The mechanisms by which a wetting, non-saturating liquid bestows macroscopic cohesion and strength to a granular material are usually not accessible to micromechanical investigations for saturations exceeding the pendular regime of isolated menisci, easily studied by discrete element models (DEM). The paper by Delenne et al. (J. Fluid Mech., 2015, vol. 762, R5) exploiting a multiphase lattice Boltzmann approach, pioneers the simulation of the micromorphology and of the mechanical effects on grains of an interstitial liquid, in equilibrium with its vapour, for the whole saturation range. Interestingly, in accordance with some experiments and phenomenological models, the results suggest that the mechanical effect of capillary forces is maximized for some intermediate saturation level (near 40 % in the model), well beyond the pendular range. In general, the proposed simulation technique opens the way to many studies of partially saturated granular assemblies, for different saturation or imbibition processes and histories.

The dynamics of spherical particles driven along an interface between two immiscible fluids is investigated asymptotically. Under the assumptions of a pinned three-phase contact line (TCL) and very different viscosities of the two fluids, a particle assumes a tilted orientation. As it moves, it causes a deformation of the fluid interface which is also computed. The case of two interacting driven particles is studied via the linear superposition approximation. It is shown that the capillary interaction force resulting from the particle motion is dipolar in terms of the azimuthal angle and decays with the fifth power of the inter-particle separation, similar to a capillary quadrupole originating from undulations of the TCL. The dipolar interaction is demonstrated to exceed the quadrupolar interaction at moderate particle velocities.

One of the principal challenges in the prediction and design of low-noise nozzles is accounting for the near-nozzle turbulent mixing layers at the high Reynolds numbers of engineering conditions. Even large-eddy simulation is a challenge because the locally largest scales are so small relative to the nozzle diameter. Model-scale experiments likewise typically have relatively thick near-nozzle shear layers, which potentially hampers their applicability to high-Reynolds-number design. To quantify the sensitivity of the far-field sound to nozzle turbulent-shear-layer conditions, a family of diameter $D$ nozzles is studied in which the exit turbulent boundary layer momentum thickness is varied from $0.0042D$ up to $0.021D$ for otherwise identical flow conditions. Measurements include particle image velocimetry (PIV) to within $0.04D$ of the exit plane and far-field acoustic spectra. The influence of the initial turbulent-shear-layer thickness is pronounced, though it is less significant than the well-known sensitivity of the far-field sound to laminar versus turbulent shear-layer exit conditions. For thicker shear layers, the nominally missing region, where the corresponding thinner shear layer would develop, leads to the noise difference. The nozzle-exit momentum thickness successfully scales the high-frequency radiated sound for nozzles of different sizes and exhaust conditions. Yet, despite this success, the detailed turbulence statistics show distinct signatures of the different nozzle boundary layers from the different nozzles. Still, the different nozzle shear-layer thicknesses and shapes have a similar downstream development, which is consistent with a linear stability analysis of the measured velocity profiles.

A comprehensive analysis of the pressure-gradient driven flow in a meandering channel has been presented. This geometry is of interest as it can be used for the creation of streamwise vortices which magnify the transverse transport of scalar quantities, e.g. heat transfer. The linear stability theory has been used to determine the meandering wavelengths required for the vortex formation. It has been demonstrated that reduction of the wavelength results in the onset of flow separation which, when combined with the wall geometry, results in an effective channel narrowing: the stream ‘lifts up’ above the wall and becomes nearly rectilinear, thus eliminating vortex-generating centrifugal forces. Increase of the wavelength also leads to a nearly rectilinear stream, as the slope of the wall modulations becomes negligible. As shear-driven instability may interfere with the formation of vortices, the conditions leading to the onset of such instability have also been investigated. The attributes of the geometry which lead to the most effective vortex generation without any interference from the shear instabilities and with the smallest drag penalty have been identified.

We examine the linear stability of a homogeneous gas–solid suspension of small Stokes number particles, with a moderate mass loading, subject to a simple shear flow. The modulation of the gravitational force exerted on the suspension, due to preferential concentration of particles in regions of low vorticity, in response to an imposed velocity perturbation, can lead to an algebraic instability. Since the fastest growing modes have wavelengths small compared with the characteristic length scale ($U_{g}/{\it\Gamma}$) and oscillate with frequencies large compared with ${\it\Gamma}$, $U_{g}$ being the settling velocity and ${\it\Gamma}$ the shear rate, we apply the WKB method, a multiple scale technique. This analysis reveals the existence of a number density mode which travels due to the settling of the particles and a momentum mode which travels due to the cross-streamline momentum transport caused by settling. These modes are coupled at a turning point which occurs when the wavevector is nearly horizontal and the most amplified perturbations are those in which a momentum wave upstream of the turning point creates a downstream number density wave. The particle number density perturbations reach a finite, but large amplitude that persists after the wave becomes aligned with the velocity gradient. The growth of the amplitude of particle concentration and fluid velocity disturbances is characterised as a function of the wavenumber and Reynolds number ($\mathit{Re}=U_{g}^{2}/{\it\Gamma}{\it\nu}$) using both asymptotic theory and a numerical solution of the linearised equations.

The structure of zero-pressure-gradient compressible turbulent boundary layers is analysed using the tools of optimal transient growth theory. The approach relies on the extension to compressible flows of the theoretical framework originally developed by Reynolds & Hussain (J. Fluid Mech., vol. 52, 1972, pp. 263–288) for incompressible flows. The model is based on a density-weighted triple decomposition of the instantaneous field into the contributions of the mean flow, the organized (coherent) motions and the disorganized background turbulent fluctuations. The mean field and the eddy viscosity characterizing the incoherent fluctuations are here obtained from a direct numerical simulation database. Most temporally amplified modes (optimal modes) are found to be consistent with scaling laws of turbulent boundary layers for both inner and outer layers, as well as in the logarithmic region, where they exhibit a self-similar spreading. Four free-stream Mach numbers are considered: $\mathit{Ma}_{\infty }=0.2$, 2, 3 and 4. Weak effects of compressibility on the characteristics length and the orientation angles are observed for both the inner- and the outer-layer modes. Furthermore, taking into account the effects of mean density variations, a universal behaviour is suggested for the optimal modes that populate the log layer, regardless of the Mach number. The relevance of the optimal modes in describing the near-wall layer dynamics and the eddies that populate the outer region is discussed.

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

We take up the old problem of Calvert (J. Fluid Mech., vol. 29, 1967, pp. 691–703) concerning the wake of a cylinder inclined with respect to the flow direction, and consider it from the viewpoint of transition to turbulence. For cylinders placed perpendicular to the flow direction, we address the disagreement between numerical simulation of the ideal axisymmetric configuration and experimental observations. We demonstrate that for a disk (a cylinder of aspect ratio infinity) and a flat cylinder of aspect ratio ${\it\chi}=6$ (ratio of diameter to height), the numerically predicted transition scenario is limited to very small inclination angles and is thus difficult to test experimentally. For inclination angles of about $4^{\circ }$ and more, a joint numerical and experimental study shows that the experimentally observed scenario agrees qualitatively well with the results of numerical simulations. For the flat cylinder ${\it\chi}=6$, we obtain satisfactory agreement with regard to dependence of the critical Reynolds number ($\mathit{Re}$) of the onset of vortex shedding on the inclination angle. Both for infinitely flat disks and cylinders of aspect ratio ${\it\chi}=6$, a small inclination tends to promote vortex shedding, that is, to lower the instability threshold, whereas for inclination angles exceeding $20^{\circ }$ the opposite effect is exhibited. The Strouhal number of oscillations is found to be only very weakly dependent on the Reynolds number, and very good agreement is obtained between values reported by Calvert (J. Fluid Mech., vol. 29, 1967, pp. 691–703) at high Reynolds numbers and our simulations at $\mathit{Re}=250$. In contrast, we observe relatively poor agreement in Strouhal numbers when comparing the results of our numerical simulations and the data acquired from the experimental set-up described in this paper. Closer analysis shows that confidence can be placed in the numerical results because the discrepancy can be attributed to the influence of the support system of the flat cylinder. Suggestions for improvement of the experimental set-up are provided.

Gas-phase velocity fluctuations due to mean slip velocity between the gas and solid phases are quantified using particle-resolved direct numerical simulation. These fluctuations are termed pseudo-turbulent because they arise from the interaction of particles with the mean slip even in ‘laminar’ gas–solid flows. The contribution of turbulent and pseudo-turbulent fluctuations to the level of gas-phase velocity fluctuations is quantified in initially ‘laminar’ and turbulent flow past fixed random particle assemblies of monodisperse spheres. The pseudo-turbulent kinetic energy $k^{(f)}$ in steady flow is then characterized as a function of solid volume fraction ${\it\phi}$ and the Reynolds number based on the mean slip velocity $\mathit{Re}_{m}$. Anisotropy in the Reynolds stress is quantified by decomposing it into isotropic and deviatoric parts, and its dependence on ${\it\phi}$ and $Re_{m}$ is explained. An algebraic stress model is proposed that captures the dependence of the Reynolds stress on ${\it\phi}$ and $Re_{m}$. Gas-phase velocity fluctuations in freely evolving suspensions undergoing elastic and inelastic particle collisions are also quantified. The flow corresponds to homogeneous gas–solid systems, with high solid-to-gas density ratio and particle diameter greater than dissipative length scales. It is found that for the parameter values considered here, the level of pseudo-turbulence differs by only 15 % from the values for equivalent fixed beds. The principle of conservation of interphase turbulent kinetic energy transfer is validated by quantifying the interphase transfer terms in the evolution equations of kinetic energy for the gas-phase and solid-phase fluctuating velocity. It is found that the collisional dissipation is negligible compared with the viscous dissipation for the cases considered in this study where the freely evolving suspensions attain a steady state starting from an initial condition where the particles are at rest.

The statistical properties of wall pressure fluctuations generated on a rigid flat plate by a tangential incompressible single stream jet are investigated experimentally. The study is carried out at moderate Reynolds number and for different distances between the nozzle axis and the flat plate. The overall aerodynamic behaviour is described through hot wire anemometer measurements, providing the effect of the plate on the mean and fluctuating velocity. The pressure field acting on the flat plate was measured by cavity-mounted microphones, providing point-wise pressure signals in the stream-wise and span-wise directions. Statistics of the wall pressure fluctuations are determined in terms of time-domain and Fourier-domain quantities and a parametric analysis is conducted in terms of the main geometrical length scales. Possible scaling laws of auto-spectra and coherence functions are presented and implications for theoretical modelling are discussed.

The stability of the natural convection parallel flow in a vertical porous slab is reconsidered, by reformulating the problem originally solved in Gill’s classical paper of 1969 (J. Fluid Mech., vol. 35, pp. 545–547). A comparison is made between the set of boundary conditions where the slab boundaries are assumed to be isothermal and impermeable (Model A), and the set of boundary conditions where the boundaries are modelled as isothermal and permeable (Model B). It is shown that Gill’s proof of linear stability for Model A cannot be extended to Model B. The question about the stability/instability of the basic flow is examined by carrying out a numerical solution of the stability eigenvalue problem. It is shown that, with Model B, the natural convection parallel flow in the basic state becomes unstable when the Darcy–Rayleigh number is larger than 197.081. The normal modes selected at onset of instability are transverse rolls. Direct numerical simulations of the nonlinear regime of instability are carried out.

Turbulence intensity variations in the outer region of turbulent shear flows are considered, in the context of the diagnostic plot first introduced by Alfredsson et al. (Phys. Fluids, vol. 23, 2011, 041702) and for both (smooth and rough) wall-bounded flows and classical free shear flows. With $U$ defined as the mean velocity within the flow, $U_{e}$ as a suitable reference velocity and $u^{\prime }$ as the root mean square of the fluctuating velocity, it is demonstrated that, for wall flows, the attached eddy hypothesis yields a closely linear diagnostic plot ($u^{\prime }/U$ versus $U/U_{e}$) over a certain Reynolds number range, explaining why the relation seems to work well for both boundary layers and channels despite its lack of any physical basis (Castro et al., J. Fluid Mech., vol. 727, 2013, pp. 119–131). It is shown that mixing layers, jets and wakes also exhibit linear variations of $u^{\prime }/U$ versus $U/U_{e}$ over much of the flows (starting roughly from where the turbulence production is a maximum), with slopes of these variations determined by the total mean strain rate, characterised by Townsend’s flow constant $R_{s}$. The diagnostic plot thus has a wider range of applicability than might have been anticipated.

A high-frequency periodic jet, issuing immediately below the point of separation, is used to force the turbulent wake of a bluff axisymmetric body, its axis aligned with the free stream. It is shown that the base pressure may be varied more or less at will: at forcing frequencies several times that of the shear layer frequency, the time-averaged area-weighted base pressure increases by as much as 35 %. An investigation of the effects of forcing is made using random and phase-locked two-component particle image velocimetry (PIV), and modal decomposition of pressure fluctuations on the base of the model. The forcing does not target specific local or global wake instabilities: rather, the high-frequency jet creates a row of closely spaced vortex rings, immediately adjacent to which are regions of large shear on each side. These shear layers are associated with large dissipation and inhibit the entrainment of fluid. The resulting pressure recovery is proportional to the strength of the vortices and is accompanied by a broadband suppression of base pressure fluctuations associated with all modes. The optimum forcing frequency, at which amplification of the shear layer mode approaches unity gain, is roughly five times the shear layer frequency.

We report the results of a complete modal and non-modal linear stability analysis of the electrohydrodynamic flow for the problem of electroconvection in the strong-injection region. Convective cells are formed by the Coulomb force in an insulating liquid residing between two plane electrodes subject to unipolar injection. Besides pure electroconvection, we also consider the case where a cross-flow is present, generated by a streamwise pressure gradient, in the form of a laminar Poiseuille flow. The effect of charge diffusion, often neglected in previous linear stability analyses, is included in the present study and a transient growth analysis, rarely considered in electrohydrodynamics, is carried out. In the case without cross-flow, a non-zero charge diffusion leads to a lower linear stability threshold and thus to a more unstable flow. The transient growth, though enhanced by increasing charge diffusion, remains small and hence cannot fully account for the discrepancy of the linear stability threshold between theoretical and experimental results. When a cross-flow is present, increasing the strength of the electric field in the high-$\mathit{Re}$ Poiseuille flow yields a more unstable flow in both modal and non-modal stability analyses. Even though the energy analysis and the input–output analysis both indicate that the energy growth directly related to the electric field is small, the electric effect enhances the lift-up mechanism. The symmetry of channel flow with respect to the centreline is broken due to the additional electric field acting in the wall-normal direction. As a result, the centres of the streamwise rolls are shifted towards the injector electrode, and the optimal spanwise wavenumber achieving maximum transient energy growth increases with the strength of the electric field.

This article presents the results of numerical simulations of three-dimensional waves on the surface of a rivulet flowing down a vertical plate. The Kapitza–Shkadov approach is used to describe the wave flow of the rivulet. Various characteristics of linear and nonlinear regular waves in the rivulet are obtained through numerical calculations as a function of the forcing frequency at different Reynolds numbers and contact wetting angles. The results of the simulations are compared with the authors’ previous experimental data. The comparison shows that the applied model adequately describes the shape of the wave surface of a rivulet, although the wave propagation velocity and wavelength are underestimated.

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner, as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner.

A recent theory (Tirumkudulu & Paramati, Phys. Fluids, vol. 25, 2013, 102107) for a radially expanding liquid sheet, that accounts for liquid inertia, interfacial tension and thinning of the liquid sheet while ignoring the inertia of the surrounding gas and viscous effects, shows that such a sheet is convectively unstable to small sinuous disturbances at all frequencies and Weber numbers $(We\equiv {\it\rho}_{l}U^{2}h/{\it\sigma})$. Here, ${\it\rho}_{l}$ and ${\it\sigma}$ are the density and surface tension of the liquid, respectively, $U$ is the speed of the liquid jet, and $h$ is the local sheet thickness. In this study we use a simple non-contact optical technique based on laser-induced fluorescence (LIF) to measure the instantaneous local sheet thickness and displacement of a circular sheet produced by head-on impingement of two laminar jets. When the impingement point is disturbed via acoustic forcing, sinuous waves produced close to the impingement point travel radially outwards. The phase speed of the sinuous wave decreases while the amplitude grows as they propagate radially outwards. Our experimental technique was unable to detect thickness modulations in the presence of forcing, suggesting that the modulations could be smaller than the resolution of our experimental technique. The measured phase speed of the sinuous wave envelope matches with theoretical predictions while there is a qualitative agreement in the case of spatial growth. We show that there is a range of frequencies over which the sheet is unstable due to both aerodynamic interaction and thinning effects, while outside this range, thinning effects dominate. These results imply that a full theory that describes the dynamics of a radially expanding liquid sheet should account for both effects.

We present an extensive compilation of direct numerical simulation (DNS) data for Poiseuille and Couette flows, from the laminar into the fully turbulent regime, with the goal of highlighting similarities and differences. The data suggest that, for a given bulk velocity, Couette flow yields less resistance than Poiseuille flow and greater turbulence kinetic energy, which may be beneficial for more efficient diffusion, thus suggesting the effectiveness of fluid transport devices based on moving belts as opposed to classical ducts. Both flows exhibit similar trends for the wall-parallel velocity variances, which increase logarithmically with the Reynolds number. The shear stress and the wall-normal stress tend to saturate faster in Couette flow, which can thus be regarded as a limit to which Poiseuille flow tends, in the limit of high Reynolds number. Excess production over dissipation is found in the outer part of Poiseuille and Couette flow, which is responsible for non-local transfer of energy. However, the structure of the core flow seems to attain an asymptotic state which consists of a parabolic and linear mean velocity profile, respectively, and it seems unlikely that substantial changes to this scenario will occur at Reynolds numbers reachable by DNS in the foreseeable future.

We present the first closed-loop separation control experiment using a novel, model-free strategy based on genetic programming, which we call ‘machine learning control’. The goal is to reduce the recirculation zone of backward-facing step flow at $\mathit{Re}_{h}=1350$ manipulated by a slotted jet and optically sensed by online particle image velocimetry. The feedback control law is optimized with respect to a cost functional based on the recirculation area and a penalization of the actuation. This optimization is performed employing genetic programming. After 12 generations comprised of 500 individuals, the algorithm converges to a feedback law which reduces the recirculation zone by 80 %. This machine learning control is benchmarked against the best periodic forcing which excites Kelvin–Helmholtz vortices. The machine learning control yields a new actuation mechanism resonating with the low-frequency flapping mode instability. This feedback control performs similarly to periodic forcing at the design condition but outperforms periodic forcing when the Reynolds number is varied by a factor two. The current study indicates that machine learning control can effectively explore and optimize new feedback actuation mechanisms in numerous experimental applications.

We develop a general framework for modelling mixing in porous media flows, in which the scalar mixture is represented as an ensemble of lamellae evolving through stretching, diffusion and coalescence. Detailed numerical simulations in Darcy scale heterogeneous permeability fields are used to analyse the lamella deformation process, which controls the local concentration gradients and thus the evolution of the concentration mixture through stretching enhanced diffusion. The corresponding Lagrangian deformation process is shown to be well modelled by a Langevin equation with multiplicative noise, which can be coupled with diffusion to predict the temporal evolution of the concentration probability density function (PDF). At late times, lamella interaction is enforced by confinement of the mixture within the dispersion area. This process is shown to be well represented by a random aggregation model, which quantifies the frequency of lamella coalescence and allows us to predict the temporal evolution of the concentration PDF in this regime. The proposed theoretical framework provides an accurate prediction of the concentration PDFs at all investigated times, heterogeneity levels and Péclet numbers. In particular, it relates the temporal behaviour of mixing, as quantified by concentration moments, scalar dissipation rate or spatial increments of concentration, to the degree of structural heterogeneity.