Cube arrays are one of the most extensively studied types of surface roughness, and there has been much research on cubical roughness with low-to-moderate surface coverage densities. In order to help populate the literature of flow over cube arrays with high surface coverage densities, we conduct direct numerical simulations (DNSs) of flow over aligned cube arrays with coverage densities $\lambda =0.25$ (for validation and comparison purposes), $0.5$, $0.6$, $0.7$, $0.8$ and $0.9$. The roughness are in the d-type roughness regime. Essential flow quantities, including the mean velocity profiles, Reynolds stresses, dispersive stresses and roughness properties, are reported. Special attention is given to secondary turbulent motions in the roughness sublayer. The spanwise-alternating pattern of the thin slots between two neighbouring cubes gives rise to spanwise-alternating regions of low- and high-momentum pathways above the cube crests. We show that the strength and spanwise location of these low- and high-momentum pathways depend on the surface coverage density, and that the high-momentum pathways are not necessarily located directly above the roughness elements. In order to determine the physical processes responsible for the generation and the destruction of these secondary turbulent motions, we analyse the dispersive kinetic energy (DKE) budget. The data shows that the secondary motions get their energy from the DKE-specific production term and the wake production term, and lose energy to the DKE-specific dissipation term.

Characteristics of small-scale shear layers are studied with direct numerical simulations of a temporally evolving turbulent planar jet. The shear layers that internally exist in turbulence are detected with a tensor of shearing motion, which is extracted from a velocity gradient tensor with a triple decomposition. Flow visualization of the shear intensity confirms the existence of layer structures with intense shear. The mean flow characteristics around local maxima of the shear intensity are investigated with averages taken in the shear coordinate system, which is defined based on the shear orientation. The mean flow pattern reveals that the shear layer is formed in a biaxial strain field, which consists of extensive strain in the vorticity direction of the shear and compressive strain in the direction perpendicular to the shear layer. The velocity components associated with the shear and biaxial strain rapidly change around the shear layer. The Kolmogorov scales characterize the mean characteristics of shear layers, such as velocity jumps, thickness and the intensities of shear and biaxial strain. These quantities normalized by the Kolmogorov scales only weakly depend on lateral positions in the planar jet. Although the turbulent planar jet evolves under the influence of mean shear, a large number of the shear layers do not align with the mean shear direction. The typical shear layer thickness is about six times the Kolmogorov length scale. Furthermore, the shear layer thickness is well predicted by the Burgers vortex layer.

This paper describes the study of instability in a transient pipe flow of decaying nature, considering variation of the base flow with time. Linear stability analysis on the decaying base flow is carried out and the effect of wavenumber on the perturbation energy growth is studied. Non-modal optimal-mode analysis, with time integration, utilising adjoint equations, is found to be suitable for the study of instability in such transient flows. The range of wavenumbers, sensitive to perturbation in providing maximum perturbation energy growth, and the magnitude of the order of growth supports the conjecture that the transient growth of the optimal perturbation is responsible for the observed instability. The findings regarding stability mechanism are substantiated by an experimental investigation accompanied by a numerical study. In an unsteady experiment, where a piston with trapezoidal velocity variation drives the flow, an impulsively blocked duct flow is emulated. Particle image velocimetry (PIV) measurement provides the velocity data; the analytical velocity profiles are obtained using a series solution available in the literature, with a trapezoidal flow-rate-variation approximation. The analytical profiles capture the centreline velocities, various time scales and the reverse-flow regions, which the experiment fails to resolve. Observation of the vorticity fields confirms the appearance of instability waves close to the reverse-flow boundary layer near the wall, and the growth and transformation of the instability waves into fully grown vortices. The coherent wave structures and their associated wavenumbers are extracted quantitatively through spatial dynamic mode decomposition (DMD) analysis. This comprehensive analysis recognises the dynamics of the flow-field development, which suggests that the loss of mean-flow energy and the perturbation energy growth compensate each other, with the remaining energy losses accounted for by viscous dissipation.

We study the effects of Archimedes number $Ar$ and volume fraction $\phi$ in three-dimensional, high concentration and monodispersed particle suspensions. Simulations were conducted using the immersed boundary method with direct forcing for triply periodic cases and with $Ar = 21 - 23\,600$ and $\phi = 0.22 - 0.43$. We find that cluster formation is strongly dependent on the Archimedes number but weakly dependent on the volume fraction for concentrated suspensions. Particles in low $Ar$ cases are characterized by less frequent but long-lived clusters, resulting in higher hindered settling, while high $Ar$ cases consist of more frequent but short-lived clusters, leading to reduced hindered settling. By quantifying the effects of collisions on the hydrodynamic fluctuations, we show that the lifespan of clusters for the low $Ar$ cases is longer because particles are subject to appreciable wake interactions without collisions. On the other hand, clusters for high $Ar$ cases are broken before being subject to appreciable wake interactions due to frequent collisions, leading to a shorter cluster lifespan. The results imply that there exists an $Ar$ for particles in fluidized bed reactors that can reduce short circuiting due to clustering and enhance performance by maximizing flow–particle interactions. This result is consistent with existing reactor studies demonstrating that optimal particle diameters and $Ar$ values correspond to cases with short-lived clusters, although more thorough experimental studies are needed.

The problem of defining oceanic mesoscale eddies remains generally unresolved because there is no unique local spatio-temporal filter that can be used for extracting the eddies, and it is unclear what part of the eddy field cannot be actually resolved and needs to be parameterized in a coarse-grid model. We propose using of the coarse-grid model itself for reconstructing dynamically unresolved eddies, which are actually field errors on the top of the dynamically resolved, large-scale reference flow. The novelties and strengths of the approach are that (i) no spatio-temporal filtering is ever needed, (ii) field errors are dynamically translated into the error-correcting forcing and (iii) the latter exactly augments the coarse-grid model solution towards the reference flow. After implementation of the proposed approach, we study statistical properties of the field errors, show their robustness and reveal their significant differences from the locally filtered eddies. We argue that dynamical effects of unresolved eddies can be ultimately parameterized by emulating field errors and closing them on the dynamically resolved flow. So far, our results are limited to the quasigeostrophic approximation, but this serves as a proof of concept and starting point for the follow-up extension into the primitive equations, which are used routinely in the comprehensive oceanic general circulation models.

We investigate the heat transfer and coherent structures in Taylor–Couette (TC) flows that undergo thermal convection driven by an axially applied temperature gradient. Direct numerical simulations are performed in a Rayleigh number range $10^6 \leq Ra \leq 3 \times 10^8$ for Prandtl number $Pr = 4.38$ and with the shear Reynolds number up to $Re = 10^4$. When the rotation number $R_f$ increases, the flows undergo a transition from buoyancy-dominated ($R_f<1$) to shear-dominated convection ($R_f>1$). In the buoyancy-dominated regime with weak rotations, the flow features are similar to those in Rayleigh–Bénard (RB) convection with large-scale plumes emanating from the thermal boundary layers. In this regime, the $Re$-dependence of heat transport $Nu$ is sensitive to $Ra$. We find that for low $Ra$, $Nu$ decreases with increasing $Re$ and becomes independent of $Re$ at high $Ra$. In the shear-dominated regime, the flow structures are characterised by Taylor vortices (TVs), which effectively enhance the heat transport. With sufficiently high Reynolds number for $2000< Re \le 10\,000$, the flow structures are dominated by turbulent TVs, and the transport scaling laws of heat and angular velocity fluxes become independent of buoyancy. We report that in this turbulent regime the axial heat-transport scaling $(Nu\sim Re^{0.578\pm 0.018})$ is consistent with the scaling of radial angular-momentum transport $(Nu_{\omega }\sim Re^{0.581\pm 0.026})$.

The present paper focuses on the structures and dynamics of flame edges in planar turbulent non-premixed flames bounded with a wall using direct numerical simulation (DNS). The global quenching behaviour was first examined and the flame edges were identified based on the intersections of mixture fraction and OH mass fraction iso-surfaces. For the upper branch of the planar jet flame, it is observed that the structures of flame edges change from tribrachial to monobrachial with increasing scalar dissipation rate. The flame edge speed is negatively correlated with the scalar dissipation rate in regions away from the wall, highlighting the role of turbulent mixing on the flame edge dynamics. During flame–wall interactions, the propagation speed of flame edges is mainly affected by the projection of edge flame normal in the wall-normal direction, i.e. $\boldsymbol {N}_{Z}\boldsymbol {\cdot }\boldsymbol {N}_{wall}$. In particular, the propagation speed increases with increasing $\boldsymbol {N}_{Z}\boldsymbol {\cdot }\boldsymbol {N}_{wall}$ in the near-wall region. The interactions of flame edges and turbulence bounded with a wall are characterized by the alignment between edge flame normal and principal strain rates. The normal of quenching edges has a tendency to align with the most extensive strain rate $\boldsymbol {e}_{1}$ in regions where the heat-release-induced dilatation is dominant over turbulent strain. In contrast, when the heat loss by cold wall effect is large enough to counteract the heat release induced by chemical reactions, turbulent strain is prevalent and the edge flame normal of the quenching edges preferentially aligns with the most compressive strain rate $\boldsymbol {e}_{3}$.

We present an asymptotic theory for analytical characterization of the high-Reynolds-number incompressible flow of a Newtonian fluid past a shear-free circular cylinder. The viscosity-induced modifications to this flow are localized and except in the neighbourhood of the rear stagnation point, behave like a linear perturbation of the inviscid flow. Our theory gives a highly accurate description of these modifications by including the contribution from the most significant viscous term in a correctional perturbation expansion about an inviscid base state. We derive the boundary layer equation for the flow and deduce a similarity transformation that leads to a set of infinite, shear-free-condition-incompatible, self-similar solutions. By suitably combining members from this set, we construct an all-boundary-condition-compatible solution to the boundary layer equation. We derive the governing equation for vorticity transport through the narrow wake region and determine its closed-form solution. The near and far-field forms of our wake solution are desirably consistent with the boundary layer solution and the well-known, self-similar planar wake solution, respectively. We analyse the flow in the rear stagnation region by formulating an elliptic partial integro-differential equation for the distortion streamfunction that specifically accounts for the fully nonlinear and inviscid dynamics of the viscous correctional terms. The drag force and its atypical logarithmic dependence on Reynolds number, deduced from our matched asymptotic analysis, are in remarkable agreement with the high-resolution simulation results. The logarithmic dependence gives rise to a critical Reynolds number below which the viscous correction term, counterintuitively, reduces the net dissipation in the flow field.

The purpose of this research is to provide a new understanding of the turbulence dynamics in a heated flow of fluid at supercritical pressure. A unified explanation has been established for the laminarisation mechanisms due to the variations of thermophysical properties, buoyancy and inertia, the last of which plays a significant role in a developing flow. In the new understanding, the various factors can all be treated similarly as (pseudo-)body forces, the effect of which is to cause a reduction in the so-called apparent Reynolds number. The partially laminarising flow is represented by an equivalent-pressure-gradient reference flow plus a perturbation flow. Full laminarisation is used in the paper referring to a region where no new vortical structures are generated. This region is akin to the pre-transition region of a boundary layer bypass transition, and in both cases, the free-stream or pipe-core turbulence decays exponentially, but elongated streaks are formed in the boundary layer. Turbulence kinetic energy in this region may still be significant due to the decaying turbulence as well as newly generated streaks. The latter lead to an increase in streamwise velocity fluctuations near the wall. Later, re-transition occurs when the streaks break down and multi-scale vortices are generated, leading to an increase in the radial and circumferential velocity fluctuations. The structural effect of buoyancy on turbulence is weak and negative in the partially laminarising flow, but is dominant in the full laminarisation and re-transition regions.

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighbouring phases, yet their closure far from the continuum needs to be modelled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. This approach is built closely upon the previous studies on the kinetic method development for dense gases [Phys. Fluids, vol. 29 (12), 2017] and long-range interactions [J. Comput. Phys., vol. 378, 2019]. It is on this background that the current work on Fokker-Planck-Poisson modelling of multi-phase phenomena is initiated. Molecular interactions are expressed via stochastic forces driven by the white noise, coupled to the long-range attractions. The former is local and pursues diffusive approximation of molecular collisions, whereas the latter takes a global feature owing to mean-field forces. The obtained Fokker-Planck-Poisson combination provides an efficient work flow for physics-driven simulations suitable for multi-phase phenomena far from the equilibrium. Besides highlighting the computational efficiency of the method, various archetypical and complex problems ranging from inverted temperature gradients between droplets to spinodal decomposition are explored. Detailed discussions are provided on different characteristics of the droplets dispersed in low/high density background gases; including the departure of heat fluxes from Fourier's law as well as droplets growth in spinodal phases.

Droplet emission from an electrified meniscus in the microdripping regime has been investigated experimentally and numerically. In this regime, the meniscus of a low viscosity, high electrical conductivity liquid hanging from the tip of a metallic tube, oscillates when subjected to a high electric field. When the liquid is fed at a constant flow rate, and for a certain range of voltages, the oscillations are periodic and, in each oscillation, the meniscus develops a ligament that eventually detaches forming a single drop. Thus, this technique is a simple way to produce monodisperse droplets at relatively high frequencies, whose diameters may be one-tenth of that of the tube. The process, governed by a dimensionless flow rate $q$ and an electric Bond number ${B_{E}}$, has been modelled as the axisymmetric motion of an inviscid meniscus of infinite conductivity, and compared against experiments. For moderate and high values of $q$, the computed meniscus mean volume and oscillation frequency agree with the experimental results, although the volume and number of emitted droplets do not. An ultrafine electrospray emitted from the ligament's conical tip during part of the oscillation cycle is probably the cause of the disagreements. To tackle this, we combine the one-dimensional approximation of an electrified meniscus with experimental meniscus profiles to compute the electric field on the meniscus. Around the tip, this electric field turns out to be substantially smaller than the field computed by the model in the absence of the space charge, and agrees with the field induced by an electrospray emitted from a Taylor cone in air.

This paper investigates the steady coherent solutions, bifurcated from the linear stability of a stationary flow, in two-dimensional (2-D) penetrative convection. The results show that the thickness of the upper stably stratified layer, which is measured by $\theta _M$ (the dimensionless temperature at which the density is maximal, with $0\le \theta _M\le 1$), plays an important role in the linear and nonlinear dynamics. First, we investigate steady solutions of fixed aspect ratio $L=2{\rm \pi} /\alpha _c$ (where $\alpha _c$ is the critical wavenumber). The results show that the instability is supercritical when $\theta _M<0.4$ and is subcritical when $\theta _M>0.4$. When $\theta _M>0.4$, the results show that the type of solution depends on the Prandtl number ($Pr$). For instance, when $Pr\lesssim 2.4$ at $\theta _M=0.5$, the solution in one type of pair of convection cells does not exist, as the Rayleigh number $Ra$ exceeds a critical value due to a saddle-node bifurcation. When $Pr>2.4$, steady solutions can be found up to $Ra=10^{8}$ for all $\theta _M$, which exhibit the scaling of heat transfer (characterized by the Nusselt number $Nu$): $Nu\sim Ra^{1/4}$. Then, the optimal 2-D steady solutions are tracked up to $Ra=10^{9}$ by varying the aspect ratio $L$, which shows that heat transfer roughly follows the $Nu\sim Ra^{\gamma }$ ($\gamma \approx 1/3$) scaling in the regime of $10^{7}< Ra<10^{9}$. It is interesting that the optimal temperature field has an arm-like horizontal structure when $Pr<10$, while it has no significant horizontal structures when $Pr>10$. Thus, the mean temperature in the mixing region is higher at large $Pr$. The steady solutions show that $Nu\sim Pr^{-1/12}$ for $\theta _M=0$ in a certain range of $Pr$ by fixing the Rayleigh numbers, e.g. $1< Pr<10$ for 2-D optimal steady solutions at $Ra=10^{8}$ and $2< Pr<30$ for 2-D steady solutions of fixed aspect ratio at $Ra=10^{7}$. But when the Prandtl number is large or the upper stably stratified layer is thick, both the steady solutions of fixed aspect ratio and the 2-D optimal steady solutions are very weakly dependent on $Pr$.

A remarkable property of geophysical fluids is that, even for nonlinear flows, a slow component can sometimes evolve independently of the fast-wave components. The dry Boussinesq equations, for instance, are known to exhibit this property for small Froude ($Fr$) and Rossby ($Ro$) numbers (i.e. strong stratification and rapid rotation). Here, we ask: Do the moist Boussinesq equations also exhibit this property, even if clouds are included as changes of water between different phases (vapour and liquid)? To investigate, the authors recently performed an asymptotic analysis and identified several ways in which phase changes could possibly induce coupling between the slow component and fast waves; however, these possibilities were not clearly settled from theoretical considerations alone. Here, to investigate further, a suite of numerical simulations is conducted, using a sequence of small values $Fr=Ro=1, 10^{-1}, 10^{-2}, 10^{-3}$. For $Fr=Ro=10^{-1}$, the influence of waves on the slow component is relatively small, but does not decrease proportional to $Fr$ and $Ro$, as $Fr$ and $Ro$ are decreased to $10^{-2}$ and $10^{-3}$. As an explanation and physical interpretation, it is shown that, while linear waves have a time average of zero, the piecewise-linear waves that arise due to phase changes actually have a non-zero time-averaged component.

Active skin-friction reduction in a turbulent boundary layer (TBL) is experimentally studied based on time-periodic blowing through one array of streamwise slits. The control parameters investigated include the blowing amplitude A+ and frequency f+, which, expressed in wall units, range from 0 to 2 and from 0.007 to 0.56, respectively. The maximum local friction reduction downstream of the slits reaches more than 70 %; friction does not fully recover to the state of the natural TBL until 500 wall units behind the slits. A positive net power saving is possible, and 4.01 % is measured with a local friction drag reduction (DR) of 49 %. A detailed analysis based on hot-wire, particle image velocimetry and smoke-wire flow visualization data is performed to understand the physical mechanisms involved. Spectral analysis indicates weakened near-wall large-scale structures. Flow visualizations show stabilized streaky structures and a locally relaminarized flow. Two factors are identified to contribute to the DR. Firstly, the jets from the slits create streamwise vortices in the near-wall region, preventing the formation of near-wall streaks and interrupting the turbulence generation cycle. Secondly, the zero-streamwise-momentum fluid associated with the jets also accounts for the DR. A closed-loop opposing control system is developed, along with an open-loop desynchronized control scheme, to quantify the two contributions. The latter is found to account for 77 % of the DR, whereas the former is responsible for 23 %. An empirical scaling of the DR is also proposed, which provides valuable insight into the TBL control physics.

The dynamics of turbulent flow structures in the wakes of barchan dunes is investigated to understand the complex, long-range interactions that occur between these three-dimensional bedforms. High-frame-rate stereo-particle image velocimetry measurements are collected from the cross-stream plane in a refractive-index-matched flume, wherein rigid models are immersed in the logarithmic region of a turbulent boundary layer. Through application of Taylor's hypothesis, limited-domain pseudo-three-dimensional reconstructions of the flow are made, wherein coherent structures are identified in the wake of an isolated barchan that resemble hairpin-like vortices. Amplitude modulation analysis, based on wavelet decomposition of velocity fluctuations and swirling strength, suggests a correlation between the shedding of these coherent structures and the passage of large-scale motions (LSMs) aloft in the turbulent boundary layer within which the barchan dune is immersed. Impulse analysis of shear stress events shows that, while the hairpin-like structures predominantly induce ejections of low-momentum fluid, the intermittent passage of an overlying high-momentum LSM yields intense sweep events as they impact the wall. Similar flow dynamics is found in dune–dune collision configurations involving barchan dunes arranged in tandem, with the exception that significant flow asymmetries are introduced, resulting in structures resembling single-legged hairpin-like (or ‘cane’) vortices being identified in conditional averages. These results provide insight into both the morphodynamics of dune interactions as well as the interactions between boundary-layer structure and roughness elements protruding into the log layer.

The statistical properties of prograde spanwise vortex cores and internal shear layers (ISLs) are evaluated for a series of high-Reynolds-number turbulent boundary layers. The considered flows span a wide range of both Reynolds number and surface roughness. In each case, the largest spanwise vortex cores in the outer layer of the boundary layer have size comparable to the Taylor microscale $\lambda _T$, and the azimuthal velocity of these large vortex cores is governed by the friction velocity ${u_\tau }$. The same scaling parameters describe the average thickness and velocity difference across the ISLs. The results demonstrate the importance of the local large-eddy turnover time in determining the strain rate confining the size of the vortex cores and shear layers. The relevance of the turnover time, and more generally the Taylor microscale, can be explained by a stretching mechanism involving the mutual interaction of coherent velocity structures such as uniform momentum zones with the evolving shear layers separating the structures.

Characteristics of particle clustering in a particle-laden turbulent boundary layer at a moderate frictional Reynolds number ($Re_\tau =5500$) are experimentally investigated based on Voronoï analysis. High-inertia sand grains with a large viscous-time-based Stokes number, i.e. $St_p=10^2 - 10^3$, are used as the dispersed phase. The bulk particle volume fraction is $\varPhi _V\sim O(10^{-5})$. Two-dimensional velocity fields of the fluid and particle phases in the streamwise–wall-normal plane are simultaneously measured via particle image/tracking velocimetry. Under the net sedimentation condition, a self-similarity of the geometries of particle clusters is clearly seen in the log layer. This can be characterized by the $-5/3$ power law of the probability density functions of the particle cluster areas and the $y$-scaling of their first- and second-order moments. Considering the self-similarity of wall-attached structures in the attached eddy hypothesis, we propose a conceptual model in which a large proportion of particle clusters prefer to reside on the back ridges of low-momentum attached $u$-structures due to the high-strain effect caused by converging sweep–ejection events. Such a scenario can be partly evidenced by the conditional streamwise spectra of the streamwise and wall-normal fluid-phase velocity components being conditioned inside cluster-occupied regions, which present a distinct $y$-scaling in the log layer. Furthermore, the fluid-phase sweep and ejection events inside particle clusters are observed to be weaker than the cases outside cluster-occupied regions, and the local rate of strain inside cluster-occupied regions is relatively higher than in all unconditional statistics. Finally, conditional statistics reveal that those sand grains with relatively small slip velocities are prone to be captured by low-momentum turbulent motions to form particle clusters.

We study the initial evolution of the coffee ring that is formed by the evaporation of a thin, axisymmetric, surface-tension-dominated droplet containing a dilute solute. When the solutal Péclet number is large, we show that diffusion close to the droplet contact line controls the coffee-ring structure in the initial stages of evaporation. We perform a systematic matched asymptotic analysis for two evaporation models – a simple, non-equilibrium, one-sided model (in which the evaporative flux is taken to be constant across the droplet surface) and a vapour-diffusion limited model (in which the evaporative flux is singular at the contact line) – valid during the early stages in which the solute remains dilute. We call this the ‘nascent coffee ring’ and describe the evolution of its features, including the size and location of the peak concentration and a measure of the width of the ring. Moreover, we use the asymptotic results to investigate when the assumption of a dilute solute breaks down and the effects of finite particle size and jamming are expected to become important. In particular, we illustrate the limited validity of this model in the diffusive evaporative flux regime.

Three eigenvalue bounds are derived for the instability of ideal compressible stratified magnetohydrodynamic shear flows in which the base velocity, density and magnetic field vary in two directions. The first bound can be obtained by combining the Howard semicircle theorem with the energy principle of the Lagrangian displacement. Remarkably, no special conditions are needed to use this bound, and for some cases, we can establish the stability of the flow. The second and third bounds come out from a generalisation of the Miles–Howard theory and have some similarity to the semi-ellipse theorem by Kochar & Jain (J. Fluid Mech., vol. 91, 1979, p. 489) and the bound found by Cally (Astrophys. Fluid Dyn., vol. 31, 1983, p. 43), respectively. An important byproduct of this investigation is that the Miles–Howard stability condition holds only when there is no applied magnetic field and, in addition, the directions of the shear and the stratification are aligned everywhere.