Experiments have been conducted on a swept wing model in a low-turbulence wind tunnel at chord Reynolds number of $2.17 \times 10^{6}$ to investigate the unsteady interaction of a forward-facing step (FFS) with incoming stationary crossflow (CF) vortices. The impact of varying the FFS height on the development and growth of primary and secondary CF disturbances and the ensuing laminar–turbulent transition is quantified through detailed hot-wire anemometry and infrared thermography measurements. The presence of the FFS results in either a critical (i.e. moderate transition advancement) or a supercritical behaviour (i.e. transition advancing abruptly to the FFS location). The arrival of the forced stationary CF vortices at the step is accompanied by their amplification. Unsteady analysis for the critical cases indicates temporal velocity fluctuations following closely the development of the baseline configuration (i.e. agreeing with the development of secondary instabilities). Consequently, laminar breakdown originates from the outer side of the upwelling region of the CF vortices. In contrast, for the supercritical FFS, the laminar breakdown unexpectedly originates from the inner side of the upwelling region. Evidence points to an unsteady mechanism possibly supported by locally enhanced spanwise-modulated shears and the recirculation region downstream of the FFS edge. This mechanism appears to govern the abrupt tripping of the flow in supercritical step cases. The findings in this work provide insight into the unsteady FFS–CF vortex interaction, which is pivotal to understanding the influence of an FFS on the laminar–turbulent boundary-layer transition in swept aerodynamic surfaces.

Periodically distributed wall-mounted hot blocks with a cubic shape located at the bottom of a layer of liquid with a free top interface tend to create patterns in their surrounding fluid that are reminiscent of the classical modes of Marangoni–Rayleigh–Bénard convection. Through direct numerical solution of the governing equations in their complete three-dimensional unsteady and nonlinear formulation, we investigate this specific subject giving much emphasis to understanding how ensemble properties arise from the interplay of localized effects. Through the used numerical framework, we identify the emerging planforms and connect the statistics of the associated heat transport mechanisms with the spatially averaged behaviour of the underlying thermal currents. In some cases, all these features can be directly mapped into the topography at the bottom of the layer. In other circumstances, these systems contain their own capacity for transformation, i.e. intrinsic evolutionary mechanisms are enabled, by which complex steady or unsteady patterns are produced. It is shown that self-organization driven by purely surface-tension or mixed buoyancy–Marangoni effects can result in ‘quantized states’, i.e. aesthetically appealing solutions that do not depend on the multiplicity of wall-mounted elements.

The propagation of dam-break waves on different rough beds was observed to be quasi-steady in the range $11.3 < x/h_{dam} < 18.8$, where $x$ is measured from the dam position. These quasi-steady propagation speeds converge with the steady ideal fluids model of Stoker (Water Waves, 1957, Interscience) when the tailwater depth $h_2$ becomes greater than ${\sim }0.5k_s$, in the range $0.001< k_s/h_{dam}< 0.2$, where $k_s$ is the roughness and $h_{dam}$ the depth behind the dam. Hence, this convergence encourages the use of Stoker's steady, ideal fluid solution to develop more general models, including friction effects due to bed roughness and/or viscosity. The new experimental data support a MacLaurin series for the celerity $c$, in analogy with the series in terms of $\sqrt [4]{{h_2}/{h_{dam}}}$, derived for Stoker's model, $h_2$ being the tailwater depth. Compared with the retarding effect of the tailwater, 1 mm of roughness is found to be equivalent to $\sim$13 mm of tailwater, and 1 $\mathrm {\mu }$m of viscous length (${\nu }/{\sqrt {gh_{dam}}}$, where ${\nu}$ is the kinematic viscosity and g the acceleration due to gravity) is equivalent to $\sim$1700 $\mathrm {\mu }$m of tailwater. While the MacLaurin series quantifies the similar effects of small roughness and small tailwater depths acting separately, the new data illustrate for the first time the complex interplay between tailwater and roughness on ‘wet beds’ with many details yet to be investigated. In particular, it was shown that a small amount of tailwater on a rough bed acts as a lubricant, so that $c(h_2, h_{dam}, k_s)$ is an increasing function of $h_2$ for $h_2 < 0.5k_s$.

We study the translational and rotational dynamics of neutrally buoyant finite-size spheroids in hydrodynamic turbulence by means of fully resolved numerical simulations. We examine axisymmetric shapes, from oblate to prolate, and the particle volume dependences. We show that the accelerations and rotations experienced by non-spherical inertial-scale particles result from volume filtered fluid forces and torques, similar to spherical particles. However, the particle orientations carry signatures of preferential alignments with the surrounding flow structures, which are reflected in distinct axial and lateral fluctuations for accelerations and rotation rates. The randomization of orientations does not occur even for particles with volume-equivalent diameter size in the inertial range, here up to $60$ dissipative units ($\eta$) at Taylor-scale Reynolds number ${Re_{\lambda }=120}$. Additionally, we demonstrate that the role of fluid boundary layers around the particles cannot be neglected in reaching a quantitative understanding of particle statistical dynamics, as they affect the intensities of the angular velocities and the relative importance of tumbling with respect to spinning rotations. This study brings to the fore the importance of inertial-scale flow structures in homogeneous and isotropic turbulence and their impacts on the transport of neutrally buoyant bodies with sizes in the inertial range.

At low Reynolds numbers, axisymmetric ellipsoidal particles immersed in a shear flow undergo periodic tumbling motions known as Jeffery orbits, with the orbit determined by the initial orientation. Understanding this motion is important for predicting the overall dynamics of a suspension. While slender fibres may follow Jeffery orbits, many such particles in nature are neither straight nor rigid. Recent work exploring the dynamics of curved or elastic fibres have found Jeffery-like behaviour along with chaotic orbits, decaying orbital constants and cross-streamline drift. Most work focuses on particles with reflectional symmetry; we instead consider the behaviour of a composite asymmetric slender body made of two straight rods, suspended in a two-dimensional shear flow, to understand the effects of the shape on the dynamics. We find that for certain geometries the particle does not rotate and undergoes persistent drift across streamlines, the magnitude of which is consistent with other previously identified forms of cross-streamline drift. For this class of particles, such geometry-driven cross-streamline motion may be important in giving rise to dispersion in channel flows, thereby potentially enhancing mixing.

The convective flow generated by a source located at a water surface containing an insoluble surfactant has been investigated experimentally. The application of various sources, which differ in the way in which they drive the interface into motion, and two surfactants with different rheological properties made it possible to generalize the results and to develop a unified approach to describing the problem. We show that the threshold occurrence of a two-zone flow structure with an axisymmetric flow nearby the source and stagnant zone at the periphery results from the competition between two counter-directed shear stresses caused by surfactant concentration inhomogeneity and source influence. We demonstrate that, regardless of the source type, the ratio of these stresses, known as the elasticity number, can be used to predict the formation of a two-zone flow and to define the position of the boundary between the zones. We examined in detail the conditions for formation of the multi-vortex flow within the stagnant zone. Although this phenomenon has been observed by many researchers, it has not yet met a consistent physical explanation. We hypothesized that the formation of vortices can be considered as the instability of the mechanical equilibrium of the surfactant layer caused by the shear on the side of the underlying bulk flow. Based on the mechanism suggested, we introduced a non-dimensional parameter, called the surface Rayleigh number, and estimated its critical value. Finally we analysed the conditions for the occurrence of this instability, called the shear-driven surfactant layer instability in some famous problems of interfacial hydrodynamics.

Non-equilibrium evolution of wave fields, as occurring over sudden bathymetry variations, can produce rogue seas with anomalous wave statistics. We handle this process by modifying the Rayleigh distribution through the energetics of second-order theory and a non-homogeneous reformulation of the Khintchine theorem. The resulting probability model reproduces the enhanced tail of the probability distribution of unidirectional wave tank experiments. It also describes why the peak of rogue wave probability appears atop the shoal, and explains the influence of depth on variations in peak intensity. Furthermore, we interpret rogue wave likelihoods in finite depth through the $H$–$\sigma$ diagram, allowing a quick prediction for the effects of rapid depth change apart from the probability distribution.

The monitoring of intracranial pressure (ICP) fluctuations, which is needed in the context of a number of neurological diseases, requires the insertion of pressure sensors, an invasive procedure with considerable risk factors. Intracranial pressure fluctuations drive the wave-like pulsatile motion of cerebrospinal fluid (CSF) along the compliant spinal canal. Systematically derived simplified models relating the ICP fluctuations with the resulting CSF flow rate can be useful in enabling indirect evaluations of the former from non-invasive magnetic resonance imaging (MRI) measurements of the latter. As a preliminary step in enabling these predictive efforts, a model is developed here for the pulsating viscous motion of CSF in the spinal canal, assumed to be a linearly elastic compliant tube of slowly varying section, with a Darcy pressure-loss term included to model the fluid resistance introduced by the trabeculae, which are thin collagen-reinforced columns that form a web-like structure stretching across the spinal canal. Use of Fourier-series expansions enables predictions of CSF flow rate for realistic anharmonic ICP fluctuations. The flow rate predicted using a representative ICP waveform together with a realistic canal anatomy is seen to compare favourably with in vivo phase-contrast MRI measurements at multiple sections along the spinal canal. The results indicate that the proposed model, involving a limited number of parameters, can serve as a basis for future quantitative analyses targeting predictions of ICP temporal fluctuations based on MRI measurements of spinal-canal anatomy and CSF flow rate.

We determine the globally minimum time $T$ needed to translate a thin submerged flat plate a given distance parallel to its surface within a work budget. The Reynolds number for the flow is assumed to be large so that the drag on the plate arises from skin friction in a thin viscous boundary layer. The minimum is determined computationally using a steepest descent, where an adjoint formulation is used to compute the gradients. Because the equations governing fluid mechanics for this problem are nonlinear, multiple local minima could exist. Exploiting the quadratic nature of the objective function and the constraining differential equations, we derive and apply a ‘spectral condition’ to show the converged local optimum to be a global one. The condition states that the optimum is global if the Hessian of the Lagrangian in the state variables constructed using the converged adjoint field is positive semi-definite at every instance. The globally optimum kinematics of the plate starts from rest with speed $\propto t^{1/4}$ and comes to rest with speed $\propto (T-t)^{1/4}$ as a function of time $t$. For distances much longer than the plate, the work-minimizing kinematics consists of an optimum startup, a constant-speed cruising, and an optimum stopping.

Rectified diffusion is a bubble growth phenomenon that occurs in acoustic fields. Despite the existence of a well-established spherically symmetric mathematical model, theoretical results have been unsuccessful in reproducing the bubble growth even in the case of a single spherical bubble in the bulk. In the latter case, the influence of surfactants and acoustic microstreaming have been speculated as the explanation for this disagreement. In this article, an exact solution for the leading-order concentration of gas in the liquid is determined. Using this exact solution, the well-established mathematical model is reduced to a system of two ordinary differential equations for the spherical bubble radius and the mass of gas in the bubble. This simplified model predicts the rapid bubble growth observed in experiments of a single spherical bubble in the bulk. The new results show that the bubble growth is asymptotically larger than at later times when the mass flux is limited by the slow diffusion of gas in a much larger region of the liquid surrounding the bubble. The new results also show that this bubble growth is relatively insensitive to a reduction in surface tension.

Turbulent fountain flow consists of two distinct stages, the initial ‘negatively buoyant jet’ (NBJ) stage, and the fully developed ‘fountain’ stage. The present study investigates both stages of the flow using particle image velocimetry and planar laser-induced fluorescence, over a range of source Froude numbers, $10\lesssim Fr_o\lesssim 30$, and Reynolds numbers, $5500\lesssim Re_o\lesssim 7700$. While the velocity and buoyancy profiles in NBJs take similar Gaussian shapes over a wide range of axial locations, this was not observed in fountains. The changing profile shape is most evident in the outer flow (OF) region, while there is a degree of similarity in the inner flow (IF). Entrainment between IF and OF is shown to depend on the local Richardson number, $Ri$. The fountains are found to have a negative entrainment coefficient, $\alpha <0$, for the majority of their height, implying a net radial outflow of fluid from the IF to the OF. An alternative description of entrainment is considered, the ‘decomposed top-hat’ model, where the radial flow is separated into inflow and outflow components that are then estimated using the present experimental data. The inflow component was found to be proportional to the axial IF velocity, which is similar to the classical description of entrainment in pure jets/plumes, while the outflow depends on the local $Ri$. Entrainment in NBJs may also be described by this framework, which, despite not having an OF, is still subject to an $Ri$-dependent radial outflow.

The shear-induced migration of dense suspensions with continuously distributed (polydisperse) particle sizes is investigated in planar channel flows for the first time. A coupled lattice Boltzmann–discrete element method numerical framework is employed and validated against benchmark experimental results of bulk shear-induced migration and segregation by particle size. Distinct dependence on the particle size distribution is shown in the flowing (non-plugged) regime (where the bulk solid volume fraction, $\bar{\phi}$, $\leq 0.3$) resulting from a dual dependence on the particle self-diffusivity and local rheology imposed by the particle pressure gradient. Close agreement between statistically equivalent bidisperse and polydisperse suspensions suggests that the bulk migration, and by extension the shear-induced diffusivity, is completely characterised by the first three statistical moments of the particle size distribution. For both bidisperse and polydisperse suspensions in the plugging regime, $\bar {\phi }\geq 0.4$, the smallest particles preferentially form the plugs, causing the largest particles to segregate to the channel walls. This effect is accentuated as $\bar {\phi }$ increases and has not been reported in the literature hitherto. It is proposed that smaller particles preferentially form the plugs due to their higher shear-rate fluctuations, which completely dominate particle motion near the plug where the mean shear rate vanishes. Finally, increasing inertia causes a greater bulk migration towards the channel walls, but increased mid-plane migration for the largest particles due to the dependence of the particle self-diffusivity on the particle Reynolds number. As $\bar {\phi }$ increases shear-induced migration dominates and these inertial effects disappear, as does dependence on the particle size distribution.

The application of Wagner theory to idealised two-dimensional inertially dominated droplet impacts is extended to incorporate non-flat substrates that are continuous functions of distance along the surface. Mixed boundary value problems are solved for the displacement and velocity potentials for both a single impact with an asymmetric substrate and a pair of impacts. The droplet free-surface position and the pressure on the wetted surface are calculated, along with the load and moment on the substrate. For double impacts a void may be formed between the substrate and the droplet free surface. Double impacts are compared with a single asymmetric impact with one half of the equivalent substrate geometry to assess how the free surface, loads and moments are affected by the separation between impact sites. Interactions between symmetric double impacts enhance the liquid penetration between the impact sites and increase the load and moment on each substrate element compared with the corresponding single impact. The time taken for the void between droplet and substrate to become saturated is found assuming the gas pressure build-up and capillary forces are negligible, giving an estimate for the transition time from a partially wetted to a fully wetted surface close to the initial impact site. After the void becomes saturated, the subsequent free-surface evolution is determined and the effect of periodic roughness on the contact line evolution is calculated. For surfaces formed of an array of asperities, secondary impacts which both traps further voids and completely wet the surface are found.

We study the hydrodynamics of a spherical and dumbbell-shaped microswimmer in a tube. Combined with a squirmer model generating tangential surface waves for self-propulsion, a direct-forcing fictitious domain method is employed to simulate the swimming of the microswimmers. We perform the simulations by considering the variations of the swimming Reynolds numbers (Re), the blockage ratios (κ) and the relative distances (ds) between the squirmers of the dumbbell. The results show that the squirmer dumbbell weakens the inertia effects of the fluid more than an individual squirmer. The constrained tube can speed up an inertial pusher (propelled from the rear) and an inertia pusher dumbbell; a greater distance ds results in a slower speed of an inertial pusher dumbbell but a faster speed of an inertial puller (propelled from the front) dumbbell. We also illustrate the swimming stability of a puller (stable) and pusher (unstable) swimming in the tube at Re = 0. At a finite Re, we find that the inertia and the tube constraint competitively affect the swimming stability of the squirmers and squirmer dumbbells. The puller and puller dumbbells swimming in the tube become unstable with increasing Re, whereas an unstable–stable–unstable evolution is found for the pusher and pusher dumbbells. With increasing κ, the puller and puller dumbbells become stable while the pusher and pusher dumbbells become unstable. In addition, we find that a greater ds yields a higher hydrodynamic efficiency η of the inertial squirmer dumbbell.

The effect of discrete roughness elements on the development and breakdown of stationary crossflow instability on a swept wing is explored. Receptivity to various element heights and chordwise locations is explored using a combination of experimental and theoretical tools. Forcing configurations, determined based on linear stability predictions, are manufactured and applied on the wing in a low turbulence facility. Measurements are performed using infrared thermography, quantifying the transition front location, and planar particle image velocimetry, providing a reconstruction of stationary crossflow instabilities and their associated growth. Measurements are corroborated with simulations based on nonlinear parabolised stability equations. Results confirm the efficacy of discrete roughness elements in introducing and conditioning stationary crossflow instabilities. Primary instability amplitudes and resulting laminar-turbulent transition location are found to strongly depend on both roughness amplitude and chordwise location. The Reynolds number based on element height is found to satisfactorily approximate the initial forcing amplitude, revealing the importance of local velocity effects in non-zero-pressure gradient flows. Direct estimation of initial perturbation amplitudes from nonlinear simulations suggests the existence of pertinent flow mechanisms in the element vicinity, active in conditioning the onset of modal instabilities. Dedicated velocimetry planes, elucidate the development of a momentum deficit wake which rapidly decays downstream of the element followed by mild growth, representing the first experimental evidence of transient behaviour in swept wing boundary layers. The outcome of this work identifies a strong scalability of the transition dynamics to roughness amplitude and location, warranting the upscaling of roughness elements to more accessible, measurable and spatially resolved configurations in future experiments.

In this study, a new well-resolved large-eddy simulation of an incompressible near-equilibrium adverse-pressure-gradient (APG) turbulent boundary layer (TBL) over a flat plate is presented. In this simulation, we have established a near-equilibrium APG over a wide Reynolds-number range. In this so-called region of interest, the Rotta–Clauser pressure-gradient parameter $\beta$ exhibits an approximately constant value of around 1.4, and the Reynolds number based on momentum thickness reaches ${\textit {Re}}_{\theta }=8700$. To the best of the authors’ knowledge, this is to date the highest ${\textit {Re}}_{\theta }$ achieved for a near-equilibrium APG TBL under an approximately constant moderate APG. We evaluated the self-similarity of the outer region using two scalings, namely the Zagarola–Smits and an alternative scaling based on edge velocity and displacement thickness. Our results reveal that outer-layer similarity is achieved, and the viscous scaling collapses the near-wall region of the mean flow in agreement with classical theory. Spectral analysis reveals that the APG displaces some small-scale energy from the near-wall to the outer region, an effect observed for all the components of the Reynolds-stress tensor, which becomes more evident at higher Reynolds numbers. In general, the effects of the APG are more noticeable at lower Reynolds numbers. For instance, the outer peak of turbulent-kinetic-energy (TKE) production is less prominent at higher $Re$. Although the scale separation increases with ${\textit {Re}}$ in zero-pressure-gradient TBLs, this effect becomes accentuated by the APG. Despite the reduction of the outer TKE production at higher Reynolds numbers, the mechanisms of energisation of large scales are still present.

The inception of a cavitation bubble in a liquid by focusing a short and intense laser pulse near its free surface develops not only an upwards directed jet, but a second jet of opposite direction into the bulk liquid. When the laser is focused a few microns below the surface, the rapid deposition of energy produces a splash, whose later sealing gives origin to two particularly elongated opposing jets. Interestingly, the evolution of the downward jet flowing into the liquid pool has many similarities to that observed in free water entry experiments, e.g. the creation of a slender and stable cavity in the liquid. The downward jet can reach speeds of up to $40$ m s$^{-1}$ and travels distances of more than 15 times the maximum radius of the laser induced cavity before losing momentum. The longer lifetime of this so-called ‘bullet’ jet as compared with conventional cavitation based jets, the alignment of the jet perpendicular to the free surface and the possibility of scaling the phenomenon opens up potential applications when generated on small droplets or in shallow liquids. In this work, the underlying mechanisms behind the formation of the bullet jets are initially investigated by performing a set of experiments designed to address specific questions about the phenomenon under study. Those were followed by numerical simulations used to give a quantitative and detailed explanation to the experimental observations.

Self-similarity of wall-attached coherent structures in a turbulent channel at $Re_\tau =543$ is explored by means of resolvent analysis. In this modelling framework, coherent structures are understood to arise as a response of the linearised mean-flow operator to generalised frequency-dependent Reynolds stresses, considered to act as an endogenous forcing. We assess the self-similarity of both the wall-attached flow structures and the associated forcing. The former are educed from direct numerical simulation data by finding the flow field correlated with the wall shear, whereas the latter is identified using a frequency space version of extended proper orthogonal decomposition (Borée, Exp. Fluids, vol. 35, issue 2, 2003, pp. 188–192). The forcing structures identified are compared to those obtained using the resolvent-based estimation introduced by Towne et al. (J. Fluid Mech., vol. 883, 2020, A17). The analysis reveals self-similarity of both wall-attached structures – in quantitative agreement with Townsend's hypothesis of self-similar attached eddies – and the underlying forcing, at least in certain components.

Thin phytoplankton layers with vertically compressed structures found in stratified lakes and coastal water bodies have been a hot-spot in marine science and fluid mechanics. Although extensive efforts have been made to explore gyrotactic trapping as a possible mechanism, obvious inconsistencies remain there between the generalised Taylor dispersion method and individual-based model. In this work, a study directly from the fundamental Smoluchowski equation is carried out on the gyrotactic trapping mechanism in representative simple shear flows. With no approximation made to the fundamental equation and applying a biorthogonal expansion to the local moments of the probability density function, the evolution and steady state of the transport process are in good agreement with results of individual-based model, thus removing the gap between the continuum approach and individual-based model. The influences of strongly varying shear rate and boundary effect are reasonably scrutinised. The average swimming orientation with fixed local shear is highlighted as time-dependent rather than steady as previously assumed. The variations of characteristic time of the transient thin layer as functions of the flow intensity, gyrotaxis intensity and swimming ability are characterised. Sedimentation of the micro-swimmers is considered in some cases to reflect that micro-organisms are possibly negatively buoyant, with corresponding boundary conditions devised. A steady thin layer can be realised in the solution by adding a small settling speed to counteract the gravitactic focusing at the upper surface.

We present a detailed derivation of the Reynolds equation and its corresponding energy equation for three-dimensional, steady, laminar, compressible flows of single-phase Navier–Stokes fluids in thrust bearings. These equations are shown to be valid over most of the dense and supercritical gas regime except for the vicinity of the thermodynamic critical point. It is shown that the primary thermodynamic function governing the lubrication flow of high-pressure gases is the effective bulk modulus defined as the ratio of the bulk modulus to the shear viscosity. Numerical solutions to our Reynolds equation are obtained using a finite difference scheme for both moderate and high-speed flows. Approximate solutions to our Reynolds equation for high-speed flows are also derived through a perturbation analysis. It is found that boundary layers form on three out of four edges of the thrust pad. At the inner and outer radii of the pad, the flow is governed by a nonlinear heat equation. As the main flow leaves the pad, the flow is governed by a nonlinear relaxation equation. These three boundary layer solutions are rendered consistent by the construction of boundary layer solutions in the corner regions. A composite solution is developed which provides a single approximation and has the same accuracy as the individual approximations in their respective regions of validity.