Uniform arrays of particles tend to cluster as they sediment in viscous fluids. Shape anisotropy of the particles enriches this dynamics by modifying the mode structure and the resulting instabilities of the array. A one-dimensional lattice of sedimenting spheroids in the Stokesian regime displays either an exponential or an algebraic rate of clustering depending on the initial lattice spacing (Chajwa et al. 2020 Phys. Rev. X vol. 10, pp. 041016). This is caused by an interplay between the Crowley mechanism, which promotes clumping, and a shape-induced drift mechanism, which subdues it. We theoretically and experimentally investigate the sedimentation dynamics of one-dimensional lattices of oblate spheroids or discs and show a stark difference in clustering behaviour: the Crowley mechanism results in clumps comprising several spheroids, whereas the drift mechanism results in pairs of spheroids whose asymptotic behaviour is determined by pair–hydrodynamic interactions. We find that a Stokeslet, or point-particle, approximation is insufficient to accurately describe the instability and that the corrections provided by the first reflection are necessary for obtaining some crucial dynamical features. As opposed to a sharp boundary between exponential growth and neutral eigenvalues under the Stokeslet approximation, the first-reflection correction leads to exponential growth for all initial perturbations, but far more rapid algebraic growth than exponential growth at large dimensionless lattice spacing $\tilde {d}$. For discs with aspect ratio $0.125$, corresponding to the experimental value, the instability growth rate is found to decrease with increasing lattice spacing $\tilde {d}$, approximately as $\tilde {d}^{ -4.5}$, which is faster than the $\tilde {d}^{-2}$ for spheres (Crowley 1971 J. Fluid Mech. vol. 45, pp. 151–159). It is shown that the first-reflection correction has a stabilising effect for small lattice spacing and a destabilising effect for large lattice spacing. Sedimenting pairs predominantly come together to form an inverted ‘T’, or ‘$\perp$’, which our theory accounts for through an analysis that builds on Koch & Shaqfeh (1989 J. Fluid Mech. vol. 209, pp. 521–542). This structure remains stable for a significant amount of time.

Suspensions of microswimmers exhibit distinct characteristics as compared with those of passive particles because the internal particles are in a state of spontaneous motion. Although there have been many studies of microswimmer suspensions, not many have carefully considered the hydrodynamics. Hydrodynamics becomes particularly important when discussing non-dilute suspensions, because the lubrication flow generates a large force when the swimmers are in close proximity. This paper focuses on hydrodynamics and describes the transport phenomena of microswimmer suspensions, such as migration, collective motion, diffusion and rheology. The paper is structured to progressively scale up from a single microswimmer to collective motion to a macroscale continuum. At each scale, the discussion also evolves from dilute to concentrated suspensions. We first introduce natural swimming microorganisms, artificial microswimmers and mathematical models, as well as the fundamentals of fluid mechanics relevant to microswimmers. We then describe the migration of microswimmers by taxis, where microswimmers respond passively or actively to their hydrodynamic environment. Microswimmers exhibit collective motions, the mechanism of which is discussed in terms of hydrodynamics. The spreading of microswimmers is often diffusive, and the diffusion coefficient is much larger than for passive particles. Similarly, the mass diffusivity in microswimmer suspensions is higher due to their swimming activity. We explain these macroscopic diffusion properties. The viscosity of microswimmer suspensions can be higher or lower depending on the characteristics and orientation of the microswimmers. We describe the rheological properties of microswimmer suspensions in shear flow and Poiseuille flow. Finally, current issues and future research perspectives are discussed.

An experimental study was conducted to investigate the impingement of a vortex ring onto a porous wall by laser-induced fluorescence and particle image velocimetry. The effects of different Reynolds numbers (${{Re}}_{\it\Gamma } = 700$ and $1800$) and hole diameters ($d_{h}^{*} = 0.067$, $0.10$, $0.133$ and $0.20$) on the flow characteristics were examined at a constant porosity ($\phi = 0.75$). To characterise fluid transport through a porous wall, we recall the model proposed by Naaktgeboren, Krueger & Lage (2012, J. Fluid Mech., vol. 707, 260–286), which shows rough agreement with the experimental results due to the absence of vortex ring characteristics. This highlights the need for a more accurate model to correlate the losses in kinetic energy ($\Delta E^{*}$) and impulse ($\Delta I^{*}$) resulting from the vortex ring–porous wall interaction. Starting from Lamb’s vortex ring model and considering the flow transition from the upstream laminar state to the downstream turbulent state caused by the porous wall disturbance, a new model is derived theoretically: $\Delta E^{*} = 1 - k(1 - \Delta I^{*})^2$, where $k$ is a parameter dependent on the dimensionless core radius $\varepsilon$, with $k = 1$ when no flow state change occurs. This new model effectively correlates $\Delta E^{*}$ and $\Delta I^{*}$ across more than 70 cases from current and previous experiments, capturing the dominant flow physics of the vortex ring–porous wall interaction.

Submerged flexible aquatic vegetation exists widely in nature and achieves multiple functions mainly through fluid–structure interactions (FSIs). In this paper, the evolution of large-scale vortices above the vegetation canopy and its effect on flow and vegetation dynamics in a two-dimensional (2-D) laminar flow are investigated using numerical simulations under different bending rigidity $\gamma$ and gap distance d. According to the variation of large-scale vortex size and intensity, the evolution process is divided into four distinct zones in the streamwise direction, namely the ‘developing’ zone, ‘transition’ zone, ‘dissipation’ zone and ‘interaction’ zone, and different evolution sequences are further classified. In the ‘developing’ zone, the size and intensity of the large-scale vortex gradually increase along the array, while they decrease in the ‘dissipation’ zone. The supplement of vegetation oscillating vortices to large-scale vortices is the key to the enhancement of the latter. The most obvious dissipation of large-scale vortices occurs in the ‘transition’ zone, where the position of the large-scale vortex is significantly uplifted. The effects of $\gamma$ and d on the evolution of the large-scale vortex are discussed. In general, the features of vegetation swaying vary synchronously with those of large-scale vortices. The flow above the canopy is dominated by large-scale vortices, and the development of flow characteristics such as time-averaged velocity profile and Reynolds stress are closely related to the evolution of large-scale vortices. The flow inside the canopy, however, is mainly affected by the vortex shed by the vegetation oscillation, which leads to the emergence of negative time-averaged velocity and negative Reynolds stress.

We investigate flow-induced choking in soft Hele-Shaw cells comprising a fluid-filled gap in between a rigid plate and a confined block of elastomer. Fluid injected from the centre of the circular rigid plate flows radially outwards, causing the elastomeric block to deform, before exiting through the cell rim. The pressure in the fluid deforms the elastomer, increasing the size of the gap near the inlet, and decreasing the gap near the cell rim, because of volume conservation of the solid. At a critical injection flow rate, the magnitude of the deformation becomes large enough that the flow is occluded entirely at the rim. Here, we explore the influence of elastomer geometry on flow-induced choking and, in particular, the case of a thick block with radius smaller than its depth. We show that choking can still occur with small-aspect-ratio elastomers, even though the confining influence of the back wall that bounds the elastomer becomes negligible; in this case, the deformation length scale is set by the radial size of the cell rather than the depth of the block. Additionally, we reveal a distinction between flow-induced choking in flow-rate-controlled flows and flow-rate-limiting behaviour in pressure-controlled flows.

The impact of two-dimensional (2-D) periodic forcing on transition dynamics in laminar separation bubbles (LSBs) generated on a flat plate is investigated experimentally. Laminar separation is caused by the favourable-to-adverse pressure gradient under an inverted modified NACA $64_3\text{-}618$ and periodic disturbances are generated by an alternating current dielectric barrier discharge plasma actuator located near the onset of the adverse pressure gradient. Surface pressure and time-resolved particle image velocimetry measurements along the centreline and several wall-parallel planes show significant reductions in bubble size with active flow control. Periodic excitation leads to amplification of the Kelvin–Helmholtz (K–H) instability resulting in strong 2-D coherent roller structures. Spanwise modulation of these structures is observed and varies with the forcing amplitude. Intermediate forcing amplitudes result in periodic spanwise deformation of the mean flow at large wavelength ($\lambda _z/L_{b,5kVpp} \approx 0.76$). For high-amplitude forcing, the spanwise modulation of the mean flow agrees with the much smaller wavelength of the difference interaction of two oblique subharmonic modes ($\lambda _z/L_{b,5kVpp} \approx 0.24$). Modal decomposition shows nonlinear interaction of the forced 2-D mode leading to growth of subharmonic and harmonic content, and the observation of several half-harmonics ($[n+1/2]f_{\textit{AFC}}$) at intermediate forcing amplitudes. Strongest amplitudes of the 2-D mode and delay of transition downstream of the time-averaged reattachment are observed for the intermediate forcing amplitudes, previously only observed in numerical simulations. Consistent with numerical results, further increase of the forcing amplitude leads to rapid breakdown to turbulence in the LSB. This suggests that the most effective exploitation of the K–H instability for transition delay is connected to an optimal (moderate) forcing amplitude.

The experimental investigation focuses on the effects of a short splitter plate on the flow physics of a circular cylinder in proximity to a wall by particle image velocimetry. The Reynolds number is Re = 3900, and the near-wall cylinder is immersed in turbulent boundary layer flow. Three gap ratios (i.e. $G/D$ = 0.25, 0.5 and 1) are considered, and the splitter plate length is $L/D=0$, 0.25, 0.5, 0.75 and 1. For $G/D$ = 0.5 and 1, as $L/D$ increases from 0 to 1, the splitter plate facilitates the cylinder shear layers to elongate downstream, and the vortex formation length is increased, which leads to the increase of the range of the recirculation region. For $G/D$ = 0.25, the wall suppression on the wake vortex formation is enhanced, and the variations of the vortex formation length and the range of the recirculation region with $L/D$ are small. The Strouhal number St presents a decrease with increasing $L/D$ for the three gap ratios. The effects of $L/D$ on the vortex evolution are revealed. For $G/D$ = 0.5 and 1, as $L/D$ increases, the induction of the lower wake vortex on the wall secondary vortex becomes weaker due to the reduction in strength of the wake vortex and the increase of the vortex formation length. Additionally, the wake fluctuation intensity is decreased with the increase of $L/D$ due to the splitter plate suppression. For $G/D$ = 0.25, theL/D influences on evolution of the wake vortices and wall secondary vortex are small, which result in weaker variation of the wake fluctuation intensity with $L/D$.

We report on the experimental and theoretical characterisation of shallow water wave guiding along a curved wave guide. A curved beam of fixed height and width positioned at the bottom of a wave tank generates an effective step-like perturbation which can guide surface water waves. We construct a linear wave theory for this wave propagation and characterise the parameter region where wave guiding can develop, as well as the possible guided modes, their profile and propagation constant. The theoretical analysis is supported by experimental surface wave data. A good agreement is found between experimental data and theoretical predictions, which gives insight into the possible harnessing of wave-guiding phenomena for energy harvesting.

In this work, we conduct particle-resolved direct numerical simulations to investigate the influence of particle inertia on the settling velocity of finite-size particles at low volume fraction in homogeneous isotropic turbulence across various settling numbers. Our results for finite-size particles show only reductions of settling velocity in turbulence compared to the corresponding laminar case. Although increased particle inertia significantly reduces the lateral motion of particles and fluctuations in settling velocity, its effect on the mean settling velocity is not pronounced, except when the settling effect is strong, where increased particle inertia leads to a noticeable reduction. Mechanistically, the nonlinear drag effect, which emphasises contributions from large turbulent scales, cannot fully account for the reduction in settling velocity. The influence of small-scale turbulence, particularly through interactions with the particle boundary layer, should not be overlooked. We also analyse the dependency of turbulence’s modification on particle settling velocity within a broader parameter space, encompassing both sub-Kolmogorov point particles and finite-size particles. Additionally, we develop a qualitative model to predict whether turbulence enhances or retards the settling velocity of particles.

In gas evolving electrolysis, bubbles grow at electrodes due to a diffusive influx from oversaturation generated locally in the electrolyte by the electrode reaction. When considering electrodes of micrometre size resembling catalytic islands, direct numerical simulations show that bubbles may approach dynamic equilibrium states at which they neither grow nor shrink. These are found in undersaturated and saturated bulk electrolytes during both pinning and expanding wetting regimes of the bubbles. The equilibrium is based on the balance of local influx near the bubble foot and global outflux. To identify the parameter regions of bubble growth, dissolution and dynamic equilibrium by analytical means, we extend the solution of Zhang & Lohse (2023 J. Fluid Mech. vol. 975, R3) by taking into account modified gas fluxes across the bubble interface, which result from a non-uniform distribution of dissolved gas. The Damköhler numbers at equilibrium are found to range from small to intermediate values. Unlike pinned nanobubbles studied earlier, for micrometre-sized bubbles the Laplace pressure plays only a minor role. With respect to the stability of the dynamic equilibrium states, we extend the methodology of Lohse & Zhang (2015a Phys. Rev. E vol. 91, 031003(R)) by additionally taking into account the electrode reaction. Under contact line pinning, the equilibrium states are found to be stable for flat nanobubbles and for microbubbles in general. For unpinned bubbles, the equilibrium states are always stable. Finally, we draw conclusions on how to possibly enhance the efficiency of electrolysis.

This study investigates the formation and evolution of fishbone patterns in oblique impinging liquid microjets through high-speed imaging experiments and numerical simulations. The results identify periodic oscillations in the upper region of the liquid sheet as the primary mechanism driving fishbone instabilities, which induce rim disturbances and lead to bifurcations into diverse fishbone morphologies. Transitions between stable and unstable flow patterns are systematically mapped across varying Weber numbers and impingement angles, providing a comprehensive framework for understanding this interfacial dynamics. Two critical transitions – marking the onset and disappearance of fishbone patterns – are characterised, offering insights into the underlying physics governing the stability and instability of these flow structures.

The primary bifurcation of the flow past three-dimensional axisymmetric bodies is investigated. We show that the azimuthal vorticity generated at the body surface is at the root of the instability, and that the mechanism proposed by Magnaudet & Mougin (2007, J. Fluid Mech., vol. 572, 311–337) in the context of spheroidal bubbles extends to axisymmetric bodies with a no-slip surface. The instability arises in a thin region of the flow in the near wake, and is associated with the occurrence of strong vorticity gradients. We propose a simple yet effective scaling law for the prediction of the instability, based on a measure of the near-wake vorticity and of the radial extent of the separation bubble. At criticality, the resulting Reynolds number collapses approximately to a constant value for bodies with different geometries and aspect ratios, with a relative variation that is one order of magnitude smaller than that of the standard Reynolds number based on the free-stream velocity and body diameter. The new scaling can be useful to assess whether the steady flow past axisymmetric bodies is globally unstable, without the need for an additional stability analysis.

We study decaying turbulence in the one-dimensional (1-D) Burgers equation (Burgulence) and 3-D Navier–Stokes (NS) turbulence. We first investigate the decay in time $t$ of the energy $E(t)$ in Burgulence, for a fractional Brownian initial potential, with Hurst exponent $H$, and demonstrate rigorously a self-similar time decay of $E(t)$, previously determined heuristically. This is a consequence of the non-trivial boundedness of the energy for any positive time. We define a spatially forgetful oblivious fractional Brownian motion (OFBM), with Hurst exponent $H$, and prove that Burgulence, with an OFBM as initial potential $\varphi _0(x)$, is not only intermittent, but it also displays a, hitherto unanticipated, large-scale bifractality or multifractality; the latter occurs if we combine OFBMs, with a distribution of $H\hbox{-}$values. This is the first rigorous proof of genuine multifractality for turbulence in a nonlinear hydrodynamical partial differential equation. We then present direct numerical simulations (DNSs) of freely decaying turbulence, capturing some aspects of this multifractality. For Burgulence, we investigate such decay for two cases: (a) $\varphi _0(x)$ a multifractal random walk that crosses over to a fractional Brownian motion beyond a cross-over scale $\mathcal{L}$, tuned to go from small- to large-scale multifractality; (b) initial energy spectra $E_0(k)$, with wavenumber $k$, having one or more power-law regions, which lead, respectively, to self-similar and non-self-similar energy decay. Our analogous DNSs of the 3-D NS equations also uncover self-similar and non-self-similar energy decay. Challenges confronting the detection of genuine large-scale multifractality, in numerical and experimental studies of NS and Magnetohydrodynamics turbulence, are highlighted.

Direct numerical simulation (DNS) of a Mach 4.9 zero-pressure-gradient turbulent boundary layer spatially developing over a cooled flat plate at wall-to-recovery temperature $T_w/T_r = 0.60$ is performed. Very long, streamwise contiguous domains are used in the DNS to achieve a wide continuous range of ‘useful’ friction Reynolds numbers of $1000 \lesssim {Re}_\tau \lesssim 2500$. The DNS datasets have been analysed to assess state-of-the-art compressibility scaling relations and turbulence modelling assumptions. The DNS data show a notable distinction in Reynolds number dependence between thermal and velocity fields. Although Reynolds stress and the budgets of turbulent kinetic energy have reached Reynolds number independence in the inner layer under semi-local scaling by ${Re}_\tau \simeq 1000$, the budget terms for temperature variance and turbulent heat flux retain a clear Reynolds number dependence near the wall over a broader range up to ${Re}_\tau \simeq 1900$. Such a stronger dependence of the thermal field on the Reynolds number may lead to inaccuracy in turbulence models that are calibrated on the basis of low-Reynolds-number data. Spectral and structural analysis suggests a more significant reduction in the prevalence of alternating positive and negative structures and an increase in the streamwise uniformity of streaks in the wall heat flux $q_w$ than in the wall shear stress $\tau _w$ when the Reynolds number increases.

This paper presents numerical results for Rayleigh–Bénard convection with suspended particles at Rayleigh numbers $Ra=10^7$ and $10^8$, and unit Prandtl number. Accounting for their finite size makes it possible to investigate in detail the mechanism by which the particles, which are 10 % heavier than the fluid, get resuspended after settling, thus maintaining a two-phase circulating flow. It is shown that an essential component of this mechanism is the formation of particle accumulations, or ‘dunes’, on the bottom of the Rayleigh–Bénard cell. Ascending plumes become localised on these dunes. Particles are dragged up the dune slopes, and when they reach the top, are entrained into the rising plumes. Direct resuspension of particles from the cell bottom, if it happens at all, is very rare. For $Ra=10^7$, aspect ratios (width/height) $\Gamma =1,2,4$ are considered. It is found that in these and in the other cases simulated, at steady state, a single dune evolves, the largest linear dimension of which is comparable to the cell size. A remarkable consequence is that even at the low volume fraction considered here, 3.27 %, the particles are able to structure the flow and to determine the size and position of the largest ascending plumes. Their effect on the Nusselt number, however, remains small. This and other results are explained on the basis of the ratio of the cell-bottom viscous boundary-layer thickness to the particle diameter.