Understanding how bubbles on a substrate respond to ultrasound is crucial for applications from industrial cleaning to biomedical treatments. Under ultrasonic excitation, bubbles can undergo shape deformations due to Faraday instability, periodically producing high-speed jets that may cause damage. While recent studies have begun to elucidate this behaviour for free bubbles, the dynamics of wall-attached bubbles is still largely unexplored. In particular, the selection and evolution of non-spherical modes in these bounded systems have not previously been resolved in three dimensions, and the resulting jetting dynamics has yet to be compared with that observed in free bubbles. In this study, we investigate individual micrometric air bubbles in contact with a rigid substrate and subjected to ultrasound. We introduce a novel dual-view imaging technique that combines top-view bright-field microscopy with side-view phase-contrast X-ray imaging, enabling visualisation of bubble shape evolution from two orthogonal perspectives. This set-up reveals the progression of bubble shape through four distinct dynamic regimes: purely spherical oscillations, onset of harmonic axisymmetric meniscus waves, emergence of half-harmonic axisymmetric Faraday waves and the superposition of half-harmonic sectoral Faraday waves. This stepwise evolution contrasts with the behaviour of free bubbles, which exhibit their ultimate Faraday wave pattern immediately upon instability onset. For the substrate chosen, the resulting shape-mode spectrum appears to be degenerate and exhibits a continuous range of shape mode degrees, in line with our theoretical predictions derived from kinematic arguments. While free bubbles also display a degenerate spectrum, their shape mode degrees remain discrete, constrained by the bubble spherical periodicity. Experimentally measured ultrasound pressure thresholds for the onset of Faraday instability agree well with classical interface stability theory, modified to incorporate the effects of a rigid boundary. Complementary three-dimensional boundary element simulations of bubble shape evolution align closely with experimental observations, validating this method’s predictive capability. Finally, we determine the acceleration threshold at which shape mode lobes initiate cyclic jetting. Unlike free bubbles, jetting in wall-attached bubbles consistently emerges from the side not restricted by the substrate.

We focus on the wake of a cylinder placed in uniform flow and forced to rotate periodically at subcritical Reynolds numbers, i.e. for Reynolds numbers smaller than 47 calculated based on the incoming flow velocity and the cylinder diameter, where vortices are not shed in the wake of a fixed cylinder. We show that in the near wake, the imposed periodic rotation causes the Föppl vortices (the symmetric steady vortices that are formed right behind a fixed cylinder within the Reynolds number range of $5\lt {Re}\lt 47$) to appear only momentarily during each rotation cycle until they disappear at higher rotation rates. In the far wake, vortices can be induced for certain values of rotation rate, $\alpha$, and rotation frequency, $f$. The shedding of these vortices in the wake results in a periodic lift force that acts on the cylinder. We have defined a new parameter $\omega /(f\alpha )\equiv 1/F$, where $\omega$ is the angular velocity of the cylinder, which is significant in describing the system. For any values of angular velocity and the frequency of change in the rotation direction, the wake pattern remains the same if the value of $1/F$ stays constant. Subsequently, the fluctuating lift coefficient and the average drag coefficient peak at the same value of $1/F$ for any value of $\omega /f\equiv \alpha /F$. The Reynolds number for the onset of shedding decreases with increasing rotation rate at a constant $\alpha /F$. We have observed shedding at Reynolds numbers as low as ${Re}=1$ for higher rotation rates.

Axisymmetric turbulent boundary layers are of great significance in industry and the fluid dynamics community. In this paper, direct numerical simulations of an axially developing axisymmetric turbulent boundary layer along a slender cylinder are performed. Periodical suction and blowing perturbation are used to trigger the transition from laminar inflow to turbulent flow downstream, resulting in the boundary layer thickness varying from 7 to 13 times the cylinder radius, and the friction Reynolds number varying from 300 to 510. Turbulence statistics including wall friction coefficient, mean velocity profile and Reynolds stresses are obtained. The turbulence intensities are weakened compared with the planar turbulent layer, and the inter-component energy transfer is also inhibited. A curvature-weighted transformation is proposed, and the transformed Reynolds stresses and mean velocity deficit collapse well with the planar case in the near-wall region. The velocity streaks and vortical structures are explored. The wall-normal variation of the mean spanwise spacing of low-speed streaks is greatly influenced by the cylindrical geometry. Quasi-streamwise vortices dominate the near-wall region, and the arch vortices are prevalent in the outer region. The prograde hairpin vortices can be commonly observed.

A rotating detonation combustor exhibits corotating $N$-wave modes with $N$ detonation waves propagating in the same direction. These modes and their responses to ignition conditions and disturbances were studied using a surrogate model. Through numerical continuation, a mode curve (MC) is obtained, depicting the relationship between the wave speed of the one-wave mode and a defined baseline of the combustor circumference ($L_{{base}}$) under fixed equation parameters, limited by deflagration and flow choking. The modes’ existence is confirmed by the equivalence between a one-wave mode within a combustor with circumference $L_{{base}}$/$N$ on the MC and an $N$-wave mode in an $L_{{base}}$ combustor. The stability, measured by the real part of the eigenvalue from linear stability analysis (LSA), revealed the dynamic properties. When multiple stable modes exist under the same parameters, ignition conditions with a spatial period of $L_{{base}}$/$N$ are more likely to form $N$-wave modes. An unstable evolution in formed modes, occurs in the dynamics from stable to unstable modes through saddle-node bifurcation and Hopf bifurcation induced by parameter perturbations and from unstable to stable modes induced by state disturbances. Eigenmodes from LSA reveal mechanisms of the unstable evolution, including the effect of secondary deflagration in the unstable one-wave mode and competitive interaction between detonation waves in the unstable multiwave mode, crucial for the combustor to mode transition.

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.