Anisotropic particles are suspended in a wide range of industrial, environmental and biological fluid flows. The orientations of these particles are sometimes randomized by turbulence, but often they are brought into preferential alignment by the fluid flow. In a recently published study, Challabotla, Zhao & Andersson (J. Fluid Mech., vol. 766, 2015, R2) performed the first numerical simulations of inertial disks in a turbulent channel flow. They find that disks can be made to preferentially align either parallel or perpendicular to the wall depending on the particle density. Particle shape also affects alignment, particularly for lower density particles, and the alignment of disks is quite different from the alignment of fibres.

Direct numerical simulations (DNS) of turbulent thermal convection in a $\mathit{Pr}=0.7$ fluid up to $\mathit{Ra}=10^{12}$ are used to study the statistics of thermal plumes. At various vertical locations in a cylindrical set-up with aspect ratio ${\it\Gamma}=\text{width}/\text{height}=1/3$, plumes are identified and their properties extracted. It is found that plumes are much less likely to be emitted from plate regions with large wind shear. Close to the plates, the plumes have a unimodal log–normal distribution, whereas at more central locations the distribution becomes weakly bimodal, which can be traced back to clustering of the plumes and influence of the large-scale circulation. The number of hot plumes decreases with height. The width of the plumes scales with $\mathit{Ra}$ approximately as $\mathit{Nu}^{-1}$, indicating that it is determined by the thermal boundary layer thickness.

Fluid motion at high Reynolds number over a flexible in-wall blip (a compliant bump or dip in an otherwise fixed wall) is considered theoretically for a very short blip buried low inside a boundary layer. Only the near-wall shear of the oncoming flow affects the local motion past the tiny blip. Slowly evolving features are examined first to allow for variations in the incident flow. Linear and nonlinear solutions show that at certain parameter values (eigenvalues) intensifications occur in which the interactive effect on flow and blip shape is larger by an order of magnitude than at most parameter values. Similar findings apply to the boundary layer with several tiny blips present or to channel flows with blips of almost any length. These intensifications lead on to fully nonlinear unsteady motion as a second stage, after some delay, thus combining with finite-time breakups to form a distinct path into transition of the flow.

Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion: $D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$, where $p$ is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio $p$, as $1/D_{0}^{r}p^{4}$ and as $1/D_{0}^{r}p^{2}$ for $p\gg 1$. For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of ${\approx}2$ and the rotational diffusion by a factor of ${\approx}40$.

Cyclone–anticyclone asymmetry in spontaneous gravity wave radiation from a co-rotating vortex pair is investigated in an $f$-plane shallow water system. The far field of gravity waves is derived analytically by analogy with the theory of aeroacoustic sound wave radiation (Lighthill theory). In the derived form, the Earth’s rotation affects not only the propagation of gravity waves but also their source. While the results correspond to the theory of vortex sound in the limit of $f\rightarrow 0$, there is an asymmetry in gravity wave radiation between cyclone pairs and anticyclone pairs for finite values of $f$. Anticyclone pairs radiate gravity waves more intensely than cyclone pairs due to the effect of the Earth’s rotation. In addition, there is a local maximum of intensity of gravity waves from anticyclone pairs at an intermediate $f$. To verify the analytical solution, a numerical simulation is also performed with a newly developed spectral method in an unbounded domain. The novelty of this method is the absence of wave reflection at the boundary due to a conformal mapping and a pseudo-hyperviscosity that acts like a sponge layer in the far field of waves. The numerical results are in excellent agreement with the analytical results even for finite values of $f$ for both cyclone pairs and anticyclone pairs.

When a droplet spreads on a solid substrate, it is unclear what the correct boundary conditions are to impose at the moving contact line. The classical no-slip condition is generally acknowledged to lead to a non-integrable singularity at the moving contact line, which a slip condition, associated with a small slip parameter, ${\it\lambda}$, serves to alleviate. In this paper, we discuss what occurs as the slip parameter, ${\it\lambda}$, tends to zero. In particular, we explain how the zero-slip limit should be discussed in consideration of two distinguished limits: one where time is held constant, $t=O(1)$, and one where time tends to infinity at the rate $t=O(|\!\log {\it\lambda}|)$. The crucial result is that in the case where time is held constant, the ${\it\lambda}\rightarrow 0$ limit converges to the slip-free equation, and contact line slippage occurs as a regular perturbative effect. However, if ${\it\lambda}\rightarrow 0$ and $t\rightarrow \infty$, then contact line slippage is a leading-order singular effect.

A 3D direct numerical simulation (DNS) study of the evolution of a self-propagating interface in forced constant-density statistically stationary homogeneous isotropic turbulence was performed by solving Navier–Stokes and level-set equations under a wide range of conditions that cover various (from 0.1 to 2.0) ratios of the interface speed $S_{L}$ to the r.m.s. turbulent velocity  $U^{\prime }$ and various (50, 100 and 200) turbulent Reynolds numbers $\mathit{Re}$. By analysing computed data, the following issues were addressed: (i) dependence of the speed and thickness of the fully developed statistically planar mean front that envelops the interface on $U^{\prime }/S_{L}$ and $\mathit{Re}$, (ii) dependence of the fully developed mean turbulent flux of a scalar $c$ that characterizes the state of the fluid ($c=0$ and 1 ahead and behind the interface respectively) on $U^{\prime }/S_{L}$ and $\mathit{Re}$, (iii) evolution of the mean front speed, its thickness, and the mean scalar flux during the front development after embedding a planar interface into the forced turbulence and (iv) relation between canonical and conditioned moments of the velocity, velocity gradient and pressure gradient fields.

We revisit and supplement the description of gravity waves based on perturbation expansions in Lagrangian coordinates. A general analytical framework is developed to derive a second-order Lagrangian solution to the motion of arbitrary surface gravity wave fields in a compact and vectorial form. The result is shown to be consistent with the classical second-order Eulerian expansion by Longuet-Higgins (J. Fluid Mech., vol. 17, 1963, pp. 459–480) and is used to improve the original derivation by Pierson (1961 Models of random seas based on the Lagrangian equations of motion. Tech. Rep. New York University) for long-crested waves. As demonstrated, the Lagrangian perturbation expansion captures nonlinearities to a higher degree than does the corresponding Eulerian expansion of the same order. At the second order, it can account for complex nonlinear phenomena such as wave-front deformation that we can relate to the initial stage of horseshoe-pattern formation and the Benjamin–Feir modulational instability to shed new light on the origins of these mechanisms.

A systematic investigation of unstable steady-state solutions of the Darcy–Oberbeck–Boussinesq equations at large values of the Rayleigh number $\mathit{Ra}$ is performed to gain insight into two-dimensional porous medium convection in domains of varying aspect ratio $L$. The steady convective states are shown to transport less heat than the statistically steady ‘turbulent’ flow realised at the same parameter values: the Nusselt number $\mathit{Nu}\sim \mathit{Ra}$ for turbulent porous medium convection, while $\mathit{Nu}\sim \mathit{Ra}^{0.6}$ for the maximum heat-transporting steady solutions. A key finding is that the lateral scale of the heat-flux-maximising solutions shrinks roughly as $L\sim \mathit{Ra}^{-0.5}$, reminiscent of the decrease of the mean inter-plume spacing observed in turbulent porous medium convection as the thermal forcing is increased. A spatial Floquet analysis is performed to investigate the linear stability of the fully nonlinear steady convective states, extending a recent study by Hewitt et al. (J. Fluid Mech., vol. 737, 2013, pp. 205–231) by treating a base convective state, and secondary stability modes, that satisfy appropriate boundary conditions along plane parallel walls. As in that study, a bulk instability mode is found for sufficiently small-aspect-ratio base states. However, the growth rate of this bulk mode is shown to be significantly reduced by the presence of the walls. Beyond a certain critical $\mathit{Ra}$-dependent aspect ratio, the base state is most strongly unstable to a secondary mode that is localised near the heated and cooled walls. Direct numerical simulations, strategically initialised to investigate the fully nonlinear evolution of the most dangerous secondary instability modes, suggest that the (long time) mean inter-plume spacing in statistically steady porous medium convection results from a balance between the competing effects of these two types of instability.

We investigate the scale invariance of combustion noise generated from turbulent reacting flows in a confined environment using complex networks. The time series data of unsteady pressure, which is the indicative of spatiotemporal changes happening in the combustor, is converted into complex networks using the visibility algorithm. We show that the complex networks obtained from the low-amplitude, aperiodic pressure fluctuations during combustion noise have scale-free structure. The power-law distributions of connections in the scale-free network are related to the scale invariance of combustion noise. We also show that the scale-free feature of combustion noise disappears and order emerges in the complex network topology during the transition from combustion noise to combustion instability. The use of complex networks enables us to formalize the identification of the pattern (i.e. scale-free to order) during the transition from combustion noise to thermoacoustic instability as a structural change in topology of the network.

We present experimental and theoretical results for the adjustment of a fluid (homogeneous or linearly stratified), which is initially rotating as a solid body with angular frequency ${\it\Omega}-{\rm\Delta}{\it\Omega}$, to a nonlinear increase ${\rm\Delta}{\it\Omega}$ in the angular frequency of all bounding surfaces. The fluid is contained in a cylinder of square cross-section which is aligned centrally along the rotation axis, and we focus on the $O(\mathit{Ro}^{-1}{\it\Omega}^{-1})$ time scale, where $\mathit{Ro}={\rm\Delta}{\it\Omega}/{\it\Omega}$ is the Rossby number. The flow development is shown to be dominated by unsteady separation of a viscous sidewall layer, leading to an eruption of vorticity that becomes trapped in the four vertical corners of the container. The longer-time evolution on the standard ‘spin-up’ time scale, $E^{-1/2}{\it\Omega}^{-1}$ (where $E$ is the associated Ekman number), has been described in detail for this geometry by Foster & Munro (J. Fluid Mech., vol. 712, 2012, pp. 7–40), but only for small changes in the container’s rotation rate (i.e. $\mathit{Ro}\ll 1$). In the linear case, for $\mathit{Ro}\ll E^{1/2}\ll 1$, there is no sidewall separation. In the present investigation we focus on the fully nonlinear problem, $\mathit{Ro}=O(1)$, for which the sidewall viscous layers are Prandtl boundary layers and (somewhat unusually) periodic around the container’s circumference. Some care is required in the corners of the container, but we show that the sidewall boundary layer breaks down (separates) shortly after an impulsive change in rotation rate. These theoretical boundary-layer results are compared with two-dimensional Navier–Stokes results which capture the eruption of vorticity, and these are in turn compared to laboratory observations and data. The experiments show that when the Burger number, $S=(N/{\it\Omega})^{2}$ (where $N$ is the buoyancy frequency), is relatively large – corresponding to a strongly stratified fluid – the flow remains (horizontally) two-dimensional on the $O(\mathit{Ro}^{-1}{\it\Omega}^{-1})$ time scale, and good quantitative predictions can be made by a two-dimensional theory. As $S$ was reduced in the experiments, three-dimensional effects were observed to become important in the core of each corner vortex, on this time scale, but only after the breakdown of the sidewall layers.

A methodology is developed for modelling entrainment in two-layer shallow water flows using non-standard conserved quantities, replacing layerwise mass conservation by global energy conservation. Thus, the energy that the standard model would regularly dissipate at internal shocks is instead available to exchange fluid between the layers. Two models are considered for the upper boundary of the flow: a rigid lid and a free surface. The latter provides a selection principle for choosing physically relevant conservation laws among the infinitely many that the former possesses, when the ratio between the baroclinic and barotropic speeds tends to zero. Solutions of the equations are studied analytically and numerically, applied to the lock-exchange problem, and compared with other closures.

The subgrid-scale (SGS) physics in the convective atmospheric surface layer is studied using the SGS stress and SGS scalar flux. We derive the budget equations for the conditional mean SGS stress and SGS temperature flux and show that, for transport-equation-based SGS models, the budget terms must be correctly predicted by the SGS model in order for large-eddy simulation (LES) to reproduce the resolvable-scale velocity and temperature probability density functions. Field data from the Advection Horizontal Array Turbulence Study, which notably includes measurements of the fluctuating pressure and the advection of the velocity and temperature fields, are then used to analyse the budget equations. The results reveal the complex behaviour of the dynamics of the convective atmospheric surface layer. The budgets of the conditional mean SGS shear stress and SGS temperature flux are an approximate balance between the conditional mean production and pressure destruction, with the latter causing return to isotropy. The budgets of the normal SGS stress components are more complex. For strongly convective surface layers, energy is redistributed from the (smaller) vertical to the (larger) horizontal stress components during downdrafts, resulting in generation of anisotropy by the conditional mean SGS pressure–strain-rate correlation; wall pressure reflections can also enhance the anisotropy. The conditional mean SGS pressure transport, meanwhile, is a significant source of energy during updrafts as a result of the near-wall pressure minima. The vertical advection also plays a significant role in the transfer of SGS energy. For weakly convective surface layers, pressure transport is small while the SGS pressure–strain-rate correlation reverts to its usual role of causing return to isotropy. The results of the present study, particularly for the conditional mean SGS pressure–strain-rate correlation, provide new insights into the SGS physics first educed in a recent analysis of the mean SGS budgets by Nguyen et al. (J. Fluid Mech., vol. 729, 2013, pp. 388–422) and have important implications for near-wall models utilizing SGS transport equations in the convective atmospheric surface layer.

Bypass transition in a two-fluid boundary layer is examined using direct numerical simulations (DNSs). A less-viscous wall film is considered and the impact on transition location is evaluated at two different viscosity ratios and free-stream turbulence intensities. The less-viscous wall film absorbs the mean shear from the outer stream, weakens the lift-up mechanism, and alters the disturbance field inside the boundary layer. These effects all favour a delay in the onset of bypass transition. However, the viscosity and mean-shear discontinuities across the two-fluid interface introduce a new mechanism for the generation of wall-normal vorticity in the boundary layer, and can therefore promote transition to turbulence. Conditionally averaged statistics and streak tracking techniques are adopted in order to examine the impact of the wall film on the bypass transition process. It is shown that the weaker amplification of the streaks in the outer fluid can delay breakdown to turbulence, despite the additional disturbance generation at the two-fluid interface. The efficacy of the wall film in delaying transition is demonstrated at moderate level of free-stream turbulence intensity, but is reduced as the turbulence intensity is increased.

Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production from mean to fluctuating velocity also increases, leading to reduced mean velocity. The profiles of normalized mean and turbulence quantities in the stratified wake exhibit little change in the vertical direction but the horizontal spread increases in comparison to the case with undisturbed background. The spatial organization of the internal wave field is disrupted even at the 1 % level of external turbulence. However, key characteristics of stratified wakes such as the formation of coherent pancake vortices and the long lifetime of the mean wake are robust to the presence of fluctuations in the background. A corresponding series of simulations for the unstratified situation is carried out at the same Reynolds number of 10 000 and with similar levels of external turbulence. The change of mean and turbulence statistics is found to be weaker in the unstratified cases compared with the corresponding stratified cases and also weaker relative to that found by Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482) at a similar level of external turbulence relative to the free stream and similar integral length scale. Theoretical arguments and additional simulations are provided to show that the level of external turbulence relative to wake turbulence (dissimilar between the present investigation and Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482)) is a key governing parameter in both stratified and unstratified backgrounds.

A novel set-up is proposed to numerically study turbulent multimaterial mixing, starting from an unperturbed material interface between a light and a heavy fluid. We conduct direct numerical simulation (DNS) to better understand the role of density gradient alone on the turbulence, specifically with regard to the mixing region dynamics and anisotropy across scales. Freely decaying isotropic turbulent fields of different densities but identical kinematic viscosities are juxtaposed. The rationale for this strategy is that conventional turbulence scalings are based on kinetic energy per unit mass and kinematic viscosity. Thus, by matching the initial kinematics (root-mean-square velocity) and the dissipation (kinematic viscosity), the turbulence (kinetic energy per unit mass) decays at the same rate in both fluids. With this set-up, the effect of the density gradient alone on the turbulence can be considered, independently from other contributions (e.g. mismatch in kinetic energy per unit mass, acceleration field, etc.). We examine the mixing region dynamics at large and small scales for different density ratios and Reynolds numbers. After an initial transient, we observe a self-similar growth of the mixing region, which we explain via theoretical arguments verified by the DNS results. Inside the mixing region, the momentum of the heavier eddies causes the mean interface location to shift toward the light fluid. A higher density ratio leads to a wider, less molecularly mixed mixing region. Although anisotropy is evident at the large scales, the dissipation scales remain essentially isotropic, even at the highest density ratio under consideration (12:1). The intermittency of the velocity field exhibits isotropy, while the mass fraction field is more intermittent in the direction of the density gradient.

We investigate drop impact dynamics near closed pits and open-ended pores experimentally. The resulting impact phenomena differ greatly in each case. For a pit, we observe three distinct phenomena, which we denote as a splash, a jet and an air bubble, whose appearance depends on the distance between impact location and pit. Furthermore, we found that splash velocities can reach up to seven times the impact velocity. Drop impact near a pore, however, results solely in splashing. Interestingly, two distinct and disconnected splashing regimes occur, with a region of planar spreading in between. For pores, splashes are less pronounced than in the pit case. We state that, for the pit case, the presence of air inside it plays the crucial role of promoting splashing and allowing for air bubbles to appear.

Streamwise streaks, their lift-up and streak instability are integral to the bypass transition process. An experimental study has been carried out to find the effect of a mesh placed normal to the flow and at different wall-normal locations in the late stages of two transitional flows induced by free-stream turbulence (FST) and an isolated roughness element. The mesh causes an approximately 30 % reduction in the free-stream velocity, and mild acceleration, irrespective of its wall-normal location. Interestingly, when located near the wall, the mesh suppresses several transitional events leading to transition delay over a large downstream distance. The transition delay is found to be mainly caused by suppression of the lift-up of the high-shear layer and its distortion, along with modification of the spanwise streaky structure to an orderly one. However, with the mesh well away from the wall, the lifted-up shear layer remains largely unaffected, and the downstream boundary layer velocity profile develops an overshoot which is found to follow a plane mixing layer type profile up to the free stream. Reynolds stresses, and the size and strength of vortices increase in this mixing layer region. This high-intensity disturbance can possibly enhance transition of the accelerated flow far downstream, although a reduction in streamwise turbulence intensity occurs over a short distance downstream of the mesh. However, the shape of the large-scale streamwise structure in the wall-normal plane is found to be more or less the same as that without the mesh.

We explore the transport of heavy particles through an upward displacement-ventilated space. The space incorporates a localised source of buoyancy which generates a turbulent buoyant plume. The plume fluid is contaminated with a small concentration of particles, which are subject to gravitational settling. A constant flow of uncontaminated fluid is supplied at a low level into the space, while an equal amount of fluid is vented from the space at a high level. At steady state, a two-layer density stratification develops associated with the source of buoyancy. New laboratory experiments are conducted to explore how particles are transported by this flow. The experiments identify that the upper layer may either become well-mixed in particles or it may develop a vertical stratification in particle concentration, with the particle concentration decreasing with height. We develop a quantitative model which identifies that such stratification develops for larger particle setting speeds, or smaller ventilation rates. In accord with our experiments, the model predicts that the number of particles extracted from the space through the high-level vent is controlled by the magnitude of the particle stratification in the upper layer, and this in turn depends on the particle settling speed relative to the ventilation speed and also the cross-sectional area and height of the space. We compare the predictions of the model with measurements of the flux of particles vented from the space for a range of operating conditions. We explore the relevance of the model for the removal of airborne contaminants by displacement ventilation in hospital rooms, and we discuss how contamination is propagated in the room as a result of lateral mixing of pathogens in the upper layer.

A fully nonlinear numerical model is used to investigate spontaneous wave generation during two-dimensional frontogenesis forced by a horizontal strain field. The model uses the idealised configuration of an infinitely long straight front and uniform potential vorticity, with a uniform imposed convergent strain across the front. Shakespeare & Taylor (J. Fluid Mech., vol. 757, 2014, pp. 817–853) formulated a generalised analytical model (ST14) for this system that extends the classical Hoskins & Bretherton (J. Atmos. Sci., vol. 29, 1972, pp. 11–37) model (HB) to large strain rates (${\it\alpha}\sim f$). Here, we use a numerical model to simulate the fully nonlinear problem and compare the results with the predictions of the analytical model for a variety of strain rates. Even for weak strains (${\it\alpha}=0.2f$), the confinement of the secondary circulation and the spontaneous generation of waves, predicted by ST14, are shown to be important corrections to the HB solution. These inviscid predictions are also robust for an equilibrated front where strain-forced frontogenesis is balanced by diffusion. For strong strains the wavefield becomes of leading-order importance to the solution. In this case the frontal circulation is tightly confined, and the vertical velocity is an order of magnitude larger than in the HB model. The addition of a strain field that weakens with time allows the release and propagation of the spontaneously generated waves. We also consider fronts with both large vorticity and strain rate, beyond the validity of the ST14 model.