We conduct direct numerical simulations (DNS) to investigate the attenuation of turbulence in a periodic cube due to the addition of prolate spheroidal solid particles. Even with a dilute volume fraction of $O(10^{-2})$, particles can drastically attenuate the turbulence. Our DNS show that the turbulent kinetic energy reduces more significantly when the particles’ Stokes number is larger, size is smaller or aspect ratio is larger. We can explain these results based on the formula proposed by Oka and Goto (2022 J. Fluid Mech. 949, A45), which relates the turbulence attenuation rate to the energy dissipation rate $\epsilon _p$ around particles. More precisely, under the condition that the volume fraction of particles is fixed, $\epsilon _p$ is larger when the Stokes number and, therefore, the relative velocity between fluid and particles are larger, the particle size is smaller or the aspect ratio is larger. These results also imply that the rotation of the anisotropic particles plays only a limited role in the attenuation of turbulence when the Stokes number of particles is sufficiently large, because the main cause of the attenuation is the relative translational velocity between fluid and particles.

Turbulent flows over porous substrates are studied via a systematic exploration of the dependence of the flow properties on the substrate parameters, including permeability $K$, grain pitch $L$ and depth $h$. The study uses direct numerical simulations mainly for staggered-cube substrates with $L^+\approx 10$–$50$, $\sqrt {K}/L\approx 0.01$–$0.25$ and depths from $h=O(L)$ to $h\gg L$, ranging from typical impermeable rough surfaces to deep porous substrates. The results indicate that the permeability has significantly greater relevance than the grain size and microscale topology for the properties of the overlying flow, including the mean-flow slip and the shear across the interface, the drag increase relative to smooth-wall flow and the statistics and spectra of the overlying turbulence, whereas the direct effect of grain size is only noticeable near the interface as grain-coherent flow fluctuations. The substrate depth also has a significant effect, with shallower substrates suppressing the effective transpiration at the interface. Based on the direct-simulation results, we propose an empirical ‘equivalent permeability’ $K_{eq}^t$ that incorporates this effect and scales well the overlying turbulence for substrates with different depths, permeabilities, etc. This result suggests that wall normal transpiration driven by pressure fluctuations is the leading contributor to the changes in the drag and the overlying turbulence. Based on this, we propose a conceptual $h^+$–$\sqrt {K^+}$ regime diagram where, for any given substrate topology, turbulence transitions smoothly from that over impermeable rough surfaces with $h=O(L)$ to that over deep porous substrates with $h^+\gtrsim 50$, with the latter limit determined by the typical lengthscale of the overlying pressure fluctuations.

As new concepts to protect marine structures from ocean waves, we propose the use of a floating elastic annulus. In this paper, two types of annuli are demonstrated. The first is a ‘wave shield’, which creates a calm free surface within an inner domain of the annulus by preventing wave penetration. The second is a ‘cloak’, which not only creates a calm space within the inner domain but also prevents wave scattering outside the annulus. To evaluate the calmness of the inner domain of the annulus, an inlet wave energy factor is newly defined. The wave shield is designed to minimise the inlet wave energy factor to nearly zero. However, the cloak is designed to minimise both the inlet wave energy factor and scattered-wave energy which evaluates the amount of wave scattering at far-field. Each annulus consists of several horizontal concentric annular plates, and the flexural rigidities of the plates are optimised to minimise objective functions at a target frequency. Numerical simulations demonstrate that both the wave shield and the cloak can create calm free surfaces within their inner domains. In addition, the cloak effectively suppresses the outgoing scattering waves and reduces the resultant wave drift force.

Lift and drag forces on moving intruders in flowing granular materials are of fundamental interest but have not yet been fully characterized. Drag on an intruder in granular shear flow has been studied almost exclusively for the intruder moving across flow streamlines, and the few studies of the lift explore a relatively limited range of parameters. Here, we use discrete element method simulations to measure the lift force, $F_{{L}}$, and the drag force on a spherical intruder in a uniformly sheared bed of smaller spheres for a range of streamwise intruder slip velocities, $u_{{s}}$. The streamwise drag matches the previously characterized Stokes-like cross-flow drag. However, $F_{{L}}$ in granular shear flow acts in the opposite direction to the Saffman lift in a sheared fluid at low $u_{{s}}$, reaches a maximum value and then decreases with increasing $u_{{s}}$, eventually reversing direction. This non-monotonic response holds over a range of flow conditions, and the $F_{{L}}$ versus $u_{{s}}$ data collapse when both quantities are scaled using the particle size, shear rate and overburden pressure. Analogous fluid simulations demonstrate that the flow around the intruder particle is similar in the granular and fluid cases. However, the shear stress on the granular intruder is notably less than that in a fluid shear flow. This difference, combined with a void behind the intruder in granular flow in which the stresses are zero, significantly changes the lift-force-inducing stresses acting on the intruder between the granular and fluid cases.

In Rayleigh–Bénard convection and Taylor–Couette flow cellular patterns emerge at the onset of instability and persist as large-scale coherent structures in the turbulent regime. Their long-term dynamics has been thoroughly characterised and modelled for the case of turbulent convection, whereas turbulent Taylor rolls have received much less attention. Here we present direct numerical simulations of axisymmetric Taylor–Couette flow in the corotating regime and reveal a transition to spatio–temporal chaos as the system size increases. Beyond this transition, Taylor rolls suddenly undergo erratic drifts evolving on a very slow time scale. We estimate an effective diffusion coefficient for the drift and compare the dynamics with analogous motions in Rayleigh–Bénard convection and Poiseuille flow, suggesting that this spontaneous diffusive displacement of large coherent structures is common among different types of wall-bounded turbulent flows.

Wind turbines operate in the atmospheric boundary layer (ABL), where Coriolis effects are present. As wind turbines with larger rotor diameters are deployed, the wake structures that they create in the ABL also increase in length. Contemporary utility-scale wind turbines operate at rotor diameter-based Rossby numbers, the non-dimensional ratio between inertial and Coriolis forces, of $\mathcal {O}(100)$ where Coriolis effects become increasingly relevant. Coriolis forces provide a direct forcing on the wake, but also affect the ABL base flow, which indirectly influences wake evolution. These effects may constructively or destructively interfere because both the magnitude and sign of the direct and indirect Coriolis effects depend on the Rossby number, turbulence and buoyancy effects in the ABL. Using large eddy simulations, we investigate wake evolution over a wide range of Rossby numbers relevant to offshore wind turbines. Through an analysis of the streamwise and lateral momentum budgets, we show that Coriolis effects have a small impact on the wake recovery rate, but Coriolis effects induce significant wake deflections which can be parsed into two regimes. For high Rossby numbers (weak Coriolis forcing), wakes deflect clockwise in the northern hemisphere. By contrast, for low Rossby numbers (strong Coriolis forcing), wakes deflect anti-clockwise. Decreasing the Rossby number results in increasingly anti-clockwise wake deflections. The transition point between clockwise and anti-clockwise deflection depends on the direct Coriolis forcing, pressure gradients and turbulent fluxes in the wake. At a Rossby number of 125, Coriolis deflections are comparable to wake deflections induced by ${\sim} 20^{\circ }$ of yaw misalignment.

Active fluids encompass a wide range of non-equilibrium fluids, in which the self-propulsion or rotation of their units can give rise to large-scale spontaneous flows. Despite the diversity of active fluids, they are commonly viscoelastic. Therefore, we develop a hydrodynamic model of isotropic active liquids by accounting for their viscoelasticity. Specifically, we incorporate an active stress term into a general viscoelastic liquid model to study the spontaneous flow states and their transitions in two-dimensional channel, annulus and disk geometries. We have discovered rich spontaneous flow states in a channel as a function of activity and Weissenberg number, including unidirectional flow, travelling-wave and vortex-roll states. The Weissenberg number acts against activity by suppressing the spontaneous flow. In an annulus confinement, we find that a net flow can be generated only if the aspect ratio of the annulus is not too large nor too small, akin to some three-dimensional active-flow phenomena. In a disk geometry, we observe a periodic chirality switching of a single vortex flow, resembling the bacteria-based active fluid experiments. The two phenomena reproduced in our model differ in Weissenberg number and frictional coefficient. As such, our active viscoelastic model offers a unified framework to elucidate diverse active liquids, uncover their connections and highlight the universality of dynamic active-flow patterns.

We study the response of a flexible prism with a square cross-section placed in cross-flow through a series of experiments conducted at increasing flow velocities. We show that as the reduced velocity (a dimensionless flow velocity that also depends on the natural frequency of the structure) is increased, the prism undergoes vortex-induced vibration (VIV) in its first mode, which then transitions to VIV in the second mode and then third mode. In these ranges, the shedding frequency is synchronised with the oscillation frequency, and the oscillations are mainly in the transverse (cross-flow – CF) direction. As we keep increasing the reduced velocity, we observe a linear increase in the amplitude of the torsional oscillations of the prism, resembling a torsional galloping. This increase in the torsional oscillations then causes an increase in the amplitudes of the CF and inline (IL) oscillations while the third structural mode is still excited in the CF direction. A transition to oscillations in the fourth structural mode is observed at higher reduced velocities, which reduces the CF and IL amplitudes, while the torsional oscillations reach a plateau. After this plateau is reached in the torsional oscillations, galloping is observed in the CF oscillations of the response, which results in large-amplitude oscillations in both the CF and IL directions. The CF galloping response at these higher reduced velocities is accompanied by a torsional VIV response and the shedding frequency is synchronised with the frequency of the torsional oscillations.

We investigate the sliding dynamics of a millimetre-sized particle trapped in a horizontal soap film. Once released, the particle moves toward the centre of the film in damped oscillations. We study experimentally and model the forces acting on the particle, and evidence the key role of the mass of the film on the shape of the film and particle dynamics. Not only is the gravitational distortion of the film measurable, it completely determines the force responsible for the motion of the particle – the catenoid-like deformation induced by the particle has negligible effect on the dynamics. Surprisingly, this is expected for all film sizes as long as the particle radius remains much smaller than the film width. We also measure the friction force, and show that ambient air and the film contribute almost equally to the friction. The theoretical model that we propose predicts exactly the friction coefficient as long as inertial effects can be neglected in air (for the smallest and slowest particles). The fit between theory and experiments sets an upper boundary $\eta _s \leqslant 10^{-8}$ Pa s m for the surface viscosity, in excellent agreement with recent interfacial microrheology measurements.

An adaptable estimation technique is presented to reconstruct time-evolving three dimensional (3-D) velocity fields from planar particle image velocimetry measurements. The methodology builds on the multi-time-delay estimation technique of Hosseini et al. (2015) by implementing the finite-impulse-response spectral proper orthogonal decomposition (FIR-SPOD) of Sieber et al. (2016). The candidate flow is the highly modulated turbulent near wake of a cantilevered square cylinder with a height-to-width ratio $h/d=4$, protruding a thin laminar boundary layer ($\delta /d=0.21$ with $\delta$ being the boundary layer thickness) at the Reynolds number $Re=10600$, based on d. The novelty of the estimation technique is in using the modal space obtained by FIR-SPOD to better isolate the spatio-temporal scales for correlating velocity and pressure modes. Using FIR-SPOD, irregular coherent contributions at frequencies centred at $f_{ac1}=(1\pm 0.05)f_s$ and $f_{ac2}=(1\pm 0.1)f_s$ (with $f_s$ the fundamental shedding frequency) could be separated, which was not possible using proper orthogonal decomposition. With the FIR-SPOD bases, the quality of the estimation improved significantly using only linear terms, and the correct phase relationships between pressure and velocity modes are retained, as is required for synchronizing coherent motions along the height of the obstacle. It is shown that a low-dimensional reconstruction of the flow field successfully captures the cycle-to-cycle variations of the dominant 3-D vortex shedding process, which give rise to vortex dislocation events. Thus, the present methodology shows promise in 3-D reconstruction of challenging turbulent flows, which exhibit non-periodic behaviour or contain multi-scale phenomena.

Low-inertia pulsatile flows in highly distensible viscoelastic vessels exist in many biological and engineering systems. However, many existing works focus on inertial pulsatile flows in vessels with small deformations. As such, here we study the dynamics of a viscoelastic tube at large deformation conveying low-Reynolds-number oscillatory flow using a fully coupled fluid–structure interaction computational model. We focus on a detailed study of the effect of wall (solid) viscosity and oscillation frequency on tube deformation, flow rate, phase shift and hysteresis, as well as the underlying flow physics. We find that the general behaviour is dominated by an elastic flow surge during inflation and a squeezing effect during deflation. When increasing the oscillation frequency, the maximum inlet flow rate increases and tube distention decreases, whereas increasing solid viscosity causes both to decrease. As the oscillation frequency approaches either $0$ (quasi-steady inflation cycle) or $\infty$ (steady flow), the behaviours of tubes with different solid viscosities converge. Our results suggest that deformation and flow rate are most affected in the intermediate range of solid viscosity and oscillation frequency. Phase shifts of deformation and flow rate with respect to the imposed pressure are analysed. We predict that the phase shifts vary throughout the oscillation; while the deformation always lags the imposed pressure, the flow rate may either lead or lag depending on the parameter values. As such, the flow rate shows hysteresis behaviour that traces either a clockwise or counterclockwise curve, or a mix of both, in the pressure–flow rate space. This directional change in hysteresis is fully characterised here in the appropriate parameter space. Furthermore, the hysteresis direction is shown to be predicted by the signs of the flow rate phase shifts at the crest and trough of the oscillation. A distinct change in the tube dynamics is also observed at high solid viscosity which leads to global or ‘whole-tube’ motion that is absent in purely elastic tubes.

When an oblate droplet translates through a viscous fluid under linear shear, it experiences a lateral lift force whose direction and magnitude are influenced by the Reynolds number, the droplet’s viscosity and its aspect ratio. Using a recently developed sharp interface method, we perform three-dimensional direct numerical simulations to explore the evolution of lift forces on oblate droplets across a broad range of these parameters. Our findings reveal that in the low-but-finite Reynolds number regime, the Saffman mechanism consistently governs the lift force. The lift increases with the droplet’s viscosity, aligning with the analytical solution derived by Legendre & Magnaudet (Phys. Fluids, vol. 9, 1997, p. 3572), and also rises with the droplet’s aspect ratio. We propose a semi-analytical correlation to predict this lift force. In the moderate- to high-Reynolds-number regime, distinct behaviours emerge: the $L\hbox{-}$ and $S\hbox{-}$mechanisms, arising from the vorticity contained in the upstream shear flow and the vorticity produced at the droplet surface, dominate for weakly and highly viscous droplets, respectively. Both mechanisms generate counter-rotating streamwise vortices of opposite signs, leading to observed lift reversals with increasing droplet viscosity. Detailed force decomposition based on vorticity moments indicates that in the $L\hbox{-}$mechanism-dominated regime for weakly to moderately viscous droplets, the streamwise vorticity-induced lift approximates the total lift. Conversely, in the $S\hbox{-}$mechanism-dominated regime, for moderately to highly viscous droplets, the streamwise vorticity-induced lift constitutes only a portion of the total lift, with the asymmetric advection of azimuthal vorticity at the droplet interface contributing additional positive lift to counterbalance the $S\hbox{-}$mechanism’s effects. These insights bridge the understanding between inviscid bubbles and rigid particles, enhancing our comprehension of the lift force experienced by droplets in different flow regimes.

We investigate the fluid–solid interaction of suspensions of Kolmogorov-size spherical particles moving in homogeneous isotropic turbulence at a microscale Reynolds number of $Re_\lambda \approx 140$. Two volume fractions are considered, $10^{-5}$ and $10^{-3}$, and the solid-to-fluid density ratio is set to $5$ and $100$. We present a comparison between interface-resolved (PR-DNS) and one-way-coupled point-particle (PP-DNS) direct numerical simulations. We find that the modulated energy spectrum shows the classical $-5/3$ Kolmogorov scaling in the inertial range of scales and a $-4$ scaling at smaller scales, with the latter resulting from a balance between the energy injected by the particles and the viscous dissipation, in an otherwise smooth flow. An analysis of the small-scale flow topology shows that the particles mainly favour events with axial strain and vortex compression. The dynamics of the particles and their collective motion studied for PR-DNS are used to assess the validity of the PP-DNS. We find that the PP-DNS predicts fairly well both the Lagrangian and Eulerian statistics of the particle motion for the low-density case, while some discrepancies are observed for the high-density case. Also, the PP-DNS is found to underpredict the level of clustering of the suspension compared with the PR-DNS, with a larger difference for the high-density case.

Many problems in elastocapillary fluid mechanics involve the study of elastic structures interacting with thin fluid films in various configurations. In this work, we study the canonical problem of the steady-state configuration of a finite-length pinned and flexible elastic plate lying on the free surface of a thin film of viscous fluid. The film lies on a moving horizontal substrate that drives the flow. The competing effects of elasticity, viscosity, surface tension and fluid pressure are included in a mathematical model consisting of a third-order Landau–Levich equation for the height of the fluid film and a fifth-order Landau–Levich-like beam equation for the height of the plate coupled together by appropriate matching conditions at the downstream end of the plate. The properties of the model are explored numerically and asymptotically in appropriate limits. In particular, we demonstrate the occurrence of boundary-layer effects near the ends of the plate, which are expected to be a generic phenomenon for singularly perturbed elastocapillary problems.

The acoustic field radiated by a system of contra-rotating propellers in wetted conditions (with no cavitation) is reconstructed by exploiting the Ffowcs Williams–Hawkings acoustic analogy and a database of instantaneous realizations of the flow. They were generated by high-fidelity computations using a large eddy simulation approach on a cylindrical grid of 4.6 billion points. Results are also compared against the cases of the front and rear propellers working alone. The analysis shows that the importance of the quadrupole component of sound, originating from wake turbulence and instability of the tip vortices, is reinforced, relative to the linear component radiated from the surface of the propeller blades. The sound from the contra-rotating propellers decays at a slower rate for increasing radial distances, compared with the cases of the isolated front and rear propellers, again due to the quadrupole component. The quadrupole sound is often neglected in the analysis of the acoustic signature of marine propellers, by considering the only linear component. In contrast, the results of this study point out that the quadrupole component becomes the leading one in the case of contra-rotating propulsion systems, due to the increased complexity of their wake. This is especially the result of the mutual inductance phenomena between the tip vortices shed by the front and rear propellers of the contra-rotating system.

Turbulence beneath a free surface leaves characteristic long-lived signatures on the surface, such as upwelling ‘boils’, near-circular ‘dimples’ and elongated ‘scars’, easily identifiable by eye, e.g. in riverine flows. In this paper, we analyse data from direct numerical simulations to explore the connection between these surface signatures and the underlying vortical structures. We investigate dimples, known to be imprints of surface-attached vortices, and scars, which have yet to be extensively studied, by analysing the conditional probabilities that a point beneath a signature is within a vortex core as well as the inclination angles of sub-signature vorticity. The analysis shows that the probability of vortex presence beneath a dimple decreases from the surface down through the viscous and blockage layers. This vertical variation in probability is approximately a Gaussian function of depth and depends on the dimple’s size and the bulk turbulence properties. Conversely, the probability of finding a vortex beneath a scar increases sharply from the surface to a peak at the edge of the viscous layer, regardless of scar size. The probability distributions of the angle between the vorticity vector and the vertical axis also show a clear pattern about vortex orientation: a strong preference for vertical alignment below dimples and an equally strong preference for horizontal alignment below scars. Our findings corroborate previous studies that tie dimples to surface-attached vertical vortices. Moreover, they suggest that scars can be defined as imprints of horizontal vortices that are located approximately a quarter of the Taylor microscale beneath the free surface.

We report laboratory experiments of long-crested irregular water surface waves propagating over a shoal, with attention to the region over the down-slope behind the shoal. We measure the surface elevation field, the horizontal velocity field in the water, and the resulting forces on a horizontal submerged cylinder placed over the down-slope of the shoal. In addition, we calculate the horizontal acceleration field. From this, we find that the presence of the shoal can modify the wave field such that the resulting forces on the submerged cylinder can be enhanced with thicker extreme tails and increased values of skewness and kurtosis depending on the location of the cylinder. The spatial dependence of the statistics of forces is different from the spatial dependence of the statistics of horizontal velocity, horizontal acceleration and surface elevation.

Dean’s approximation for curved pipe flow, valid under loose coiling and high Reynolds numbers, is extended to study three-dimensional travelling waves. Two distinct types of solutions bifurcate from the Dean’s classic two-vortex solution. The first type arises through a supercritical bifurcation from inviscid linear instability, and the corresponding self-consistent asymptotic structure aligns with the vortex–wave interaction theory. The second type emerges from a subcritical bifurcation by curvature-induced instabilities and satisfies the boundary region equations. A connection to the zero-curvature limit was not found. However, by continuing from known self-sustained exact coherent structures in the straight pipe flow problem, another family of three-dimensional travelling waves can be shown to exist across all Dean numbers. The self-sustained solutions also possess the two high-Reynolds-number limits. While the vortex–wave interaction type of solutions can be computed at large Dean numbers, their branch remains unconnected to the Dean vortex solution branch.

The bi-stable dynamics of a one-degree-of-freedom disk pendulum swept by a flow and allowed to rotate in the cross-flow direction is investigated experimentally. For increasing flow velocity, a subcritical bifurcation is observed from a Pendulum state, characterised by an increasing time-averaged pendulum angle with large amplitude fluctuations, to a rotating state with a non-zero mean rotation velocity at a critical free stream velocity $U_{P2W}$. The rotating state, referred to as Windmill state, presents a strong hysteresis: once initiated, it is sustained down to velocities $U_{W2P}\lt U_{P2W}$ before bifurcating towards the Pendulum state. A thorough experimental characterisation of the dynamical features of each state is reported, with a particular focus on the influence of the static yaw angle of the disk $\beta _0$ and the free stream velocity. In the Pendulum state, the system behaves differently depending on whether $\beta _0$ lies below or above the stall angle of the disk, with more regular dynamics below. We demonstrate that the bifurcation between the Pendulum state and the Windmill state is triggered by aerodynamic fluctuations, while the bifurcation between the Windmill state and the Pendulum state is deterministic. A stochastic model faithfully reproduces the dynamical features of both states, as well as the characteristics of the bifurcations.

The interaction between a turbulent flow and a porous boundary is analysed with focus on the sensitivity of the roughness function, $\Delta U^+$, to the upscaled coefficients characterizing the wall. The study is aimed at (i) demonstrating that imposing effective velocity boundary conditions at a virtual plane boundary, next to the physical one, can efficiently simplify the direct numerical simulations (DNS); and (ii) pursuing correlations to estimate $\Delta U^+$ a priori, once the upscaled coefficients are calculated. The homogenization approach employed incorporates near-interface advection via an Oseen-like linearization, and the macroscopic coefficients thus depend on both the microstructural details of the wall and a slip-velocity-based Reynolds number, $Re_{slip}$. A set of homogenization-simplified DNS is run to study the channel flow over transversely isotropic porous beds, testing values of the grains’ pitch within $0\lt \ell ^+\lt 40$. Reduction of the skin-friction drag is attainable exclusively over streamwise-aligned inclusions for $\ell ^+$ values up to $20{-}30$. The drag increase over spanwise-aligned inclusions (or streamwise-aligned ones at large $\ell ^+$) is accompanied by enhanced turbulence levels, including intensified sweep and ejection events. The root-mean-square of the transpiration velocity fluctuations at the virtual plane, $\tilde V_{rms}$, is the key control parameter of $\Delta U^+$; our analysis shows that, provided $\tilde V_{rms} \lesssim 0.25$, then $\tilde V_{rms}$ is strongly correlated to a single macroscopic quantity, $\Psi$, which comprises the Navier-slip and interface/intrinsic permeability coefficients. Fitting relationships for $\Delta U^+$ are proposed, and their applicability is confirmed against reference results for the turbulent flow over impermeable walls roughened with three-dimensional protrusions or different geometries of riblets.