Injecting a less viscous fluid into a more viscous fluid in a Hele-Shaw cell triggers two-dimensional viscous fingering patterns which are characterised by increasingly long fingers undergoing tip splitting and branching events. These complex structures are considered to be a paradigm for interfacial pattern formation in porous media flow and other related phenomena. Over the past five years, there has been a flurry of interest in manipulating these interfacial fingering patterns by altering the physical components of the Hele-Shaw apparatus. In this Focus on Fluids article, we summarise some of this work, concentrating on a very recent study in which the alterations include replacing one of the two bounding plates with an elastic membrane (Ducloué et al., J. Fluid Mech., vol. 826, 2017, R2). The resulting experimental set-up gives rise to a wide variety of novel interfacial patterns including periodic sideways fingers, dendritic-like patterns and short, flat-tipped viscous fingers that appear to resemble molar teeth. These latter fingers are similar to those observed in the printer’s instability and when peeling off a layer of adhesive tape. This delightful work brings together a number of well-studied themes in interfacial fluid mechanics, including how viscous and surface tension forces compete to drive fingering patterns, how interfaces are affected by fluid–solid interactions and, finally, how novel strategies can be implemented to control interfacial instabilities.

This paper investigates the energy exchanges associated with the half-trace of the velocity fluctuation correlation tensor in a strongly anisothermal low Mach fully developed turbulent channel flow. The study is based on direct numerical simulations of the channel within the low Mach number hypothesis and without gravity. The overall flow behaviour is governed by the variable fluid properties. The temperature of the two channel walls are imposed at 293 K and 586 K to generate the temperature gradient. The mean friction Reynolds number of the simulation is 180. The analysis is carried out in the spatial and spectral domains. The spatial and spectral studies use the same decomposition of the terms of the evolution equation of the half-trace of the velocity fluctuation correlation tensor. The importance of each term of the decomposition in the energy exchanges is assessed. This lets us identify the terms associated with variations or fluctuations of the fluid properties that are not negligible. Then, the behaviour of the terms is investigated. The spectral energy exchanges are first discussed in the incompressible case since the analysis is not present in the literature with the decomposition used in this study. The modification of the energy exchanges by the temperature gradient is then investigated in the spatial and spectral domains. The temperature gradient generates an asymmetry between the two sides of the channel. The asymmetry can in a large part be explained by the combined effect of the mean local variations of the fluid properties, combined with a Reynolds number effect.

We present a weakly nonlinear theory on the natural modes’ resonance of an array of oscillating wave surge converters (OWSCs) in a channel. We first derive the evolution equation of the Stuart–Landau type for the gate oscillations in uniform and modulated incident waves and then evaluate the nonlinear effects on the energy conversion performance of the array. We show that the gates are unstable to side-band perturbations so that a Benjamin–Feir instability similar to the case of Stokes’ waves is possible. The non-autonomous dynamical system presents period doubling bifurcations and strange attractors. We also analyse the competition of two natural modes excited by one incident wave. For weak damping and power take-off coefficient, the dynamical effects on the generated power of the OWSCs are investigated. We show that the occurrence of subharmonic resonance significantly increases energy production.

Two-dimensional (2-D) gravity–capillary solitary waves are generated using a moving pressure jet from a 2-D narrow slit as a forcing onto the surface of deep water. The forcing moves horizontally over the surface of the deep water at speeds close to the minimum phase speed $c_{min}=23~\text{cm}~\text{s}^{-1}$. Four different states are observed according to the forcing speed. At relatively low speeds below $c_{min}$, small-amplitude depressions are observed and they move steadily just below the moving forcing. As the forcing speed increases towards $c_{min}$, nonlinear 2-D gravity–capillary solitary waves are observed, and they move steadily behind the moving forcing. When the forcing speed is very close to $c_{min}$, periodic shedding of a 2-D local depression is observed behind the moving forcing. Finally, at relatively high speeds above $c_{min}$, a pair of short and long linear waves is observed, respectively ahead of and behind the moving forcing. In addition, we observe the transverse instability of free 2-D gravity–capillary solitary waves and, further, the resultant formation of three-dimensional gravity–capillary solitary waves. These experimental observations are compared with numerical results based on a model equation that admits gravity–capillary solitary wave solutions near $c_{min}$. They agree with each other very well. In particular, based on a linear stability analysis, we give a theoretical proof for the transverse instability of the 2-D gravity–capillary solitary waves on deep water.

A model devised by Thorpe & Li (J. Fluid Mech., vol. 758, 2014, pp. 94–120) that predicts the conditions in which stationary turbulent hydraulic jumps can occur in the flow of a continuously stratified layer over a horizontal rigid bottom is applied to, and its results compared with, observations made at several locations in the ocean. The model identifies two positions in the Samoan Passage at which hydraulic jumps should occur and where changes in the structure of the flow are indeed observed. The model predicts the amplitude of changes and the observed mode 2 form of the transitions. The predicted dissipation of turbulent kinetic energy is also consistent with observations. One location provides a particularly well-defined example of a persistent hydraulic jump. It takes the form of a 390 m thick and 3.7 km long mixing layer with frequent density inversions separated from the seabed by some 200 m of relatively rapidly moving dense water, thus revealing the previously unknown structure of an internal hydraulic jump in the deep ocean. Predictions in the Red Sea Outflow in the Gulf of Aden are relatively uncertain. Available data, and the model predictions, do not provide strong support for the existence of hydraulic jumps. In the Mediterranean Outflow, however, both model and data indicate the presence of a hydraulic jump.

Inviscid computational results are presented on a self-propelled swimmer modelled as a virtual body combined with a two-dimensional hydrofoil pitching intermittently about its leading edge. Lighthill (Proc. R. Soc. Lond. B, vol. 179, 1971, pp. 125–138) originally proposed that this burst-and-coast behaviour can save fish energy during swimming by taking advantage of the viscous Bone–Lighthill boundary layer thinning mechanism. Here, an additional inviscid Garrick mechanism is discovered that allows swimmers to control the ratio of their added-mass thrust-producing forces to their circulatory drag-inducing forces by decreasing their duty cycle, $DC$, of locomotion. This mechanism can save intermittent swimmers as much as 60 % of the energy it takes to swim continuously at the same speed. The inviscid energy savings are shown to increase with increasing amplitude of motion, increase with decreasing Lighthill number, $Li$, and switch to an energetic cost above continuous swimming for sufficiently low $DC$. Intermittent swimmers are observed to shed four vortices per cycle that give rise to an asymmetric time-averaged jet structure with both momentum surplus and deficit branches. In addition, previous thrust and power scaling laws of continuous self-propelled swimming are further generalized to include intermittent swimming. The key is that by averaging the thrust and power coefficients over only the bursting period then the intermittent problem can be transformed into a continuous one. Furthermore, the intermittent thrust and power scaling relations are extended to predict the mean speed and cost of transport of swimmers. By tuning a few coefficients with a handful of simulations these self-propelled relations can become predictive. In the current study, the mean speed and cost of transport are predicted to within 3 % and 18 % of their full-scale values by using these relations.

The present experiments explored the dynamical character of the gaseous jet injected flush into cross-flow for variable jet-to-cross-flow momentum flux ratios $J$ (5, 12 and 41) and density ratios $S$ (0.35 and 1.0). Contoured nozzle and straight pipe injectors were studied here, with the jet Reynolds number fixed at 1900 as other flow parameters were varied. Simultaneous acetone planar laser-induced fluorescence (PLIF) imaging and stereo particle image velocimetry (PIV) were used to study the relationships between scalar and velocity/vorticity fields, with a special focus on comparing PLIF-based extraction of scalar dissipation rates and local strain rates with PIV-based local strain rates in the upstream and downstream shear layers of the jet. There was remarkable similarity between the scalar and vorticity fields for the jet in cross-flow, spanning conditions for absolutely unstable upstream jet shear layers at low $J$ or $S$ values to conditions for convectively unstable shear layers for larger $J$, equidensity conditions (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93–129; Getsinger et al., Exp. Fluids, vol. 53, 2012, pp. 783–801). Proper orthogonal decomposition applied to both scalar and velocity fields revealed strengthening instabilities in both the upstream shear layer and in the jet’s wake as $J$ was reduced. The simultaneous measurements allowed PLIF-extracted scalar dissipation rates and strain rates to be determined via a flamelet-like model and compared with PIV-extracted strain rates, each in the diffusion layer-normal direction. There was generally very good qualitative and quantitative agreement for these metrics in both the jet upstream and downstream shear layers for most flow conditions, with excellent correspondence to locations of shear layer vorticity roll up, although downstream shear layer strain rates in some cases showed lesser correspondence between PLIF- and PIV-based data. Such differences are shown to potentially result from diffusion and resolution effects as well as the influence of three-dimensional and transient effects which can be more significant in the lee side of the jet. Nevertheless, the present results reveal interesting dynamics and demonstrate the importance of strain fields in enhanced diffusion and transport phenomena.

In this paper we express the linearized dynamics of interacting interfacial waves in stratified shear flows in the compact form of action-angle Hamilton’s equations. The pseudo-energy serves as the Hamiltonian of the system, the action coordinates are the contribution of the interfacial waves to the wave action and the angles are the phases of the interfacial waves. The term ‘generalized action angle’ aims to emphasize that the action of each wave is generally time dependent and this allows for instability. An attempt is made to relate this formalism to the action at a distance resonance instability mechanism between counter-propagating vorticity waves via the global conservations of pseudo-energy and pseudo-momentum.

Particle image velocimetry and filtered Rayleigh scattering experiments were performed over a range of Reynolds numbers to study the scaling and structure of a smooth, flat-plate turbulent boundary layer with a free stream Mach number of 7.5. The measurements indicate few, if any, dynamic differences due to Mach number. Mean and fluctuating streamwise velocities in the outer layer show strong similarity to incompressible flows at comparable Reynolds numbers when scaled according to van Driest and Morkovin. In addition, correlation lengths and structure angles based on velocity statistics were found to be less sensitive to compressibility than indicated by previous studies based on density fields or mass-weighted statistics, suggesting that the density and velocity fields obey different scaling. Finally, the boundary layer displays uniform momentum zones, with the number of these zones similar to incompressible boundary layers at comparable Reynolds numbers.

In this paper, the structure and the dynamics of the flow in the left heart ventricle are studied for different pumping efficiencies and mitral valve types (natural, biological and mechanical prosthetic). The problem is investigated by direct numerical simulation of the Navier–Stokes equations, two-way coupled with a structural solver for the ventricle and mitral valve dynamics. The whole solver is preliminarily validated by comparisons with ad hoc experiments. It is found that the system works in a highly synergistic way and the left ventricular flow is heavily affected by the specific type of mitral valve, with effects that are more pronounced for ventricles with reduced pumping efficiency. When the ventricle ejection fraction (ratio of the ejected fluid volume to maximum ventricle volume over the cycle) is within the physiological range (50 %–70 %), regardless of the mitral valve geometry, the mitral jet sweeps the inner ventricle surface up to the apex, thus preventing undesired flow stagnation. In contrast, for pathological ejection fractions (⩽40 %), the flow disturbances introduced by the bileaflet mechanical valve reduce the penetration capability of the mitral jet and weaken the recirculation in the ventricular apex. Although in clinical practice the fatality rates in the five-year follow-ups for mechanical and biological mitral valve replacements are essentially the same, a breakdown of the deaths shows that the causes are very different for the two classes of prostheses and the present findings are consistent with the clinical data. This might have important clinical implications for the choice of prosthetic device in patients needing mitral valve replacement.

We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations. In the simulations we use a direct-forcing immersed boundary method to account for the dispersed phase together with a volume-of-fluid approach to solve the temperature field inside and outside the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed in the literature. In addition, an average composite diffusivity can be used to approximate the effective diffusivity of the suspension in the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, smoothly saturating at higher volume fractions. By phase-ensemble-averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated with fluid and particle velocity. We also show that the contribution of the heat conduction in the solid phase to the total wall-normal heat flux reduces when increasing the particle Reynolds number, so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increases the total heat transfer.

We report an experimental and theoretical study of the global stability and nonlinear dynamics of vertical jets of viscous liquid confined in the axial direction due to their impact on a bath of the same liquid. Previous works demonstrated that in the absence of axial confinement the steady liquid thread becomes unstable due to an axisymmetric global mode for values of the flow rate, $Q$, below a certain critical value, $Q_{c}$, giving rise to oscillations of increasing amplitude that finally lead to a dripping regime (Sauter & Buggisch, J. Fluid Mech., vol. 533, 2005, pp. 237–257; Rubio-Rubio et al., J. Fluid Mech., vol. 729, 2013, pp. 471–483). Here we focus on the effect of the jet length, $L$, on the transitions that take place for decreasing values of $Q$. The linear stability analysis shows good agreement with our experiments, revealing that $Q_{c}$ increases monotonically with $L$, reaching the semi-infinite jet asymptote for sufficiently large values of $L$. Moreover, as $L$ decreases a quasi-static limit is reached, whereby $Q_{c}\rightarrow 0$ and the neutral conditions are given by a critical length determined by hydrostatics. Our experiments have also revealed the existence of a new regime intermediate between steady jetting and dripping, in which the thread reaches a limit-cycle state without breakup. We thus show that there exist three possible states depending on the values of the control parameters, namely steady jetting, oscillatory jetting and dripping. For two different combinations of liquid viscosity, $\unicode[STIX]{x1D708}$, and injector radius, $R$, the boundaries separating these regimes have been determined in the $(Q,L)$ parameter plane, showing that steady jetting exists for small enough values of $L$ or large enough values of $Q$, dripping prevails for small enough values of $Q$ or sufficiently large values of $L$, and oscillatory jetting takes place in an intermediate region whose size increases with $\unicode[STIX]{x1D708}$ and decreases with $R$.

The present work consists of an investigation of the turbulence radiation interaction (TRI) in a radiative turbulent channel flow of grey gas bounded by isothermal hot and cold walls. The optical thickness $\unicode[STIX]{x1D70F}$ of the channel is varied from 0.1 to 10 to observe different regimes of TRI. A high-resolution finite volume method for radiative heat transfer is employed and coupled with the direct numerical simulation (DNS) of the flow. The resulting effects of TRI on temperature statistics are strongly dependent on the considered optical depth. In particular, the contrasting role of emission and absorption is highlighted. For a low optical thickness the effect of radiative fluctuations on temperature statistics is low and causes the reduction of temperature variance through the dissipating action of emission. On the other hand, while increasing optical thickness to relatively high levels, the dissipation of temperature variance is balanced, at low wavenumbers in the turbulence spectrum, through the preferential action of absorption, which increases the large-scale temperature fluctuations. A significant rise in the effect of radiation on the temperature variance can be observed as a consequence of the reduction of radiative heat transfer length scales.

We examine the wave-induced flow of small-amplitude, quasi-monochromatic, three-dimensional, Boussinesq internal gravity wavepackets in a uniformly stratified ambient. It has been known since Bretherton (J. Fluid Mech., vol. 36 (4), 1969, pp. 785–803) that one-, two- and three-dimensional wavepackets induce qualitatively different flows. Whereas the wave-induced mean flow for compact three-dimensional wavepackets consists of a purely horizontal localized circulation that translates with and around the wavepacket, known as the Bretherton flow, such a flow is prohibited for a two-dimensional wavepacket of infinite spanwise extent, which instead induces a non-local internal wave response that is long compared with the streamwise extent of the wavepacket. One-dimensional (horizontally periodic) wavepackets induce a horizontal, non-divergent unidirectional flow. Through perturbation theory for quasi-monochromatic wavepackets of arbitrary aspect ratio, we predict for which aspect ratios which type of induced mean flow dominates. We compose a regime diagram that delineates whether the induced flow is comparable to that of one-, two- or compact three-dimensional wavepackets. The predictions agree well with the results of fully nonlinear three-dimensional numerical simulations.

Mean momentum equation based analysis of polymer drag-reduced channel flow is performed to evaluate the redistribution of mean momentum and the mechanisms underlying the redistribution processes. Similar to channel flow of Newtonian fluids, polymer drag-reduced channel flow is shown to exhibit a four layer structure in the mean balance of forces that also connects, via the mean momentum equation, to an underlying scaling layer hierarchy. The self-similar properties of the flow related to the layer hierarchy appear to persist, but in an altered form (different from the Newtonian fluid flow), and dependent on the level of drag reduction. With increasing drag reduction, polymer stress usurps the role of the inertial mechanism, and because of this the wall-normal position where inertially dominated mean dynamics occurs moves outward, and viscous effects become increasingly important farther from the wall. For the high drag reduction flows of the present study, viscous effects become non-negligible across the entire hierarchy and an inertially dominated logarithmic scaling region ceases to exist. It follows that the state of maximum drag reduction is attained only after the inertial sublayer is eradicated. According to the present mean equation theory, this coincides with the loss of a region of logarithmic dependence in the mean profile.

The fluid mechanics of the interaction between a porous material confiner and a steady propagating high explosive (HE) detonation in a two-dimensional slab geometry is investigated through analytical oblique wave polar analysis and multi-material numerical simulation. Two HE models are considered, broadly representing the properties of either a high- or low-detonation-speed HE, which permits studies of detonation propagating at speeds faster or slower than the confiner sound speed. The HE detonation is responsible for driving the compaction front in the confiner, while, in turn, the high material density generated in the confiner as a result of the compaction process can provide a strong confinement effect on the HE detonation structure. Polar solutions that describe the local flow interaction of the oblique HE detonation shock and equilibrium state behind an oblique compaction wave with rapid compaction relaxation rates are studied for varying initial solid volume fractions of the porous confiner. Multi-material numerical simulations are conducted to study the effect of detonation wave driven compaction in the porous confiner on both the detonation propagation speed and detonation driving zone structure. We perform a parametric study to establish how detonation confinement is influenced both by the initial solid volume fraction of the porous confiner and by the time scale of the dynamic compaction relaxation process relative to the detonation reaction time scale, for both the high- and low-detonation-speed HE models. The compaction relaxation time scale is found to have a significant influence on the confinement dynamics, with slower compaction relaxation time scales resulting in more strongly confined detonations and increased detonation speeds. The dynamics of detonation confinement by porous materials when the detonation is propagating either faster or slower than the confiner sound speed is found to be significantly different from that with solid material confiners.

Instabilities at the deformable free surface of a thin nematic liquid crystal film can develop interesting patterns when exposed to an external electrostatic field. A general linear stability analysis is performed involving the Ericksen–Leslie governing equations for the dynamics of the nematic film coupled with the anisotropic Maxwell stresses for the electric field to uncover the salient features of these instabilities. The study reveals the coexistence of twin instability modes: (i) long-wave interfacial mode – stimulated when the sole destabilizing influence of the electric field overcomes the Frank bulk elasticity and surface tension force, and (ii) finite-wavenumber mode – engendered by the combined destabilizing influence originating from the anisotropic electric field and Ericksen stress, for the films with positive dielectric anisotropy and weaker Frank bulk elasticity. The results reported here are in contrast with the same obtained from the more frequently employed long-wave approach. The air-to-liquid-crystal filling ratio between the electrodes as well as thermodynamic parameters such as the dielectric anisotropy, Frank elasticity, and director orientations across the film and boundaries are found to play crucial roles in the selection of modes, whereas kinetic parameters such as Leslie viscosity coefficients influence only the time scale of instability. Importantly, at higher field intensities a symmetry-breaking Fréedericksz-type transition of director orientations is found to happen, which also causes the transition of the dominant mode of instability from the long-wave to the finite-wavenumber mode for films with relatively lower values of Frank bulk elasticity and positive dielectric anisotropy.

We investigate the excitation and radiation of near-inertial internal gravity waves continuously excited by a latitudinally confined temporally fluctuating wind in a numerical model of a stratified ocean on a $\unicode[STIX]{x1D6FD}$-plane at mid-latitude. The surface wind forcing contains both high- and low-frequency components which excite propagating waves and a baroclinically unstable zonal jet respectively. Wentzel–Kramers–Brillouin (WKB) ray theory implies that near-inertial waves propagate strictly towards the equator. We seek to refine this view here by (i) adding the non-traditional Coriolis force (accounting for the horizontal component of the Earth’s rotation) into the equations of motion, in order to allow poleward sub-inertial propagation to occur, and (ii) relaxing the conceptual constraint of no zonal variability, to allow the zonal jet to undergo instability, to meander and to sustain an active field of mesoscale eddies, potentially impacting the excitation of near-inertial waves. The key results are that, while (i) permits weakly stratified waveguides with sub-inertial poleward wave propagation to develop in accord with theory, the sub-inertial energy flux observed is very small compared with the equatorward flux. Thus, in terms of energy radiated from the storm track, non-traditional effects are small for wind-driven near-inertial waves. The consequences of (ii) are much more pronounced. Refinement (ii) produces a radiating wave field that is bidirectional, i.e. with both poleward and equatorward components. We show that the presence of regions of significant background vorticity with horizontal scales significantly smaller than the width of the storm track provides the scale selection mechanism to excite waves with sufficiently super-inertial frequencies to propagate poleward distances of the order of 1000 km.

Several recent studies have reported that there exists a self-similar form of invariant solutions down to the Kolmogorov microscale in the bulk region of turbulent Couette flow. While their role in a fully developed turbulent flow is yet to be identified, here we report that there exists a related mechanism of turbulence production at the Kolmogorov microscale in the bulk region of turbulent Couette flow by performing a set of minimal-span direct numerical simulations up to friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\simeq 800$. This mechanism is found to essentially originate from the non-zero mean shear in the bulk region of the Couette flow, and involves eddy turn-over dynamics remarkably similar to the so-called self-sustaining process (SSP) and/or vortex–wave interaction (VWI). A numerical experiment that removes all other motions except in the core region is also performed, which demonstrates that the eddies at a given wall-normal location in the bulk region are sustained in the absence of other motions at different wall-normal locations. It is proposed that the self-sustaining eddies at the Kolmogorov microscale correspond to those in uniform shear turbulence at transitional Reynolds numbers, and a quantitative comparison between the eddies in uniform shear and near-wall turbulence is subsequently made. Finally, it is shown that turbulence production by the self-sustaining eddies at the Kolmogorov microscale is much smaller than that of full-scale simulations, and that the difference between the two increases with Reynolds number.

The paper presents a low-order prediction scheme for the noise change in multistream jets when the nozzle geometry is altered from a known baseline. The essence of the model is to predict the changes in acoustics due to the redistribution of the mean flow as computed by a Reynolds-averaged Navier–Stokes (RANS) solver. A RANS-based acoustic analogy framework is developed that addresses the noise in the polar direction of peak emission and uses the Reynolds stress as a time-averaged representation of the action of the coherent turbulent structures. The framework preserves the simplicity of the Lighthill acoustic analogy, using the free-space Green’s function, while accounting for azimuthal effects via special forms for the space–time correlation combined with source–observer relations based on the Reynolds stress distribution in the jet plume. Results are presented for three-stream jets with offset secondary and tertiary flows that reduce noise in specific azimuthal directions. The model reproduces well the experimental noise reduction trends. Principal mechanisms of noise reduction are elucidated.