. On the basis of these observations, and the von Neumann and detachment criteria for the asymmetric intersection of shock waves, we derive the critical incident shock deflection angles at which the shock pattern may/must become irregular. Numerical data for a free-stream Mach number of $\mathit{Ma}_{0}=3$ confirm the existence of the dual-solution domain predicted by theory.

We investigate source mechanisms for subsonic jet noise using experimentally obtained datasets of high-Reynolds-number Mach 0.4 and 0.6 turbulent jets. The focus is on the axisymmetric mode which dominates downstream sound radiation for low polar angles and the frequency range at which peak noise occurs. A linearized Euler equation (LEE) solver with an inflow boundary condition is used to generate single-frequency hydrodynamic instability waves, and the resulting near-field fluctuations and far-field acoustics are compared with those from experiments and linear parabolized stability equation (LPSE) computations. It is found that the near-field velocity fluctuations closely agree with experiments and LPSE computations up to the end of the potential core, downstream of which deviations occur, but the LEE results match experiments better than the LPSE results. Both the near-field wavepackets and the sound field are observed directly from LEE computations, but the far-field sound pressure levels (SPLs) obtained are more than an order of magnitude lower than experimental values despite close statistical agreement of the near hydrodynamic field up to the potential core region. We explore the possibility that this discrepancy is due to the mismatch between the decay of two-point coherence with increasing distance in experimental flow fluctuations and the perfect coherence in linear models. To match the near-field coherence, experimentally obtained coherence profiles are imposed on the two-point cross-spectral density (CSD) at cylindrical and conical surfaces that enclose near-field structures generated with LEEs. The surface pressure is propagated to the far field using boundary value formulations based on the linear wave equation. Coherence matching yields far-field SPLs which show improved agreement with experimental results, indicating that coherence decay is the main missing component in linear models. The CSD on the enclosing surfaces reveals that the application of a decaying coherence profile spreads the hydrodynamic component of the linear wavepacket source on to acoustic wavenumbers, resulting in a more efficient acoustic source.

The extensional flow of a polymeric fluid during the fibre spinning process is studied for finite-amplitude stability behaviour. The spinning flow is assumed to be inertialess and isothermal. The nonlinear extensional rheology of the polymer is described with the help of the eXtended Pom-Pom (XXP) model, which is known to exhibit a significant strain hardening effect necessary for fibre spinning applications. The linear stability analysis predicts an instability known as draw resonance when the draw ratio, $\mathit{DR}$, defined as the ratio of the velocities at the two ends of the fibre in the air gap, exceeds a certain critical value, $\mathit{DR}_{c}$. The critical draw ratio $\mathit{DR}_{c}$ depends on the fluid elasticity represented by the Deborah number, $\mathit{De}={\it\lambda}v_{0}/L$, the ratio of the polymer relaxation time to the flow time scale, thus constructing a stability diagram in the $\mathit{DR}_{c}$–$\mathit{De}$ plane. Here, ${\it\lambda}$ is the characteristic relaxation time of the polymer, $v_{0}$ is the extrudate velocity through the die exit and $L$ is the length of the air gap for the spinning flow. In the present study, we carry out a weakly nonlinear stability analysis to examine the dynamics of the disturbance amplitude in the vicinity of the transition point. The analysis reveals the nature of the bifurcation at the transition point and constructs a finite-amplitude manifold providing insight into the draw resonance phenomena. The effect of the fluid elasticity on the nature of the bifurcation and the finite-amplitude branch is examined, and the findings are correlated to the extensional rheological behaviour of the polymer fluid. For flows at small Deborah number, the Landau constant, which captures the role of nonlinearities, is found to be negative, indicating supercritical Hopf bifurcation at the transition point. In the linearly unstable region, the equilibrium amplitude of the disturbance is estimated and shows a limit cycle behaviour. As the fluid elasticity is increased, initially the equilibrium amplitude is found to decrease below its Newtonian value, reaching the lowest value for $\mathit{De}$ when the strain hardening effect is maximum. With further increase in elasticity, the material undergoes strain softening behaviour which leads to an increase in the equilibrium amplitude of the oscillations in the fibre cross-section area, indicating a destabilizing effect of elasticity in this regime. Interestingly, at a certain high Deborah number, the bifurcation crosses over from supercritical to subcritical nature. In the subcritical regime, a threshold amplitude branch is constructed from the amplitude equation.

In this work we have obtained exact analytical formulae expressing the wave resistance of a two-dimensional body by the parameters of the downstream non-breaking waves. The body moves horizontally at a constant speed $c$ in a channel of finite depth $h$. We have analysed the relationships between the parameters of the upstream flow and the downstream waves. Making use of some results by Keady & Norbury (J. Fluid Mech., vol. 70, 1975, pp. 663–671) and Benjamin (J. Fluid Mech., vol. 295, 1995, pp. 337–356), we have rigorously proved that realistic steady free-surface flows with a positive wave resistance exist only if the upstream flow is subcritical, i.e. the Froude number $\mathit{Fr}=c/\sqrt{gh}<1$. For all solutions with downstream waves obtained by a perturbation of a supercritical upstream uniform flow the wave resistance is negative. Applying a numerical technique, we have calculated accurate values of the wave resistance depending on the wavelength, amplitude and mean depth.

As an abstraction of natural samara flight, steadily rotating plates in a free-stream flow have been studied. Particle image velocimetry on span-normal planes has been conducted to show that increasing rotation, as captured by the dimensionless parameter of tip speed ratio, causes a transition of the mean wake topology from that of a bluff body to that of a stable leading-edge vortex. Despite its notable effect on topology, a change in tip speed ratio has negligible effect on leading-edge circulation at a given spanwise position, local effective angle of attack and local effective velocity. The effective angle-of-attack distribution was held constant at different tip speed ratios by comparing rotating plates with different twist profiles. The shear-layer velocity profile at the leading edge was also resolved, allowing quantification of the vorticity flux passing through the leading-edge shear layer. Interestingly, the observed equilibrium values of circulation are not sensitive to changes in shear-layer vorticity flux.

We present the effect of noise on the hysteresis characteristics of a prototypical thermoacoustic system, a horizontal Rijke tube. As we increase the noise intensity, we find that the width of the hysteresis zone decreases. However, we find that the rate of decrease in hysteresis width is constant for all the mass flow rates considered in the present study. We also show that the subcritical transition observed in the absence of noise is no longer discernible once the intensity of noise is above a threshold value and the transition appears to be continuous. We compare our experimental observations with the results obtained from a numerical model perturbed with additive Gaussian white noise and we find a qualitative agreement between the experimental and the numerical results.

In this paper, the response of circular Couette flow of shear-thinning fluids between two infinitely long coaxial cylinders to weak disturbances is addressed. It is highlighted by transient growth analysis. Both power-law and Carreau models are used to describe the rheological behaviour of the fluid. The first part of the paper deals with the asymptotic long-time behaviour of three-dimensional infinitesimal perturbations. Using the normal-mode approach, an eigenvalue problem is derived and solved by means of the spectral collocation method. An extensive description and the classification of eigenspectra are presented. The influence of shear-thinning effects on the critical Reynolds numbers as well as on the critical azimuthal and axial wavenumbers is analysed. It is shown that with a reference viscosity defined with the characteristic scales $\hat{{\it\mu}}_{ref}=\hat{K}(\hat{R}_{1}\hat{{\it\Omega}}_{1}/\hat{d})^{(n-1)}$ for a power-law fluid and $\hat{{\it\mu}}_{ref}=\hat{{\it\mu}}_{0}$ for a Carreau fluid, the shear-thinning character is destabilizing for counter-rotating cylinders. Moreover, the axial wavenumber increases with $\mathit{Re}_{2}$ and with shear-thinning effects. The second part investigates the short-time behaviour of the disturbance using the non-modal approach. For the same inner and outer Reynolds numbers, the amplification of the kinetic energy perturbation becomes much more important with increasing shear-thinning effects. Two different mechanisms are used to explain the transient growth, depending on whether or not there is a stratification of the angular momentum. On the Rayleigh line and for Newtonian fluids, the optimal perturbation is in the form of azimuthal streaks, which transform into Taylor vortices through the anti-lift-up mechanism. In the other cases, the optimal perturbation is initially oriented against the base flow, then it tilts to align with the base flow at optimal time. The scaling laws for the optimal energy amplification proposed in the literature for Newtonian fluids are extended to shear-thinning fluids.

In the present study, we attempt to analyse the electro-osmotic flow of two superimposed fluids through narrow confinements in the presence of axially modulated surface charges. We attempt to solve for the flow structure as well as the interface deformation by both analytical and numerical techniques. Approximate analytical solutions are obtained through asymptotic analysis for low deformations, whereas numerical solutions are obtained by applying the phase field formalism; the numerical solutions are obtained for small as well as large interfacial deformations. The analytical solutions are derived only for the transient deformation of the interface, neglecting the transience in the flow, i.e. the flow is assumed to be quasisteady. The numerical solutions, however, are derived including the effects of inertia and transients in the flow. We attempt to compare our analytical and numerical results and explore the effects of several physico-chemical parameters on the deformation of the interface as well as the nature of the flow. Our analysis reveals that parameters such as the modulation wavelength, surface tension (described through the capillary number), viscosity ratio, permittivity ratio and extent of asymmetry in the potential on the two walls are the major contributors to the deformation and the resulting flow features.

We consider the periodic injection and extraction of fluid from a horizontal line well in an inclined saturated aquifer of finite thickness, $H$, as part of an aquifer thermal energy storage system. We focus on the case in which the injected fluid is dense relative to the original fluid in the aquifer and hence tends to run off downslope, so that during the extraction cycle a mixture of original aquifer fluid and injected fluid is produced. We study the controls on the composition of the extracted fluid, distinguishing between the cases where there is an open boundary downslope or upslope of the source, with the other boundary being sealed. We find that initially the fraction of original aquifer fluid recovered during an extracted cycle decreases from cycle to cycle, and at long times this fraction asymptotes to a value, $\mathscr{F}>0$, that depends on ${\it\Gamma}=H(S\cos ({\it\theta}){\it\phi}^{2}/{\it\tau}Q^{2})^{1/3}$ and ${\it\Pi}=HS\sin ({\it\theta}){\it\phi}/Q$, where ${\it\tau}$ is the time period of injection, ${\it\phi}$ is the porosity of the aquifer, $Q$ is the injection rate, $S$ is the speed of the buoyancy driven flow and ${\it\theta}$ is the angle of inclination to the horizontal. At long times the flow asymptotes to a quasi-steady exchange flow solution that develops in an inclined saturated porous layer of thickness $H$ in contact with a stratified fluid reservoir, filled to thickness $h_{0}({\it\Gamma},{\it\Pi})<H$ with relatively dense fluid. This enables us to calculate the average composition of the extracted fluid, which is of concern if the original aquifer fluid contains contaminants. Since the produced aquifer fluid is driven by this quasi-steady exchange flow, we show that contaminants downslope of the well will be produced after a finite time, whereas contaminants upslope of the well typically remain in the aquifer, irrespective of the far-field boundary conditions. We successfully test the models with a series of analogue experiments of both the injection extraction flow and the exchange flow using a Hele-Shaw cell.

This work reports an experimental investigation of the dispersion of a low-diffusive dye within a homogeneous swarm of high-Reynolds-number rising bubbles at gas volume fractions ${\it\alpha}$ ranging from 1 % to 13 %. The capture and transport of dye within bubble wakes is found to be negligible and the mixing turns out to result from the bubble-induced turbulence. It is described well by a regular diffusion process. The diffusion coefficient corresponding to the vertical direction is larger than that corresponding to the horizontal direction, owing to the larger intensity of the liquid fluctuations in the vertical direction. Two regimes of diffusion have been identified. At low gas volume fraction, the diffusion time scale is given by the correlation time of the bubble-induced turbulence and the diffusion coefficients increase roughly as ${\it\alpha}^{0.4}$. At large gas volume fraction, the diffusion time scale is imposed by the time interval between two bubbles and the diffusion coefficients become almost independent of ${\it\alpha}$. The transition between the two regimes occurs sooner in the horizontal direction ($1\,\%\leqslant {\it\alpha}\leqslant 3\,\%$) than in the vertical direction ($3\,\%\leqslant {\it\alpha}\leqslant 6\,\%$). Physical models based on the hydrodynamic properties of the bubble swarm are introduced and guidelines for practical applications are suggested.

This study investigated the physics of separated turbulent flows near the vertical intersection of a flat wall with a cylindrical obstacle. The geometry imposes an adverse pressure gradient on the incoming boundary layer. As a result, flow separates from the wall and reorganizes to a system of characteristic flow patterns known as the horseshoe vortex. We studied the time-averaged and instantaneous behaviour of the turbulent horseshoe vortex using planar time-resolved particle image velocimetry (TRPIV). In particular, we focused on the effect of Reynolds number based on the diameter of the obstacle and the bulk approach velocity, $\mathit{Re}_{D}$. Experiments were carried out at $\mathit{Re}_{D}$: $2.9\times 10^{4}$, $4.7\times 10^{4}$ and $12.3\times 10^{4}$. Data analysis emphasized time-averaged and turbulence quantities, time-resolved flow dynamics and the statistics of coherent flow patterns. It is demonstrated that two large-scale vortical structures dominate the junction flow topology in a time-averaged sense. The number of additional vortices with intermittent presence does not vary substantially with $\mathit{Re}_{D}$. In addition, the increase of turbulence kinetic energy (TKE), momentum and vorticity content of the flow at higher $\mathit{Re}_{D}$ is documented. The distinctive behaviour of the primary horseshoe vortex for the $\mathit{Re}_{D}=12.3\times 10^{4}$ case is manifested by episodes of rapid advection of the vortex to the upstream, higher spatio-temporal variability of its trajectory, and violent eruptions of near-wall fluid. Differences between this experimental run and those at lower Reynolds numbers were also identified with respect to the spatial extents of the bimodal behaviour of the horseshoe vortex, which is a well-known characteristic of turbulent junction flows. Our findings suggest a modified mechanism for the aperiodic switching between the dominant flow modes. Without disregarding the limitations of this work, we argue that Reynolds number effects need to be considered in any effort to control the dynamics of junction flows characterized by the same (or reasonably similar) configurations.

Direct numerical simulations (DNS) are carried out to study the passive heat transport in a turbulent channel flow with either square bars or circular rods on one wall. Several values of the pitch (${\it\lambda}$) to height ($k$) ratio and two Reynolds numbers are considered. The roughness increases the heat transfer by inducing ejections at the leading edge of the roughness elements. The amounts of heat transfer and mixing depend on the separation between the roughness elements, an increase in heat transfer accompanying an increase in drag. The ratio of non-dimensional heat flux to the non-dimensional wall shear stress is higher for circular rods than square bars irrespectively of the pitch to height ratio. The turbulent heat flux varies within the cavities and is larger near the roughness elements. Both momentum and thermal eddy diffusivities increase relative to the smooth wall. For square cavities (${\it\lambda}/k=2$) the turbulent Prandtl number is smaller than for a smooth channel near the wall. As ${\it\lambda}/k$ increases, the turbulent Prandtl number increases up to a maximum of 2.5 at the crests plane of the square bars (${\it\lambda}/k=7.5$). With increasing distance from the wall, the differences with respect to the smooth wall vanish and at three roughness heights above the crests plane, the turbulent Prandtl number is essentially the same for smooth and rough walls.