Rewetting is the establishment of water–surface contact that occurs during quenching of high temperature surfaces by water jet impingement. Rewetting is an unexpectedly complex phenomenon that has been reported to occur at surface temperatures significantly higher than the superheating limit of water. The presence of intermittently wet and dry episodes, and in particular the occurrence of so-called explosive boiling, is one of the theories to explain the contact of water with high temperature surfaces. However, there is a lack of experimental data in the literature to prove the presence of explosive boiling and intermittent wetting due to the small duration and scale of the rewetting phenomenon. In this study, recordings of the jet stagnation zone during rewetting are provided at a frame rate of 81 kfps. The high-speed recordings show a flashing regime consisting of intermittent (dry) bubble-rich and (wet) bubble-free periods at frequencies up to 40 kHz when the rewetted surface temperature exceeds the water superheat limit. As far as the authors know, these are the first direct observations of intermittent dry–wet periods occurring in the jet stagnation zone during quenching by water jet impingement. The dependency of the flashing frequency on initial surface temperature is quantified. A correlation between the size of the rewetting patch and the flashing frequency is found. Finally, a hypothesis to explain the role of water subcooling in maintaining the water–surface contact at surface temperatures well above the superheating limit of water is presented.

The link between jet-installation noise and the near-field flow features of the corresponding isolated jet is studied by means of lattice-Boltzmann numerical simulations. The computational set-up consists of a flat plate placed in proximity to a jet, replicating the interaction benchmark study carried out at NASA Glenn. Installation effects cause low-frequency noise increase with respect to the isolated case, mainly occurring in the direction normal to the plate and upstream of the jet’s exit plane. It is shown that the Helmholtz number, based on the wavelength of eddies in the mixing layer and their distance to the plate trailing edge, predicts the frequency range where installation noise occurs. Based on the isolated jet near field, scaling laws are also found for the far-field noise produced by different plate geometries. The linear hydrodynamic field of the isolated jet shows an exponential decay of pressure fluctuations in the radial direction; it is shown that the far-field spectrum follows the same trend when moving the plate in this direction. In the axial direction, spectral proper orthogonal decomposition is applied to filter out jet acoustic waves. The resultant hydrodynamic pressure fluctuations display a wavepacket behaviour, which can be fitted with a Gaussian envelope. It is found that installation noise for different plate lengths is proportional to the amplitude of the Gaussian curve at the position of the plate trailing edge. These analyses show that trends of jet-installation noise can be predicted by analysing the near field of the isolated case, reducing the need for extensive parametric investigations.

In nonlinear dynamics, there are three classic routes to chaos, namely the period-doubling route, the Ruelle–Takens–Newhouse route and the intermittency route. The first two routes have previously been observed in self-excited thermoacoustic systems, but the third has not. In this experimental study, we present evidence of the intermittency route to chaos in the self-excited regime of a prototypical thermoacoustic system – a laminar flame-driven Rijke tube. We identify the intermittency to be of type II from the Pomeau–Manneville scenario through an analysis of (i) the probability distribution of the quiescent epochs between successive bursts of chaos, (ii) the first return map, and (iii) the recurrence plot. By establishing the last of the three classic routes to chaos, this study strengthens the universality of how strange attractors arise in self-excited thermoacoustic systems, paving the way for the application of generic suppression strategies based on chaos control.

If a droplet smaller than the capillary length is placed on a substrate with a conical shape, it spreads by itself in the direction of growing fibre radius. We describe this capillary spreading dynamics by developing a lubrication flow approximation on a cone and by using the perturbation method of matched asymptotic expansions. Our results show that the droplet appears to adopt a quasi-static shape and the predictions of the droplet shape and the spreading velocity from the two mathematical models are in excellent agreement. At the contact line regions, a large pressure gradient is generated by the mismatch between the equilibrium contact angle and the apparent contact angle that maintains the viscous flow. It is the conical shape of the substrate that breaks the front/rear droplet symmetry in terms of the apparent contact angle, which is larger at the thicker part of the cone than at its thinner part. Consequently, the droplet is predicted to move from the cone tip to its base, consistent with experimental observations.

In the problem of horizontal convection a non-uniform buoyancy, $b_{s}(x,y)$, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy, $\boldsymbol{J}$, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline{\boldsymbol{J}\boldsymbol{\cdot }\unicode[STIX]{x1D735}b_{s}}=-\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$; the overbar denotes a space–time average over the top surface, angle brackets denote a volume–time average and $\unicode[STIX]{x1D705}$ is the molecular diffusivity of buoyancy $b$. This connection between $\boldsymbol{J}$ and $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ justifies the definition of the horizontal-convective Nusselt number, $Nu$, as the ratio of $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition of $Nu$ over other definitions of horizontal-convective Nusselt number. We investigate transient effects and show that $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ equilibrates more rapidly than other global averages, such as the averaged kinetic energy and bottom buoyancy. We show that $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$ is the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux through the top surface. This leads to an equivalent ‘surface Nusselt number’, defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy $b_{s}(x,y)$. In experimental situations it is easier to evaluate the surface entropy flux, rather than the volume integral of $|\unicode[STIX]{x1D735}b|^{2}$ demanded by $\unicode[STIX]{x1D705}\langle |\unicode[STIX]{x1D735}b|^{2}\rangle$.

A multi-scale Euler–Lagrange method was developed and applied to numerically assess cavitation-induced erosion based on the collapse dynamics of Lagrangian bubbles. This approach linked macroscopic and microscopic scales and captured large vapour volumes on an Eulerian frame, while small vapour volumes were treated as spherical Lagrangian bubbles. Interactions between vapour bubbles and the liquid phase were considered via a two-way coupling scheme. A verification and sensitivity study of the developed procedure to transform vapour volumes between Eulerian and Lagrangian frames was performed. First, the developed method was validated for bubble dynamics, using analytical and experimental data. Second, the cavitating flow through an axisymmetric nozzle was simulated using a measurement-based distribution of cavitation nuclei. Details of single bubble collapses were used to assess cavitation erosion. Based on well-recognised fundamental experiments and theoretical considerations from the literature, model assumptions were derived to account for the effects of a bubble’s stand-off distance on the bubble’s motion and its radiated pressure during an asymmetric near-wall bubble collapse. Computed maximum collapse radii of bubbles correlated well with diameters of measured erosion pits. Considering a nonlinear dependence of erosion on impact pressure, calculated erosion potentials compared well to measured erosion depths.

We examine the critical viscous mode of the Taylor–Couette strato-rotational instability, concentrating on cases where the buoyancy frequency $N$ and the inner cylinder rotation rate $\unicode[STIX]{x1D6FA}_{in}$ are comparable, giving a detailed account for $N=\unicode[STIX]{x1D6FA}_{in}$. The ratio of the outer to the inner cylinder rotation rates $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D6FA}_{out}/\unicode[STIX]{x1D6FA}_{in}$ and the ratio of the inner to the outer cylinder radius $\unicode[STIX]{x1D702}=r_{in}/r_{out}$ satisfy $0<\unicode[STIX]{x1D707}<1$ and $0<\unicode[STIX]{x1D702}<1$. We find considerable variation in the structure of the mode, and the critical Reynolds number $Re_{c}$ at which the flow becomes unstable. For $N=\unicode[STIX]{x1D6FA}_{in}$, we classify different regions of the $\unicode[STIX]{x1D702}\unicode[STIX]{x1D707}$-plane by the critical viscous mode of each region. We find that there is a triple point in the $\unicode[STIX]{x1D702}\unicode[STIX]{x1D707}$-plane where three different viscous modes all onset at the same Reynolds number. We also find a discontinuous change in $Re_{c}$ along a curve in the $\unicode[STIX]{x1D702}\unicode[STIX]{x1D707}$-plane, on one side of which exist closed unstable domains where the flow can restabilise when the Reynolds number is increased. A new form of viscous instability occurring for wide gaps has been detected. We show for the first time that there is a region of the parameter space for which the critical viscous mode at the onset of instability corresponds to the inviscid radiative instability of Le Dizès & Riedinger (J. Fluid Mech., vol. 660, 2010, pp. 147–161). Focusing on small-to-moderate wavenumbers, we demonstrate that the viscous and inviscid systems are not always correlated. We explore which viscous modes relate to inviscid modes and which do not. For asymptotically large vertical wavenumbers, we have extended the inviscid analysis of Park & Billant (J. Fluid Mech., vol. 725, 2013, pp. 262–280) to cover the cases where $N$ and $\unicode[STIX]{x1D6FA}_{in}$ are comparable.

Gravity-driven liquid film flows laden with a soluble surfactant are considered, and aqueous solutions of sodium dodecyl sulphate (SDS) are taken as a case-study. Literature measurements of the critical Reynolds number for the onset of instability are set in perspective with predictions of linear stability theory. The theory is based on a Frumkin model of adsorption equilibrium, modified by the inclusion of finite compressibility of the adsorbed monolayer. Quantitative comparison between data and theory is first attempted in the limit of infinite wavelength. Though wave characteristics are satisfactorily predicted, the theoretical critical Reynolds number is an order of magnitude below measurements. This discrepancy is understood in terms of the large difference between momentum and mass diffusivities and indicates that the assumption of infinite wavelength is far more restrictive for the mass transfer than for the flow problem. Finite-wavelength effects are taken into account by numerical solution of the Orr–Sommerfeld eigenvalue problem, leading to predictions of maximum stabilization in good agreement with the measurements. Introduction of realistic values of monolayer compressibility improves further the agreement at high surfactant loadings. Finally, a strong stabilizing effect of salinity is confirmed.

Flow physics plays a key role in nearly every facet of the COVID-19 pandemic. This includes the generation and aerosolization of virus-laden respiratory droplets from a host, its airborne dispersion and deposition on surfaces, as well as the subsequent inhalation of these bioaerosols by unsuspecting recipients. Fluid dynamics is also key to preventative measures such as the use of face masks, hand washing, ventilation of indoor environments and even social distancing. This article summarizes what we know and, more importantly, what we need to learn about the science underlying these issues so that we are better prepared to tackle the next outbreak of COVID-19 or a similar disease.

The interaction of motile micro-organisms with a nearby solid substrate is a well-studied phenomenon. However, the effects of hydrodynamic slippage on the substrate have received little attention. In the present study, within the framework of the squirmer model, we impose a tangential velocity at the swimmer surface as a representation of the ciliary propulsion, and subsequently obtain an exact solution of the Stokes equation based on a combined analytical–numerical approach. We illustrate how the near-wall swimming velocities are non-trivially altered by the interaction of wall slip and hydrodynamic forces. We report a characteristic transition of swimming trajectories for both puller- and pusher-type microswimmers by hydrodynamic slippage if the wall slip length crosses a critical value. In the case of puller microswimmers that are propelled by a breaststroke-like action of their swimming apparatus ahead of their cell body, the wall slip can cause wall-bound trapping swimming states, as either periodic or damped periodic oscillations, which would otherwise escape from a no-slip wall. The associated critical slip length has a non-monotonic dependence on the initial orientation of the swimmer, which is represented by novel phase diagrams. Pushers, which get their propulsive thrust from posterior flagellar action, also show similar swimming state transitions, but in this case the wall-slip-mediated reorientation dynamics and the swimming modes compete in a different fashion from that of the pullers. Although neutral swimmers lack a sufficient reorientation torque to exhibit any wall-bound trajectory, their detention time near the substrate can be significantly increased by tailoring the extent of hydrodynamic slippage at the nearby wall. The present results pave the way for understanding the motion characteristic of biological microswimmers near confinements with hydrophobic walls or strategize the design of microfluidic devices used for sorting and motion rectification of artificial swimmers by tailoring their surface wettability.

Assuming an inviscid incompressible liquid (with irrotational flows) partly filling a square base tank, which performs a small-amplitude sway/surge/pitch/roll periodic motion whose frequency is close to the lowest natural sloshing frequency, a nine-dimensional Narimanov–Moiseev-type (modal) system of ordinary differential equations with respect to the hydrodynamic generalised coordinates was derived in the Part 1 (Faltinsen et al., J. Fluid Mech., vol. 487, 2003, pp. 1–42). Constructing and analysing asymptotic periodic solutions of the system made it possible to classify steady-state resonant sloshing and its stability for the harmonic reciprocating (longitudinal, diagonal and oblique) forcing. The results were supported by experimental observations and measurements. The present paper finalises the case studies by considering the three-dimensional non-parametric (combined sway, pitch, surge, roll and yaw, but no heave) cyclic tank motions. It becomes possible after establishing an asymptotic equivalence of the associated periodic solutions of the modal system to those for a suitable horizontal translatory elliptic forcing so that, as a consequence, resonant steady-state waves and their stability can be considered versus angular position, semi-axis ratio $|\unicode[STIX]{x1D6FF}_{1}|$ and direction (counter- or clockwise) of the equivalent orbits. The circular orbit causes stable swirling waves (co-directed with the orbit) but may also excite stable nearly standing waves. The orbit direction does not affect the response curves for wall-symmetric (canonic) and diagonal orbit positions. This is not true for the oblique-type elliptic forcing. When the semi-axis ratio $|\unicode[STIX]{x1D6FF}_{1}|$ changes from 0 to 1, the response curves exhibit astonishing metamorphoses significantly influencing the frequency ranges of stable nearly standing/swirling waves and ‘irregular’ sloshing. For the experimental input data by Ikeda et al. (J. Fluid Mech., vol. 700, 2012, pp. 304–328), the counter-directed swirling disappears as $0.5\lesssim |\unicode[STIX]{x1D6FF}_{1}|$ but the frequency range of irregular waves vanishes for $0.75\lesssim |\unicode[STIX]{x1D6FF}_{1}|$.

Kang et al. (J. Fluid Mech., vol. 874, 2019, pp. 339–358) studied viscous dissipation within a permeable body with a view to maximizing the damping of oscillations of the body. They found that dissipation is maximal when the length scale for diffusion of vorticity in the fluid outside the body is similar to the length scale for decay of fluid motion within the body. Their results are examined in the context of the simpler problem of a porous half-space oscillating parallel to the interface between porous solid and fluid. The analysis is then extended to consider the impulsive start-up from rest of a porous plane surface adjacent to unbounded fluid.

Here we characterize the origin and subsequent disintegration into droplets of the type of high-speed jets formed after the sudden implosion of a locally spherical cavity. The full spatio-temporal evolution of these types of impulsively generated jets is described here making use of just the initial values of the interfacial normal velocity at the axis of symmetry and of its corresponding second derivative along the azimuthal direction, obtained straightforwardly from the solution of the Laplace equation subjected to standard boundary conditions. The predicted time evolutions of the jet tip radius and velocity, and of the radii of the ejected droplets, are shown to agree well with experimental observations.

The Mach–Zehnder interferometer with the finite fringe method is applied for the first time to diagnose the three-dimensional density field of a shock-containing microjet issued from a convergent nozzle with an inner diameter of 1 mm at the exit. Experiments are performed at a nozzle pressure ratio of 4.0 to produce an underexpanded free jet with a Mach disk in the first shock-cell where the Reynolds number, based upon the diameter and flow properties at the nozzle exit, is $5.91\times 10^{4}$. Interferogram analyses for reconstructing the jet density fields are performed using the Abel inversion method, in which the analysis of the phase shift of the deformed fringe relative to the background fringe is carried out by the Fourier transform method. In addition to experiments, the flow field of the shock-containing microjet is simulated by solving the Reynolds-averaged Navier–Stokes equations with the SST $k$–$\unicode[STIX]{x1D714}$ turbulence model for a quantitative mutual comparison between the simulation and the experiment. The detailed variation of the density field associated with the Mach disk, the slip streams and the outer shear layers near the jet boundaries are successfully captured. Furthermore, the density profile along the jet centreline obtained by the present experiment is quantitatively compared with those from prior quantitative visualization studies, such as rainbow schlieren deflectometry, background oriented schlieren, moiré schlieren and Mach–Zehnder interferometer. The three-dimensional contour map coloured by the magnitude of the density gradient vector inside the microjet reveals the flow topology of the near-field shock systems and elucidates the spatial variation of the shock strength.

Previous measurements and numerical simulations of buoyant turbulent plumes that develop from area sources provide convincing evidence that entrainment varies locally in response to an imbalance from the asymptotic state of equilibrium, a state referred to as a pure plume. Across the wide spectrum of possible source conditions, that span forced and lazy plume releases, this variation of entrainment has been successfully captured by a single, or universal, description in which the entrainment function $\unicode[STIX]{x1D6FC}$ varies linearly with the local Richardson number. Herein, an analytical solution for the virtual origin of forced, pure and lazy turbulent plumes from circular sources in unstratified environments is derived based on this universal description of entrainment. Prior to this, the analytical solutions reported were limited to those based on the simplifying assumption of invariant entrainment, so-called constant-$\unicode[STIX]{x1D6FC}$ solutions of the plume conservation equations. Analytical solutions for the fluxes of volume and specific momentum are first developed. These solutions highlight the deficit in near-field entrainment in forced plumes and enable the general imbalance from the equilibrium state to be predicted via the streamwise variation of the local Richardson number. Focus then turns to the virtual origin due to the practical benefits that a knowledge of this location offers experimentalists (e.g. in comparing measurement with theory) and theoretical modellers (e.g. in incorporating a turbulent plume within a broader modelling framework).

We use interface-resolved direct numerical simulations to study the dynamics of a single sediment particle in a turbulent open channel flow over a fixed porous bed. The relative strength of the gravitational acceleration, quantified by the Galileo number, is varied so as to reproduce the different modes of sediment transport – resuspension, saltation and rolling. The results show that the sediment dynamics at lower Galileo numbers (i.e. resuspension and saltation) are mainly governed by the mean flow. Here, the regime of motion can be predicted by the ratio between the gravity and the shear-induced boundary force. In these cases, the sediment particle rapidly takes off when exposed to the flow, and proceeds with an oscillatory motion. Increasing the Galileo number, the frequency of these oscillations increases and their amplitude decreases, until the transport mode switches from resuspension to saltation. In this case, the sediment travels by short successive collisions with the bed. Further increasing the Galileo number, the particle rolls without detaching from the bed. Differently from the previous modes, the motion is triggered by extreme turbulent events, and the particle response depends on the specific initial conditions, at fixed Reynolds number. The results reveal that close to the onset of sediment motion, only turbulent sweeps can effectively trigger the particle motion by increasing the stagnation pressure upstream. We show that for the parameters in this study, a criterion based on the streamwise flow-induced force can successfully predict the incipient movement.

The generation mechanism of screech harmonics in supersonic exhausts is revealed using shadowgraph imaging and acoustic far-field measurements for a rectangular, high aspect-ratio nozzle. The coherent information associated with screech and its harmonics, i.e. flow structures and acoustic radiation pattern, is extracted from the time-resolved shadowgraph images. We show that, for large lateral distortions of the jet plume, the passage of screech associated flow structures triggers the screech-cyclic formation of shocks, which travel downstream and merge with the original shocks. The interaction of the shock waves with the flow structures associated with screech alters the appearance of the perturbations in the mixing layer, which constitute the higher harmonics of screech. Visualisations of the acoustic radiation pattern expose that the third and higher screech tone harmonics originate from these interaction locations. Further, the occurrence of mode resonance between the screech and its harmonics is demonstrated, where the mode resonance location coincides with the screech tone origin.

The control of bluff-body wakes for reduced drag and enhanced stability has traditionally relied on the so-called direct-wake control approach. By the use of actuators or passive devices, one can manipulate the aerodynamic loads that act on the rear of the model. An alternative approach for the manipulation of the flow is to move the position of the actuator upstream, hence interacting with an easier-to-manipulate boundary layer. The present paper comprises a bluff-body flow study via large-eddy simulations to investigate the effectiveness of an upstream actuator (positioned at the leading edge) with regard to the manipulation of the wake dynamics and its aerodynamic loads. A rectangular cylinder with rounded leading edges, equipped with actuators positioned at the front curvatures, is simulated at $Re=40\,000$. A genetic algorithm (GA) optimization is performed to find an effective actuation that minimizes drag. It is shown that the GA selects superharmonic frequencies of the natural vortex shedding. Hence, the induced disturbances, penetrating downstream in the wake, significantly reduce drag and lateral instability. A comparison with a side-recirculation-suppression approach is also presented, the latter case being worse in terms of reduced drag (only 8 % drag reduction achieved), despite the total suppression of the side recirculation bubble. In contrast, the GA optimized case contributes to a 20 % drag reduction with respect to the unactuated case. In addition, the large drag reduction is associated with a reduced shedding motion and an improved lateral stability.

Buoyancy-driven exchange flows arise in the natural and built environment wherever bodies of fluids at different densities are connected by a narrow constriction. In this paper we study these flows in the laboratory using the canonical stratified inclined duct experiment, which sustains an exchange flow in an inclined duct of rectangular cross-section over long time periods (Meyer & Linden, J. Fluid Mech., vol. 753, 2014, pp. 242–253). We study the behaviour of these sustained stratified shear flows by focusing on three dependent variables of particular interest: the qualitative flow regime (laminar, wavy, intermittently turbulent or fully turbulent), the mass flux (net transport of buoyancy between reservoirs) and the interfacial thickness (thickness of the layer of intermediate density between the two counter-flowing layers). Dimensional analysis reveals five non-dimensional independent input parameters: the duct aspect ratios in the longitudinal direction $A$ and spanwise direction $B$, the tilt angle $\unicode[STIX]{x1D703}$, the Reynolds number $Re$ (based on the initial buoyancy difference driving the flow) and the Prandtl number $Pr$ (we consider both salt and temperature stratifications). After reviewing the literature and open questions on the scaling of regimes, mass flux and interfacial thickness with $A,B,\unicode[STIX]{x1D703},Re,Pr$, we present the first extensive, unified set of experimental data where we varied systematically all five input parameters and measured all three output variables with the same methodology. Our results in the $(\unicode[STIX]{x1D703},Re)$ plane for five sets of $(A,B,Pr)$ reveal a variety of scaling laws, and a non-trivial dependence of all three variables on all five parameters, in addition to a sixth elusive parameter. We further develop three classes of candidate models to explain the observed scaling laws: (i) the recent volume-averaged energetics of Lefauve et al. (J. Fluid Mech., vol. 848, 2019, pp. 508–544); (ii) two-layer frictional hydraulics; (iii) turbulent mixing models. While these models provide significant qualitative and quantitative descriptions of the experimental results, they also highlight the need for further progress on shear-driven turbulent flows and their interfacial waves, layering, intermittency and mixing properties.

We study the fragmentation of a liquid drop that is hit by a laser pulse. The drop expands into a thin sheet that breaks by the radial expulsion of ligaments from its rim and the nucleation and growth of holes on the sheet. By combining experimental data from two liquid systems with vastly different time and length scales, we show how the early-time laser–matter interaction affects the late-time fragmentation. We identify two Rayleigh–Taylor instabilities of different origins as the prime cause of the fragmentation and derive scaling laws for the characteristic breakup time and wavenumber. The final web of ligaments results from a subtle interplay between these instabilities and deterministic modulations of the local sheet thickness, which originate from the drop deformation dynamics and spatial variations in the laser-beam profile.