In this paper, we present a novel extension of impedance (Liebau) wave pumping to a free-surface condition where resonance pumping could be used for hydraulic energy harvesting. Similar pumping behaviours are reported. Surface envelopes of the free surface are shown and outline two different dynamics: U-tube oscillator and wave/resonance pumping. The latter is particularly interesting, since, from an oscillatory motion, a unidirectional flow with small to moderate oscillations is generated. A linear theory is developed to evaluate pseudo-analytically the resonance frequencies of the pump using eigenfunction expansions, and a simplified model is proposed to understand the main pumping mechanism in this type of pump. It is found that the Stokes mass transport is driving the pump. The conversion of energy from paddle oscillation to mean flow is evaluated. Efficiency up to 22 % is reported.

A constantly accelerating circular plate was investigated towards understanding the effect of non-stationarity on shear-layer entrainment and topology. Dye visualizations and time-resolved particle image velocimetry measurements were collected for normalized accelerations spanning three orders of magnitude. Increasing acceleration acts to organize shear-layer topology. Specifically, the Kelvin–Helmholtz instabilities within the shear layer better adhered to a circular path and exhibited consistent and repeatable spacing. Normalized starting-vortex circulation was observed to collapse with increasing acceleration, which one might not expect due to increased levels of mixing at higher instantaneous Reynolds numbers. The entrainment rate was shown to increase nonlinearly with increasing acceleration. This was attributed to closer spacing between instabilities, which better facilitates the roll-up of fluid between the shear layer and vortex core. The shear-layer organization observed at higher accelerations was associated with smaller spacings between instabilities. Specifically, analogous point-vortex simulations demonstrated that decreasing the spacing between instabilities acts to localize and dampen perturbations within an accelerating shear layer.

Couder et al. (Nature, vol. 437 (7056), 2005, p. 208) discovered that droplets walking on a vibrating bath possess certain features previously thought to be exclusive to quantum systems. These millimetric droplets synchronize with their Faraday wavefield, creating a macroscopic pilot-wave system. In this paper we exploit the fact that the waves generated are nearly monochromatic and propose a hydrodynamic model capable of quantitatively capturing the interaction between bouncing drops and a variable topography. We show that our reduced model is able to reproduce some important experiments involving the drop–topography interaction, such as non-specular reflection and single-slit diffraction.

We present a new model for an axisymmetric vortex ring confined in a tube. The model takes into account the elliptical (elongated) shape of the vortex ring core and thus extends our previous model (Danaila et al. J. Fluid Mech., vol. 774, 2015, pp. 267–297) derived for vortex rings with quasi-circular cores. The new model offers a more accurate description of the deformation of the vortex ring core, induced by the lateral wall, and a better approximation of the translational velocity of the vortex ring, compared with the previous model. The main ingredients of the model are the following: the description of the vorticity distribution in the vortex ring is based on the previous model of unconfined elliptical-core vortex rings (Kaplanski et al. Phys. Fluids, vol. 24, 2012, 033101); Brasseur’s approach (Brasseur, NASA Tech. Rep. JIAA TR-26, 1979) is then applied to derive a wall-induced correction for the Stokes streamfunction of the confined vortex ring flow. We derive closed formulae for the flow streamfunction and vorticity distributions. An asymptotic expression for the long-time evolution of the drift velocity of the vortex ring as a function of the ellipticity parameter is also derived. The predictions of the model are shown to be in agreement with direct numerical simulations of confined vortex rings generated by a piston–cylinder mechanism. The predictions of the model support the recently suggested heuristic relation (Krieg & Mohseni Trans. ASME J. Fluids Engng, vol. 135, 2013, 124501) between the energy and circulation of vortex rings with converging radial velocity. A new procedure for fitting experimental and numerical data with the predictions of the model is described. This opens the way for applying the model to realistic confined vortex rings in various applications including those in internal combustion engines.

Linear instability waves, or wavepackets, are key building blocks for the jet-noise problem. It has been shown in previous work that linear models correctly predict the evolution of axisymmetric wavepackets up to the end of the potential core of subsonic turbulent jets. Beyond this station, linear models fail, and nonlinearity is the likely missing piece. The essential underlying nonlinear mechanisms are unknown, and it remains unclear how these should be incorporated in a reduced-order model. The nonlinear interactions are considered in this work as an ‘external’ harmonic forcing added to the standard linear model. This modelling framework is explored using a locally parallel resolvent analysis to determine optimal forcing and associated responses, and a global approach based on 4D-Var data assimilation aimed at finding the optimal forcing of the parabolised stability equations that would minimise errors in the predictions of wavepackets. In all of the problems considered, the critical layer is found to be relevant: it is the position where sensitivity of wavepackets to nonlinearity is greatest. It is seen that disturbances are forced around the critical layer, and tilted by shear as they are advected, in a manner suggestive of an Orr-like mechanism. The ensemble of results suggests that critical-layer effects play a central role in the dynamics of wavepackets in subsonic turbulent jets, and that inclusion of such effects may remedy the shortcomings of linear reduced-order models.

This paper presents a novel method for generating vortex rings that circumvents some of the drawbacks associated with existing methods in producing them. The predominant effects that occur in previously used methods are due to the presence of some of the other vortices such as the stopping vortex, piston vortex, image vortex and orifice lip generated vortices in the early stage of development. These disturbances influence the geometric, kinematic and dynamic characteristics of a vortex ring and lead to mismatches with classical theoretical predictions. It is shown in the present study that the disturbance free vortex rings produced follow the classical theory. Flow visualization and particle image velocimetry experiments are carried out in the Reynolds number (defined as the ratio of circulation ($\unicode[STIX]{x1D6E4}$) and kinematic viscosity ($\unicode[STIX]{x1D708}$)) range, $2270<Re_{\unicode[STIX]{x1D6E4}}<6790$, to find the translational velocity, total and core circulation, core diameter, ring diameter and bubble diameter. In reference to the earlier studies, significant differences are noted in the variations of the vortex ring diameter and core diameter. A model for the core diameter during the formation stage is proposed. The translational velocity variation with time shows that the second-order accurate formula derived using Hamilton’s equation by Fraenkel (J. Fluid Mech., vol. 51, 1972, pp. 119–135) predicts it best.

A key hurdle in turbulence modelling is the closure for the pressure–strain correlation. Herein, the challenge stems from the fact that the non-local dynamics due to pressure cannot be comprehensively incorporated in a single-point closure expression. In this article, we analyse different aspects of the dynamics due to pressure for their amenability with the single-point modelling framework. Based on this, an approach is proposed that incorporates a set of pragmatic compromises in the form and the scope of the model to augment the degree of non-local dynamics that may be approximated by a single-point pressure strain correlation model. Thence, this framework is utilized to formulate an illustrative model. The predictions of this model are compared to numerical and experimental data and contrasted against other established closures over a range of homogeneous flows, under diverse conditions. Finally, the regions of validity in anisotropy space for this illustrative model are delineated using the process realizability criteria for different flows.

A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real-world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high-speed ferry data have identified additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time–frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. We use a simple weakly nonlinear theory to identify higher-order effects in a spectrogram and, while the high-speed ferry data are very noisy, we propose that certain additional features in the experimental data are caused by nonlinearity. Finally, we provide a possible explanation for a further discrepancy between the high-speed ferry spectrograms and linear theory by accounting for ship acceleration.

Using a fully analytical theory, we compute the leading-order corrections to the translational, rotational and translation–rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an elastic cell membrane that exhibits resistance towards stretching and bending. The frequency-dependent mobility corrections are expressed as general relations involving separately the particle’s shape-dependent bulk mobility and the shape-independent parameters such as the membrane–particle distance, the particle orientation and the characteristic frequencies associated with shearing and bending of the membrane. This makes the equations applicable to an arbitrary-shaped axisymmetric particle provided that its bulk mobilities are known, either analytically or numerically. For a spheroidal particle, these general relations reduce to simple expressions in terms of the particle’s eccentricity. We find that the corrections to the translation–rotation coupling mobility are primarily determined by bending, whereas shearing manifests itself in a more pronounced way in the rotational mobility. We demonstrate the validity of the analytical approximations by a detailed comparison with boundary integral simulations of a truly extended spheroidal particle. They are found to be in a good agreement over the whole range of applied frequencies.

A semianalytical model for installed jet noise is proposed in this paper. We argue and conclude that there exist two distinct sound source mechanisms for installed jet noise, and the model is therefore composed of two parts to account for these different sound source mechanisms. Lighthill’s acoustic analogy and a fourth-order space–time correlation model for the Lighthill stress tensor are used to model the sound induced by the equivalent turbulent quadrupole sources, while the trailing-edge scattering of near-field evanescent instability waves is modelled using Amiet’s approach. A non-zero ambient mean flow is taken into account. It is found that, when the rigid surface is not so close to the jet as to affect the turbulent flow field, the trailing-edge scattering of near-field evanescent waves dominates the low-frequency amplification of installed jet noise in the far-field. The high-frequency noise enhancement on the reflected side is due to the surface reflection effect. The model agrees well with experimental results at different observer angles, apart from deviations caused by the mean-flow refraction effect at high frequencies at low observer angles.

We present a theory for Mach reflection of a detonation undergoing glancing incidence reflection off of a rigid wall. Our focus is on condensed-phase explosives, which we describe with a constant adiabatic gamma equation of state and an irreversible and either state-independent or weakly state-dependent reaction rate. We consider two detonation models: (1) the instantaneous reaction heat-release Chapman–Jouguet (CJ) limit and (2) the spatially resolved reaction heat-release Zeldovich–von Neumann–Dø̈ring (ZND) limit, where here we only consider that a small fraction of the detonation energy release is spatially resolved (the SRHR limit). We observe a three-shock reflection in the CJ limit case, with a Mach shock that is curved. We develop an analytical expression for the triple-point track angle as a function of the angle of incidence. For the SRHR model, we observe a smooth lead shock, akin to von Neumann reflection, with no reflected shock in the reaction zone. Only at larger angles of incidence is a three-shock Mach reflection observed.

We investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid–gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.

When a fluid enters a rotating circular pipe, an angular momentum or swirl boundary layer appears at the wall and interacts with the axial momentum boundary layer. In the centre of the pipe, the fluid is free of swirl and is accelerated due to boundary layer growth. Below a critical flow number, defined as the ratio of average axial velocity to circumferential velocity of the pipe, there is flow separation, known in the turbomachinery context as part load recirculation. To describe this phenomenon analytically, we extended boundary layer theory to a swirl boundary layer interacting with the axial momentum boundary layer. The solution of the resulting generalized von Kármán momentum equation takes into account the influence of the Reynolds number and flow number. We show the impact of swirl on the axial boundary layer and conduct experiments in which we vary Reynolds number, flow number and surface roughness to validate the analytical results. The extended boundary layer theory predicts a critical flow number which is analytically derived and validated. Below this critical flow number, separation is expected.

We study the problem of mass transport to surfaces with heterogeneous reaction rates in the presence of shear flow over these surfaces. The reactions are first order and the heterogeneity is due to the existence of inert regions on the surfaces. Such problems are ubiquitous in the field of heterogeneous catalysis, electrochemistry and even biological mass transport. In these problems, the microscale reaction rate is characterized by a Damköhler number $\unicode[STIX]{x1D705}$, while the Péclet number $P$ is the dimensionless ratio of the bulk shear rate to the inverse diffusion time scale. The area fraction of the reactive region is denoted by $\unicode[STIX]{x1D719}$. The objective is to calculate the yield of reaction, which is directly related to the mass flux to the reactive region, denoted by the dimensionless Sherwood number $S$. Previously, we used boundary element simulations and examined the case of first-order reactive disks embedded in an inert surface (Shah & Shaqfeh J. Fluid Mech., vol. 782, 2015, pp. 260–299). Various correlations for the Sherwood number as a function of $(\unicode[STIX]{x1D705},P,\unicode[STIX]{x1D719})$ were obtained. In particular, we demonstrated that the ‘method of additive resistances’ provides a good approximation for the Sherwood number for a wide range of values of $(\unicode[STIX]{x1D705},P)$ for $0<\unicode[STIX]{x1D719}<0.78$. When $\unicode[STIX]{x1D719}\approx 0.78$, the reactive disks are in a close packed configuration where the inert regions are essentially disconnected from each other. In this work, we develop an understanding of the physics when $\unicode[STIX]{x1D719}>0.78$, by examining the inverse problem of inert disks on a reactive surface. We show that the method of resistances approach to obtain the Sherwood number fails in the limit as $\unicode[STIX]{x1D719}\rightarrow 1$, i.e. in the dilute limit of periodic inert disks, due to the existence of a surface concentration boundary layer around each disk that scales with ($1/\unicode[STIX]{x1D705}$). This boundary layer controls the screening length between inert disks and allows us to introduce a new theory, thus providing new correlations for the Sherwood number that are highly accurate in the limit of $\unicode[STIX]{x1D719}\rightarrow 1$.

Here we show that there exist internal gravity waves that are inherently unstable, that is, they cannot exist in nature for a long time. The instability mechanism is a one-way (irreversible) harmonic-generation resonance that permanently transfers the energy of an internal wave to its higher harmonics. We show that, in fact, there are a countably infinite number of such unstable waves. For the harmonic-generation resonance to take place, the nonlinear terms in the free surface boundary condition play a pivotal role, and the instability does not occur in a linearly stratified fluid if a simplified boundary condition, such as a rigid lid or a linearized boundary condition, is employed. Harmonic-generation resonance presented here provides a mechanism for the transfer of internal wave energy to the higher-frequency part of the spectrum hence affecting, potentially significantly, the evolution of the internal waves spectrum.

The streamwise mean velocity profile in a turbulent boundary layer is classically described as the sum of a log law extending all the way to the edge of the boundary layer and a wake function. While there is theoretical support for the log law, the wake function, defined as the deviation of the measured velocity profile from the log law, is essentially an empirical fit and has no real physical underpinning. Here, we present a new physically motivated formulation of the velocity profile in the outer region, and hence for the wake function. In our approach, the entire flow is represented by a two-state model consisting of an inertial self-similar region designated as ‘pure wall flow state’ (featuring a log-law velocity distribution) and a free stream state, which results in a jump in velocity at the interface separating the two. We show that the model provides excellent agreement with the available high Reynolds number mean velocity profiles if this interface is assumed to fluctuate randomly about a mean position with a Gaussian distribution. The new concept can also be extended to internal geometries in the same form, again confirmed by the data. Furthermore, adopting the same interface distribution in a two-state model for the streamwise turbulent intensities, with unchanged parameters, also yields a reliable and consistent prediction for the decline in the outer region of these profiles in all geometries considered. Finally, we discuss differences between our model interface and the turbulent/non-turbulent interface (TNTI) in turbulent boundary layers. We physically interpret the two-state model as lumping the effects of internal shear layers and the TNTI into a single discontinuity at the interface.

Microfluidic experiments and discrete particle simulations using the lattice-Boltzmann method are used to study interactions of finite size hard spheres and vortical flow inside confined cavities in a microchannel. The work focuses on entrapment of particles inside confined cavities and particle dynamics after entrapment. Numerical simulations and imaging of fluorescent tracers demonstrate that spiralling flow generates exchange of fluid mass between the vortical flow and the channel, contrary to the concept of a well-defined separatrix in unconfined cavities. An isolated finite size particle entrapped in the cavity migrates towards a stable orbit, i.e. a limit cycle trajectory. The topology of the limit cycle depends on cavity size, particle diameter and flow inertia, represented by Reynolds number. By studying various factors affecting the acceleration of a particle before entrapment, it is discussed that entrapment is a collective effect of flow morphology and particle dynamics. The effect of hydrodynamic interaction between particles inside the cavity, which results in deviation from the stable limit cycle orbit and depletion of cavities, will also be discussed. It is shown that a wall-confined microcavity entraps particles based on particle size, therefore it provides a platform for microfiltration.

We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph colouring and spectral graph drawing algorithms, examines a measure of the kinematic dissimilarity of all pairs of fluid trajectories, measured either experimentally, e.g. using particle tracking velocimetry, or numerically, by advecting fluid particles in the Eulerian velocity field. Coherence is assigned to groups of particles whose kinematics remain similar throughout the time interval for which trajectory data are available, regardless of their physical proximity to one another. Through the use of several analytical and experimental validation cases, this algorithm is shown to robustly detect coherent structures using significantly less flow data than are required by existing spectral graph theory methods.

The interaction between swimming micro-organisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyse the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer–tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers.

In this paper, we derive a lubrication model to describe the non-stationary free liquid film that is created when a vertical frame is pulled out of a liquid reservoir at a given velocity. We here focus on the case of a pure liquid, corresponding to a stress-free boundary condition at the liquid/air interfaces of the film, and thus employ an essentially extensional description of the flow. Taking into account van der Waals interactions between the interfaces, we observe that film rupture is well defined in time as well as in space, which allows us to compute the critical thickness and the film height at the moment of rupture. The theoretical predictions of the model turn out to be in quantitative agreement with experimental measurements of the break-up height of silicone oil films in a wide range of pulling velocities and supporting fibre diameters.