We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$, while the length-to-height ratio $1/6< L/H<3$ covers a wide range of geometries from thin plates to elongated Ahmed bodies. First, global linear stability analysis yields a series of pitchfork and Hopf bifurcations: (i) at lower Reynolds numbers $Re$, two stationary modes, $A$ and $B$, become unstable, breaking the top/bottom and left/right planar symmetries, respectively; (ii) at larger $Re$, two oscillatory modes become unstable and, again, each mode breaks one of the two symmetries. The critical $Re$ values of these four modes increase with $L/H$, reproducing qualitatively the trend of stationary and oscillatory bifurcations in axisymmetric wakes (e.g. thin disk, sphere and bullet-shaped bodies). Next, a weakly nonlinear analysis based on the two stationary modes $A$ and $B$ yields coupled amplitude equations. For Ahmed bodies, as $Re$ increases, state $(A,0)$ appears first, followed by state $(0,B)$. While there is a range of bistability of those two states, only $(0,B)$ remains stable at larger $Re$, similar to the static wake deflection (across the larger base dimension) observed in the turbulent regime. The bifurcation sequence, including bistability and hysteresis, is validated with fully nonlinear direct numerical simulations, and is shown to be robust to variations in $W$ and $L$ in the range of common Ahmed bodies.

Ventilated cavitating flows are investigated via direct numerical simulations, using a coupled level set and volume of fluid method to capture the interface between the air and water phases. A ventilated disk cavitator is used to create the cavity and is modelled by a sharp-interface immersed boundary method. The simulation data provide a comprehensive description of the two-phase flow and the air leakage and vortex shedding processes in the cavitating flow. The mean velocity of the air phase suggests the existence of three characteristic flow structures, namely the shear layer (SL), recirculating area (RA) and jet layer (JL). The turbulent kinetic energy (TKE) is concentrated in the JL in the closure region, and streamwise turbulent fluctuations dominate transverse fluctuations in both SL and JL. Budget analyses of the TKE show that the production term causes the TKE to increase in the SL due to the high velocity gradients, and decrease in the JL due to streamwise stretching effects. Air leakage and vortex shedding occur periodically in the closure region, and the one-to-one correspondence between these two processes is confirmed by the velocity and volume fluid spectra results, and the autocorrelation function of the air volume fraction. Moreover, the coherent flow structures are analysed using the spectral proper orthogonal decomposition method. We identify several fine coherent structures, including $SL_{KH}$ induced by the Kelvin–Helmholtz instability, $SL_{out}$ associated with large-scale vortex shedding, $SL_{in}$ associated with small-scale vortex shedding, and $SL_{r}$ associated with upstream turbulent convection. The present study complements previous research by providing detailed descriptions of the turbulent motions associated with the violent mixing of air and water, and the complex interactions between different characteristic structures in cavitating flows.

A novel experiment was performed in rotating Rayleigh–Bénard convection (RRBC), wherein the convection cell with radius $R$ was shifted away from the rotation axis by a distance $d$. In this case, the centrifugal force felt by a fluid parcel (characterized by the Froude number $Fr$) can be decomposed into an axisymmetrical part $Fr_R$ and a directed one $Fr_d$. It has been reported that the global heat transport enhances at $Fr_{d,c}$ and then reaches an optimal state at $Fr_{d,max}$ (Hu et al., Phys. Rev. Lett., vol. 127, 2021, 244501). In this paper, the local properties after the offset effects set in are investigated further, which show different features before and after $Fr_{d,max}$. The local temperature measurements at the cell centre reveal that the bulk flow turns from a turbulent state into a laminar state at $Fr_{d,max}$, which is consistent with the particle image velocimetry results. This transition can be qualitatively understood by an equivalent tilted RRBC system. As for the hot and cold coherent structures near the sidewall, their vertical temperature variations reach a minimum at $Fr_{d,max}$, implying that these structures are mostly uniform in the vertical direction at $Fr_{d,max}$. Their temperature contrasts show a linear dependence on $Fr_d$ and start to deviate from this linear behaviour when $Fr_d>Fr_{d,max}$. Besides the dominant effects of $Fr_d$, the secondary effects of $Fr_R$ are also investigated. Due to the positive effect of $+Fr_R$ on the cold structure and the negative effect of $-Fr_R$ on the hot one, the cold structure is more coherent than the hot one, but its size is smaller. The shift of the cold cluster centre from the farthest point is also larger than the shift of the hot one from the nearest point.

The primary instability of the steady two-dimensional flow past rectangular cylinders moving parallel to a solid wall is studied, as a function of the cylinder length-to-thickness aspect ratio ${A{\kern-4pt}R} =L/D$ and the dimensionless distance from the wall $g=G/D$. For all ${A{\kern-4pt}R}$, two kinds of primary instability are found: a Hopf bifurcation leading to an unsteady two-dimensional flow for $g \ge 0.5$, and a regular bifurcation leading to a steady three-dimensional flow for $g < 0.5$. The critical Reynolds number $Re_{c,2\text{-}D}$ of the Hopf bifurcation ($Re=U_\infty D/\nu$, where $U_\infty$ is the free stream velocity, $D$ the cylinder thickness and $\nu$ the kinematic viscosity) changes with the gap height and the aspect ratio. For ${A{\kern-4pt}R} \le 1$, $Re_{c,2\text{-}D}$ increases monotonically when the gap height is reduced. For ${A{\kern-4pt}R} >1$, $Re_{c,2\text{-}D}$ decreases when the gap is reduced until $g \approx 1.5$, and then it increases. The critical Reynolds number $Re_{c,3\text{-}D}$ of the three-dimensional regular bifurcation decreases monotonically for all ${A{\kern-4pt}R}$, when the gap height is reduced below $g < 0.5$. For small gaps, $g < 0.5$, the hyperbolic/elliptic/centrifugal character of the regular instability is investigated by means of a short-wavelength approximation considering pressureless inviscid modes. For elongated cylinders, ${A{\kern-4pt}R} > 3$, the closed streamline related to the maximum growth rate is located within the top recirculating region of the wake, and includes the flow region with maximum structural sensitivity; the asymptotic analysis is in very good agreement with the global stability analysis, assessing the inviscid character of the instability. For cylinders with $AR \leq 3$, however, the local analysis fails to predict the three-dimensional regular bifurcation.

Many microorganisms use cilia to propel themselves in low Reynolds number ($Re$) environments. In this work, we study the dynamics of a composite cilium consisting of an elastic filament and a spherical particle attached at the filament tip driven by an external time-periodic force acting on the particle. The elastic filament is modelled numerically using a slender body theory with hydrodynamic interactions. When tilted at a large angle from the normal direction of the wall, the filament buckles, and the induced velocity field by the cilium shows a large net flux. By varying the tilt angle or the force amplitude, the particle trajectory and the net flux display abrupt changes along with a reversal of the buckling direction. We further demonstrate through a segmental model that the abrupt changes arise from the deviation of the cilium orientation at the start of the recovery stroke from the natural orientation. Our results suggest a simple approach to engineering particle motions and designing artificial cilia for fluid pumping in low $Re$ environments.

The flow in and around a pair of plumes from sources that are vertically and horizontally offset is investigated. An analytical potential flow model is developed using an adapted version of the Milne–Thomson circle theorem to represent the flow due to adjacent circular and point sinks. This approximates the horizontal section through offset plumes, which have differing radii at the same vertical position. The predictions of this model are compared against Reynolds-averaged Navier–Stokes (RANS) simulations of the same system. These yield time-averaged results and so are particularly suitable for investigating the relatively weak entrainment field. Single and double plume results from RANS are also presented to compare with known results. Good agreement is found between the features in the analytical model and in the numerical solutions including the location of the stagnation point between the two plumes.

We present the results of a theoretical investigation into the existence, evolution and excitation of resonant triads of nonlinear free-surface gravity waves confined to a cylinder of finite depth. It is well known that resonant triads are impossible for gravity waves in laterally unbounded domains; we demonstrate, however, that horizontal confinement of the fluid may induce resonant triads for particular fluid depths. For any three correlated wave modes arising in a cylinder of arbitrary cross-section, we prove necessary and sufficient conditions for the existence of a depth at which nonlinear resonance may arise, and show that the resultant critical depth is unique. We enumerate the low-frequency triads for circular cylinders, including a new class of resonances between standing and counter-propagating waves, and also briefly discuss annular and rectangular cylinders. Upon deriving the triad amplitude equations for a finite-depth cylinder of arbitrary cross-section, we deduce that the triad evolution is always periodic, and determine parameters controlling the efficiency of energy exchange. In order to excite a particular triad, we explore the influence of external forcing; in this case, the triad evolution may be periodic, quasi-periodic or chaotic. Finally, our results have potential implications on resonant water waves in man-made and natural basins, such as industrial-scale fluid tanks, harbours and bays.

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$. Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$, especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

We experimentally investigate the transport of liquid by a toroidal bubble that rises vertically and penetrates a horizontal interface between two immiscible liquids. Experiments are conducted with various strengths of vortex circulation in the bubble, and with different liquid densities and viscosities. In contrast to a spherical bubble, a rising toroidal bubble carries a great amount of the lower liquid by virtue of the self-induction of circulating flow. The lower liquid is entrained by the toroidal bubble and forms an ellipsoidal body enclosing the bubble after it penetrates the interface. The downward net force acting on the ellipsoidal body results in the radial contraction of the bubble, reducing the volume of the entrained lower liquid. As the entrained volume decreases, the nearby upper liquid eventually pierces the ellipsoidal body, making the bubble unstable. At this instant, the net force acting on the ellipsoidal body approaches zero, and the volume ratio of the entrained lower liquid and bubble converges to a specific value. For smaller vortex circulation and larger density difference between the liquids, the volume of the entrained lower liquid within the ellipsoidal body becomes smaller and the travel distance of the bubble from the initial interface until it becomes unstable decreases. The effective Froude number, which accounts for both the inertial effect of vortex circulation and the gravitational effect of liquid density difference, is found to characterise the temporal changes in the ring radius, propagation speed and entrained volume.

Self-organization of the vorticity condensate of forced two-dimensional turbulence is examined in analogy with the mixing of a background planetary vorticity gradient in geophysical flows. Starting from the theoretical vorticity profile of the condensate, different scenarios are illustrated by the construction of idealized angular momentum conserving rearrangements of vorticity into a staircase profile similar to the potential vorticity staircase of $\beta$-plane turbulence. Two sets of numerical experiments are then presented that illustrate a similar self-organization of the background vorticity gradient in fully turbulent flows. In the first set of experiments, the flow is initialized with a laminar vortex dipole corresponding to the theoretical condensate vorticity profile. A fluctuation vorticity field is then induced by a stochastic forcing at smaller scales, which induces an azimuthally symmetric self-organization of the laminar flow into distinct annular bands. In the second set of experiments, the flow is initialized from rest with stochastic forcing generating a turbulent inverse energy cascade, out of which emerges the condensate in a self-consistent evolution as the turbulent energy accumulates at the domain scale. A self-organization of the condensate is again observed, giving a distinct annular structure on top of the theoretically predicted condensate profile. A major difference from the potential vorticity staircase of geophysical flows is the emergence in many cases of significantly non-monotonic radial vorticity profiles.

Active emulsions can spontaneously form self-propelled droplets or phoretic micropumps. However, it remains unclear how these active systems interact with their self-generated chemical fields, which can lead to emergent chemodynamic phenomena and multistable interfacial flows. Here, we simultaneously measure the flow and chemical concentration fields using dual-channel fluorescence microscopy for active micropumps, i.e. immobilised oil droplets that dynamically solubilise in a supramicellar aqueous surfactant solution. With increasing droplet radius, we observe (i) a migration of vortices from the posterior to the anterior, analogous to a transition from pusher- to puller-type swimmers, (ii) a bistability between dipolar and quadrupolar flows and, eventually, (iii) a transition to multipolar modes. We also investigate the long-time dynamics. Together, our observations suggest that a local build-up of chemical products leads to a saturation of the surface, which controls the propulsion mechanism. These multistable dynamics can be explained by the competing time scales of slow micellar diffusion governing the chemical buildup and faster molecular diffusion powering the underlying transport mechanism. Our results are directly relevant to phoretic micropumps, but also shed light on the interfacial activity dynamics of self-propelled droplets and other active emulsion systems.

Energy-harvesting systems in complex flow environments, such as floating offshore wind turbines, tidal turbines and ground-fixed turbines in axial gusts, encounter unsteady streamwise flow conditions that affect their power generation and structural loads. In some cases, enhancements in time-averaged power generation above the steady-flow operating point are observed. To characterize these dynamics, a nonlinear dynamical model for the rotation rate and power extraction of a periodically surging turbine is derived and connected to two potential-flow representations of the induction zone upstream of the turbine. The model predictions for the time-averaged power extraction of the turbine and the upstream flow velocity and pressure are compared against data from experiments conducted with a surging-turbine apparatus in an open-circuit wind tunnel at a diameter-based Reynolds number $Re_D = 6.3\times 10^5$ and surge-velocity amplitudes up to 24 % of the wind speed. The combined modelling approach captures trends in both the time-averaged power extraction and the fluctuations in upstream flow quantities, while relying only on data from steady-flow measurements. The sensitivity of the observed increases in time-averaged power to steady-flow turbine characteristics is established, thus clarifying the conditions under which these enhancements are possible. Finally, the influence of unsteady fluid mechanics on time-averaged power extraction is explored analytically. The theoretical framework and experimental validation provide a cohesive modelling approach that can drive the design, control and optimization of turbines in unsteady flow conditions, as well as inform the development of novel energy-harvesting systems that can leverage unsteady flows for large increases in power-generation capacities.

Cavitation inception in the turbulent shear layer developing behind a backward-facing step occurs at multiple points along quasi-streamwise vortices (QSVs), at a rate that increases with the Reynolds number (Re). This study investigates the evolution of the unsteady pressure field and the distribution of nuclei within and around the QSVs. The time-resolved volumetric velocity in the non-cavitating flow is measured using tomographic particle tracking, and the pressure is determined by spatial integration of the material acceleration. Analysis in Eulerian and Lagrangian reference frames reveals that the pressure is lower, and its minima last longer within the QSVs compared with the surrounding flow. The intermittent low pressure regions, whose sizes and shapes are consistent with those of the cavities, are likely to be preceded by axial vortex stretching and followed by contraction. Such phenomena have been observed before in simulations of stretched vortex elements. For the same axial straining, the pressure minima last longer with increasing Re, a trend elucidated in terms of viscous diffusion of the stretched vortex core. The impact of nuclei availability is studied under ‘natural’ and controlled seeding. Owing to differences in the saturation level of non-condensable gas, the microbubble concentration in the shear layer decreases with increasing Re, in contrast to the rate of cavitation events. Minor differences in entrainment rate into the shear layer also do not explain the substantial Re effects on cavitation inception. Hence, the Re scaling of inception appears to be dominated by trends of the pressure field.

A large-scale, fully resolved direct simulation Monte Carlo (DSMC) computation of a non-equilibrium, reactive flow of pure oxygen over a double cone is presented. Under the simulated near-continuum conditions, the computational demands are shown to be significant because of the wide range of length scales that must be resolved. Therefore, robust grid adaption capabilities and efficient parallelization of the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code that is utilized in this work are essential. The thermochemical and transport collision models were selected for efficiency and simplicity. First-principles data, obtained from the highly accurate direct molecular simulation method, were used to inform the collision models’ parameters. Importantly, because SPARTA implements molecular collision models using collision-specific energies, the resulting macroscopic relaxation rates were evaluated a posteriori via zero-dimensional heat bath simulations. The comparisons of surface properties, namely heat flux and pressure, show very close agreement with previous computational fluid dynamics (CFD) results. Differences with the measurements were found to be similar to the CFD simulations. The unresolved discrepancy with the measurements could be due to inconsistent free stream conditions with the actual experimental data or missing physical phenomena altogether, for example atomic and molecular oxygen electronically excited states, three-dimensional effects, or more complex gas–surface interactions. As shown in this work, the advantages of obtaining a DSMC particle solution for these flows reside in the method's ability to be directly informed from first principles and to seamlessly describe internal energy non-equilibrium for all modes. With the advent of exascale computing and beyond, particle methods will be an increasingly important tool to verify the validity of physical assumptions in reduced-order models via fully resolved, experimental-scale simulations, down to the level of molecular-level distributions.

In this study, the transport equation for scalar iso-surface area density ($\varSigma$) in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the $\varSigma$ transport equation is vital to improving our understanding of turbulent flows characterized by distinct interfaces, e.g. the flame surface or the turbulent/non-turbulent interface. Previous work reported by the authors identified that $\varSigma$ exhibits self-similar behaviour consistent with the development of the temporal mixing layer (Blakeley et al., J. Fluid Mech., vol. 951, 2022, A44). Accordingly, each of the terms in the $\varSigma$ transport equation is found to behave in a self-similar manner, though there are notable differences in the self-similar behaviours for each term. Based on the results presented herein, it is suggested that the rate of change of $\varSigma$ ($\partial \varSigma /\partial t$) and the advection term scale with $h\lambda _\varPhi /\Delta U$, where $h$ is the width of the mixing layer, $\lambda _\varPhi$ is the scalar Taylor length scale and $\Delta U$ is the velocity difference. The production and destruction terms are found to scale with an additional factor $({Re}\,Sc)^{1/2}$. In contrast, the molecular diffusion term is found to scale with a factor $({Re}\,Sc)^{-1/2}$ compared to $\partial \varSigma /\partial t$. Importantly, it is found that the difference between the production and destruction terms, or net surface ‘stretch’, scales with the same factor as $\partial \varSigma /\partial t$ and the advection term, which may have a significant impact on how the evolution of $\varSigma$ is understood and modelled in turbulent flows.

The two-dimensional stability of vertically sheared inertial oscillations at ocean fronts is explored through a linear stability analysis and nonlinear simulations. Baroclinic effects reduce the minimum frequency of inertia-gravity waves to an extent determined by the balanced Richardson number ${{Ri}}$ of the front. Below a critical value of ${{Ri}}$, which depends on the strength of the inertial shear, the inertial oscillations become unstable to parametric subharmonic instability (PSI) resulting in growing perturbations that oscillate at half the inertial frequency $f$. Since the critical value is always greater than 1, PSI can occur at fronts stable to symmetric instability. Although modest in weak inertial shear, growth rates exceeding $f/2$ can be achieved for inertial shear greater than or equal to the thermal wind shear. Our formulation allows for non-hydrostatic perturbations and can be applied to initially unstratified geostrophic adjustment problems. We find that PSI will almost totally damp the transient oscillations that arise during geostrophic adjustment. The perturbations gain energy at the expense of the inertial oscillations through ageostrophic shear production. The perturbations then themselves become unstable to secondary Kelvin–Helmholtz instabilities creating a pathway by which the inertial oscillations can be dissipated rapidly. In contrast to symmetric and baroclinic instabilities that draw on a front's kinetic or potential energy, PSI acts to increase the energy stored in the balanced front as the convergence and divergence of the eddy-momentum fluxes set up a secondary circulation in the sense to stand up the front.

As is known, the presence of surfactants can profoundly influence the dynamics of Newtonian viscous threads. Also, it is known that non-Newtonian viscoelastic threads behave differently from Newtonian ones, particularly in the nonlinear regime. A naturally arising question is how surfactants affect the dynamic behaviour of non-Newtonian viscoelastic threads. To gain some insights into it, we build a one-dimensional model for an Oldroyd-B/finitely extensible nonlinear elastic-Peterlin approximation (FENE-P) viscoelastic liquid thread covered with an insoluble surfactant monolayer based on the slender body theory. A parametric study is performed to examine the effects of the dimensionless numbers related to the surfactant, including the initial concentration, the Marangoni number, the surface Péclet number, the shear Boussinesq number and the dilatational Boussinesq number. It is found that the formation of the beads-on-a-string structure can be greatly delayed by the surfactant. At large values of the surface Péclet number, the exponential thinning of the Oldroyd-B viscoelastic thread is little influenced, but the surfactant may lead to the disappearance of secondary droplets. At moderate values of the surface Péclet number, the surfactant induces the formation of secondary droplets. The primary droplets are axially stretched by the Marangoni or surface viscous stresses and evolve into a prolate or a more singular shape eventually. The surfactant can delay the pinch-off of the FENE-P viscoelastic thread to a great extent, but it affects little the decrease in the minimum thread radius prior to pinch-off when the surface Péclet number is large.

With a growing interest in low Reynolds number compressible flows, compressibility effects on the secondary instabilities developing on the circular cylinder periodic wake are investigated. The unsteady and time-averaged two-dimensional flows are characterised for Reynolds numbers ${{Re}} \in [200;350]$ and Mach numbers up to ${{M}}_{\infty }=0.5$, revealing different flow structures which influence the characteristics of the secondary unstable modes. The two-dimensional time-periodic solution is used as the base state for a global linear stability analysis performed by means of Floquet theory coupled with a time-stepping finite-difference approach of the nonlinear operator. The influence of compressibility on mode A and mode B secondary instabilities which are responsible for the three-dimensionalisation of the two-dimensional periodic wake is analysed. A stabilising or a destabilising effect of compressibility is observed on mode A, depending on the Reynolds number and the spanwise wavelength of the mode, while mode B is stabilised by the increase of the Mach number. Compressibility is indeed found to decrease the mode kinetic energy production due to base flow shear conversion, which drives the growth of mode B. This results in a delay of the three-dimensionalisation process of the wake due to compressibility.

High-Froude-number flows become self-aerated when the destabilizing effect of turbulence overcomes gravity and surface tension forces. Traditionally, the resulting air concentration profile has been explained using single-layer approaches that invoke solutions of the advection–diffusion equation for air in water, i.e. bubbles’ dispersion. Based on a wide range of experimental evidence, we argue that the complete air concentration profile shall be explained through the weak interaction of different canonical turbulent flows, namely a turbulent boundary layer (TBL) and a turbulent wavy layer (TWL). Motivated by a decomposition of the streamwise velocity into a pure wall flow and a free-stream flow (Krug et al., J. Fluid Mech., vol. 811, 2017, pp. 421–435), we present a physically consistent two-state formulation of the structure of a self-aerated flow. The air concentration is mathematically built upon a modified Rouse profile and a Gaussian error function, resembling vertical mass transport in the TBL and the TWL. We apply our air concentration theory to over 500 profiles from different data sets, featuring excellent agreement. Finally, we show that the turbulent Schmidt number, characterizing the momentum-mass transfer, ranges between 0.2 and 1, which is consistent with previous mass-transfer experiments in TBLs. Altogether, the proposed flow conceptualization sets the scene for more physically based numerical modelling of turbulent mass diffusion in self-aerated flows.

The statistical characteristics and the evolution of the backflow structures are investigated in wall-bounded flows at Reynolds numbers up to $Re_{\tau }=1000$. The backflow is caused by the joining of large-scale high- and low-speed structures in the vicinity of the wall and is formed at the tail tip of the low-speed structure. The distribution density of the backflow structures and the percentage area of the backflow region on the wall both increase with the Reynolds number. The backflow structures have an average lifespan of 8 wall units which is found to be slightly longer in the pipe than the channel, and they are convected downstream at the average velocities of the buffer region of approximately 10 wall units, similar to Cardesa et al. (J. Fluid Mech., vol. 880, 2019, R3). The backflow structures occasionally split and merge, and can form detached from the wall. Evidence shows that the split, merged and wall-detached backflow structures are caused by the near-wall structures. The split backflow structures are on average, larger and more spanwise-elongated which are split due to the spanwise shearing of the near-wall streaks. A backflow structure is formed detached from the wall when the trailing end of its carrier low-speed structure ‘sits’ on the near-wall high-speed streaks. The wall-detached backflow structures tend to become wall-attached by approaching the wall when undergoing a similar life cycle to the normal backflow of growth and decay with spanwise elongation because the backflow region at the tail of the low-speed structure is continuously pressed down to the wall by the high-speed structure driven by persistent vortical structures in the buffer region.