Wetting of a planar solid substrate is investigated in the presence of a macroscopic particle in the complete wetting regime. A drop of silicone oil spreads on the substrate and its macroscopic edge is incident on the particle at the late stage of spreading. The drop–particle interaction is observed in detail by shadowgraph and interferometry. Although the spreading drop edge is pinned by the particle for a short time, a sharp acceleration occurs when the liquid starts wetting the extra surface area offered by the particle and forming a meniscus. This process yields a net gain in spreading speed. A theoretical model based on the classical wetting dynamics dictated by Cox’s law is developed. It predicts that the capillary energy of the meniscus gives rise to a rapid motion of the liquid edge, showing good agreement with the dynamics observed in the experiments.

We present detailed experiments on transient growth of turbulent spots induced by external forcing in plane Couette–Poiseuille flow, which are studied in the framework of linear transient growth. The experimental investigation is supplemented with full theoretical analysis. We compare quantitatively the experimental and theoretical results, including maximal gain and the time at which it occurs. We also present the limits of validity for the application of the linear theory at high amplitude perturbation and Reynolds number, showing experiments with self-sustained states.

A generalized reciprocal theorem is formulated for the motion and hydrodynamic force moments of an active particle in an arbitrary background flow of a (weakly nonlinear) complex fluid. This formalism includes as special cases a number of previous calculations of the motion of both passive and active particles in Newtonian and non-Newtonian fluids.

Turbulent wakes past bluff bodies commonly present asymmetric flow states reminiscent of bifurcations in the laminar regime. Understanding the sensitivity of these states to flow forcing is crucial to the modelling and control of flow symmetry properties. In this study, the near wake of a rectangular bluff body in proximity to a wall is disturbed by the use of passive devices located between the model and the wall, upstream of the massive flow separation occurring at the blunt trailing edges. Due to the proximity to the boundary, the wake initially presents wall-normal asymmetry and a negative wall-normal pressure gradient along the base. The application of disturbances with variable size, however, sets flow symmetry along the wall-normal plane, leading to the intermittent spanwise wake reversals reported recently in the literature. A further increase in the size of perturbation suppresses wake switching, and wall-normal asymmetry is recovered, but with a positive wall-normal pressure gradient. The dynamical features of this bifurcation scenario can be retrieved using two coupled symmetry-breaking models for spanwise and wall-normal pressure gradients. This confirms the high sensitivity of the separated flow to external perturbations. More importantly, the results unify observations of the bluff-body wake topologies covered in previous investigations.

The nonlinear stability of viscous, immiscible multilayer flows in plane channels driven both by a pressure gradient and gravity is studied. Three fluid phases are present with two interfaces. Weakly nonlinear models of coupled evolution equations for the interfacial positions are derived and studied for inertialess, stably stratified flows in channels at small inclination angles. Interfacial tension is demoted and high-wavenumber stabilisation enters due to density stratification through second-order dissipation terms rather than the fourth-order ones found for strong interfacial tension. An asymptotic analysis is carried out to demonstrate how these models arise. The governing equations are $2\times 2$ systems of second-order semi-linear parabolic partial differential equations (PDEs) that can exhibit inertialess instabilities due to interaction between the interfaces. Mathematically this takes place due to a transition of the nonlinear flux function from hyperbolic to elliptic behaviour. The concept of hyperbolic invariant regions, found in nonlinear parabolic systems, is used to analyse this inertialess mechanism and to derive a transition criterion to predict the large-time nonlinear state of the system. The criterion is shown to predict nonlinear stability or instability of flows that are stable initially, i.e. the initial nonlinear fluxes are hyperbolic. Stability requires the hyperbolicity to persist at large times, whereas instability sets in when ellipticity is encountered as the system evolves. In the former case the solution decays asymptotically to its uniform base state, while in the latter case nonlinear travelling waves can emerge that could not be predicted by a linear stability analysis. The nonlinear analysis predicts threshold initial disturbances above which instability emerges.

A one-dimensional, unsteady nozzle flow is modelled to identify the sources of indirect noise in multicomponent gases. First, from non-equilibrium thermodynamics relations, it is shown that a compositional inhomogeneity advected in an accelerating flow is a source of sound induced by inhomogeneities in the mixture (i) chemical potentials and (ii) specific heat capacities. Second, it is shown that the acoustic, entropy and compositional linear perturbations evolve independently from each other and they become coupled through mean-flow gradients and/or at the boundaries. Third, the equations are cast in invariant formulation and a mathematical solution is found by asymptotic expansion of path-ordered integrals with an infinite radius of convergence. Finally, the transfer functions are calculated for a supersonic nozzle with finite spatial extent perturbed by a methane–air compositional inhomogeneity. The proposed framework will help identify and quantify the sources of sound in nozzles with relevance, for example, to aeronautical gas turbines.

In low-density axisymmetric jets, the onset of global instability is known to depend on three control parameters, namely the jet-to-ambient density ratio $S$, the initial momentum thickness $\unicode[STIX]{x1D703}_{0}$ and the Reynolds number $Re$. For sufficiently low values of $S$ and $\unicode[STIX]{x1D703}_{0}$, these jets bifurcate from a steady state (a fixed point) to a self-excited oscillatory state (a limit cycle) when $Re$ increases above a critical value corresponding to the Hopf point, $Re_{H}$. In the literature, this Hopf bifurcation is often regarded as supercritical. In this experimental study, however, we find that under some conditions, there exists a hysteretic bistable region at $Re_{SN}<Re<Re_{H}$, where $Re_{SN}$ denotes a saddle-node point. This shows that, contrary to expectations, the Hopf bifurcation can also be subcritical, which we explore by evaluating the coefficients of a truncated Landau model. The existence of subcritical bifurcations implies the potential for triggering and the need for weakly nonlinear analyses to be performed to at least fifth order if one is to be able to predict saturation and bistability. We conclude by proposing a universal scaling for $Re_{H}$ in terms of $S$ and $\unicode[STIX]{x1D703}_{0}$. This scaling, which is insensitive to the super/subcritical nature of the bifurcations, can be used to predict the onset of self-excited oscillations, providing further evidence to support Hallberg & Strykowski’s concept (J. Fluid Mech., vol. 569, 2006, pp. 493–507) of universal global modes in low-density jets.

Pressure- and volume-imposed rheology is used to study suspensions of non-colloidal, rigid fibres in the concentrated regime for aspect ratios ranging from 3 to 15. The suspensions exhibit yield stresses. Subtracting these apparent yield stresses reveals a viscous scaling for both the shear and normal stresses. The variation in aspect ratio does not affect the friction coefficient (ratio of shear and normal stresses), but increasing the aspect ratio lowers the maximum volume fraction at which the suspension flows. Constitutive laws are proposed for the viscosities and the friction coefficient close to the jamming transition.

In this study, we experimentally investigate the turbulent drag-reduction (DR) mechanism in flow through ducts of circular, rectangular and square cross-sections using two grades of polyacrylamide in aqueous solution having different molecular weights and various semidilute concentrations. Specifically, we explore the relationship between drag reduction and fluid elasticity, purposely exploiting the mechanical degradation of polymer molecules to vary their rheological properties. We also obtain time-resolved velocity data for various DR levels using particle image velocimetry and laser Doppler velocimetry. Elasticity is quantified via relaxation times determined from uniaxial extensional flow using a capillary breakup apparatus. A plot of DR against Weissenberg number ($Wi$) is found to approximately collapse the data, with the onset of DR occurring at $Wi\approx 0.5$ and the maximum drag-reduction asymptote being approached for $Wi\gtrsim 5$. Thus quantitative predictions of DR in a range of shear flows can be made from a single measurable material property of a polymer solution, at least for this particular flexible linear polymer.

New variational principles are given for the two-dimensional interactions between gravity-driven water waves and a rotating and translating rectangular vessel dynamically coupled to its interior potential flow with uniform vorticity. The complete set of equations of motion for the exterior water waves, the exact nonlinear hydrodynamic equations of motion for the vessel in the roll/pitch, sway/surge and heave directions, and also the full set of equations of motion for the interior fluid of the vessel, relative to the body coordinate system attached to the rotating–translating vessel, are derived from two Lagrangian functionals.

In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al. (Phys. Rev. Lett., vol. 110, 2013, 224502) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low Reynolds number. Combining slicing methods for continuous symmetry reduction with Poincaré sections for the first time in a shear flow setting, we compute and visualize the unstable manifold of the lower-branch solution and show that it extends towards the neighbourhood of the upper-branch solution. Surprisingly, this connection even persists far above the bifurcation point and appears to mediate the first stage of the puff generation: amplification of streamwise localized fluctuations. When the state-space trajectories on the unstable manifold reach the vicinity of the upper branch, corresponding fluctuations expand in space and eventually take the usual shape of a puff.

The stability of an accelerating cylindrical blob of a time-varying radius is considered with the goals of understanding the effects of time dependence of the underlying base state on a Rayleigh–Plateau instability as well as of evaluating a contribution due to a lateral acceleration of the blob, treated as a perturbation here. All of the key processes contributing to instability development are dissected, with analytical analyses of the exact incompressible inviscid potential flow formulation. Herein, without invoking the ‘frozen’ base state assumption, the entire time interval of the evolution of a perturbation is explored, discerning physical mechanisms at each stage of development. It transpires that the stability picture proves to be cardinally different from Rayleigh’s standard analysis.

Large-scale motions (LSMs) in wall-bounded turbulent flows have well-characterised instantaneous structural features (Kovasznay et al., J. Fluid Mech., vol. 41 (2), 1970, pp. 283–325; Meinhart & Adrian, Phys. Fluids, vol. 7 (4), 1995, pp. 694–696) and a known spectral signature (Monty et al., J. Fluid Mech., vol. 632, 2009, pp. 431–442). This work aims to connect these previous observations through the development and analysis of a representative model for LSMs. The model is constructed to be consistent with the streamwise energy spectrum (Monty et al. 2009) and amplification characteristics of the Navier–Stokes equations (McKeon & Sharma, J. Fluid Mech., vol. 658, 2010, pp. 336–382), and is found to naturally recreate characteristics of instantaneous turbulent structures, including a bulge shape (Kovasznay et al. 1970) and the presence of uniform momentum zones (Meinhart & Adrian 1995) in the streamwise velocity field. The observed structural similarity between the LSM representative model and instantaneous experimental data supports the use of travelling wave models to connect statistical and instantaneous descriptions of coherent structures, and clarifies a simple general equivalency between symmetry in a Reynolds-decomposed velocity field and asymmetry in the laboratory frame.

This paper reports on near-wall two-component–two-dimensional (2C–2D) particle image velocimetry (PIV) measurements of a turbulent pipe flow at shear Reynolds numbers up to $Re_{\unicode[STIX]{x1D70F}}=40\,000$ acquired in the CICLoPE facility of the University of Bologna. The 111.5 m long pipe of 900 mm diameter offers a well-established turbulent flow with viscous length scales ranging from $85~\unicode[STIX]{x03BC}\text{m}$ at $Re_{\unicode[STIX]{x1D70F}}=5000$ down to $11~\unicode[STIX]{x03BC}\text{m}$ at $Re_{\unicode[STIX]{x1D70F}}=40\,000$. These length scales can be resolved with a high-speed PIV camera at image magnification near unity. Statistically converged velocity profiles were determined using multiple sequences of up to 70 000 PIV recordings acquired at sampling rates of 100 Hz up to 10 kHz. Analysis of the velocity statistics shows a well-resolved inner peak of the streamwise velocity fluctuations that grows with increasing Reynolds number and an outer peak that develops and moves away from the inner peak with increasing Reynolds number.

We study the inviscid linear stability of a vertical interface separating two fluids of different densities and subject to a gravitational acceleration field parallel to the interface. In this arrangement, the two free streams are constantly accelerated, which means that the linear stability analysis is not amenable to Fourier or Laplace solution in time. Instead, we derive the equations analytically by the initial-value problem method and express the solution in terms of the well-known parabolic cylinder function. The results, which can be classified as an accelerating Kelvin–Helmholtz configuration, show that even in the presence of surface tension, the interface is unconditionally unstable at all wavemodes. This is a consequence of the ever increasing momentum of the free streams, as gravity accelerates them indefinitely. The instability can be shown to grow as the exponential of a quadratic function of time.

In this paper, we analyse the dispersion of a dye by a Landau–Squire plume, generated by a jet flow emerging from a nanocapillary into a reservoir. We demonstrate analytically that the dye concentration profile exhibits a long-range profile decaying as the inverse of the distance to the origin, whereas the plume shape is only a function of a Péclet number defined in terms of the flow characteristics inside the nanocapillary. These predictions are successfully compared with experiments on fluorescent dye dispersion from nanocapillaries under pressure-driven flow. The plume shape allows extraction of the nanojet force characterizing the Landau–Squire velocity profile for a given pressure drop, with results in full agreement with direct velocimetry measurements and finite-element calculations. The peculiarities of the Landau–Squire plume make it a sensitive probe of the flow properties inside the seeding nanocapillary.

Here, we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high-Reynolds-number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26 000. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise ($\unicode[STIX]{x1D706}_{x}$) and spanwise ($\unicode[STIX]{x1D706}_{y}$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows $\unicode[STIX]{x1D706}_{y}/z\sim (\unicode[STIX]{x1D706}_{x}/z)^{1/2}$ behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship ($\unicode[STIX]{x1D706}_{y}\sim \unicode[STIX]{x1D706}_{x}$), as required for self-similarity and predicted by the attached eddy hypothesis.

We present an experimental investigation of interfacial fingering instabilities in a compliant channel, where the interface can adopt a planar front orthogonal to the direction of propagation over most of the channel width. Finite-length fingers develop on that front, similarly to the previously studied radial configuration with injection of air at constant flow rate (Pihler-Puzović et al., Phys. Rev. Lett., vol. 108 (7), 2012, 074502), but, unlike the radial case, the interface propagates steadily. This allows us to present the first quantification of the nonlinearly saturated fingering pattern and to demonstrate that the morphological features of the fingers are selected in a simple way by the local geometry of the compliant cell. In contrast, the local geometry itself is determined from a complex fluid–solid interaction. Furthermore, we find that changes to the geometry of the channel cross-section lead to a rich variety of possible interfacial patterns.

Dense suspensions are non-Newtonian fluids that exhibit strong shear thickening and normal stress differences. Using numerical simulation of extensional and shear flows, we investigate how rheological properties are determined by the microstructure that is built under flows and by the interactions between particles. By imposing extensional and shear flows, we can assess the degree of flow-type dependence in regimes below and above thickening. Even when the flow-type dependence is hindered, non-dissipative responses, such as normal stress differences, are present and characterise the non-Newtonian behaviour of dense suspensions.

Analytical solutions are found for both longitudinal and transverse shear flow, at zero Reynolds number, over immobilized superhydrophobic surfaces comprising a periodic array of near-circular menisci penetrating into a no-slip surface and where the menisci are no longer shear-free but are taken to be no-slip zones. Explicit formulae for the associated longitudinal and transverse effective slip lengths are derived; these are then compared with analogous results for superhydrophobic surfaces of the same characteristic geometry but where the menisci are shear-free. The new formulae give results that are consistent with recent experimental observations that have prompted suggestions that menisci that are assumed to be free of shear have in fact been immobilized. Significantly, for transverse shear flow, it is found that at critical downward meniscus protrusion angles of around $47^{\circ }$, for many surface geometries, it is impossible to distinguish, purely from the effective slip length, between a no-shear and a no-slip boundary condition. We also find that immobilized menisci bowing into the grooves at supercritical angles just below $90^{\circ }$ can be almost twice as slippery to transverse shear as no-shear menisci. The results are relevant to recent discussion as to whether surface immobilization, due to contamination by surfactants or other physical mechanisms, is compromising drag reduction properties expected from an assumed no-shear condition.