Aircraft with bio-inspired flapping wings that are operated in low-density atmospheric environments encounter unique challenges associated with the low density. The low density results in the requirement of high operating velocities of aircraft to generate sufficient lift resulting in significant compressibility effects. Here, we perform numerical simulations to investigate the compressibility effects on the lift generation of a bio-inspired wing during hovering flight using an immersed boundary method. The aim of this study is to develop a scaling law to understand how the lift is influenced by the Reynolds and Mach numbers, and the associated flow physics. Our simulations have identified a critical Mach number of approximately $0.6$ defined by the average wing-tip velocity. When the Mach number is lower than 0.6, compressibility does not have significant effects on the lift or flow fields, while when the Mach number is greater than $0.6$, the lift coefficient decreases linearly with increasing Mach number, due to the drastic change in the pressure on the wing surface caused by unsteady shock waves. Moreover, the decay rate is dependent on the Reynolds number and the angle of attack. Based on these observations, we propose a scaling law for the lift of a hovering flapping wing by considering compressible and viscous effects, with the scaled lift showing excellent collapse.

Hydrodynamic interactions between swimming or flying organisms can lead to complex flows on the scale of the group. These emergent fluid dynamics are often more complex than a linear superposition of individual organism flows, especially at intermediate Reynolds numbers. This paper presents an approach to estimate the flow induced by multiple swimmer wakes in proximity using a semianalytical model that conserves mass and momentum in the aggregation. The key equations are derived analytically, while the implementation and solution of these equations are carried out numerically. This model was informed by and compared with empirical measurements of induced vertical migrations of brine shrimp, Artemia salina. The response of individual swimmers to ambient background flow and light intensity was evaluated. In addition, the time-resolved three-dimensional spatial configuration of the swimmers was measured using a recently developed laser scanning system. Numerical results using the model found that the induced flow at the front of the aggregation was insensitive to the presence of downstream swimmers, with the induced flow tending towards asymptotic beyond a threshold aggregation length. Closer swimmer spacing led to higher induced flow speeds, in some cases leading to model predictions of induced flow exceeding swimmer speeds required to maintain a stable spatial configuration. This result was reconciled by comparing two different models for the near-wake of each swimmer. The results demonstrate that aggregation-scale flows result from a complex, yet predictable interplay between individual organism wake structure and aggregation configuration and size.

We analyse the motion of a flagellated bacterium in a two-fluid medium using slender body theory. The two-fluid model is useful for describing a body moving through a complex fluid with a microstructure whose length scale is comparable to the characteristic scale of the body. This is true for bacterial motion in biological fluids (entangled polymer solutions), where the entanglement results in a porous microstructure with typical pore diameters comparable to or larger than the flagellar bundle diameter, but smaller than the diameter of the bacterial head. Thus, the polymer and solvent satisfy different boundary conditions on the flagellar bundle and move with different velocities close to it. This gives rise to a screening length $L_B$ within which the fluids exchange momentum and the relative velocity between the two fluids decays. In this work, both the solvent and polymer of the two-fluid medium are modelled as Newtonian fluids with different viscosities $\mu _s$ and $\mu _p$ (viscosity ratio $\lambda = \mu _p/\mu _s$), thereby capturing the effects solely introduced by the microstructure of the complex fluid. From our calculations, we observe an increased drag anisotropy for a rigid, slender flagellar bundle moving through this two-fluid medium, resulting in an enhanced swimming velocity of the organism. The results are sensitive to the interaction between the bundle and the polymer, and we discuss two physical scenarios corresponding to two types of interaction. Our model provides an explanation for the experimentally observed enhancement of swimming velocity of bacteria in entangled polymer solutions and motivates further experimental investigations.

We present new constrained and free-swimming experiments and simulations in the inertial regime, with Reynolds number $\mbox{Re} = O(10^4)$, of a pair of two-dimensional and three-dimensional pitching hydrofoils interacting in a minimal school. The hydrofoils have an out-of-phase synchronisation, and they are varied through in-line, staggered and side-by-side formations within the two-dimensional interaction plane. It is discovered that there is a two-dimensionally stable equilibrium point for a side-by-side formation. This formation is super-stable, meaning that hydrodynamic forces will passively maintain this formation even under external perturbations, and the school as a whole has no net forces acting on it that cause it to drift to one side or the other. Previously discovered one-dimensionally stable equilibria driven by wake vortex interactions are shown to be, in fact, two-dimensionally unstable, at least for an out-of-phase synchronisation. Additionally, it is discovered that a trailing-edge vortex mechanism provides the restorative force to stabilise a side-by-side formation. The stable equilibrium is further verified by experiments and simulations for freely swimming foils where dynamic recoil motions are present. When constrained, swimmers in compact side-by-side formations experience collective efficiency and thrust increases up to 40 % and 100 %, respectively, whereas slightly staggered formations output an even higher efficiency improvement of 84 %, with an 87 % increase in thrust. Freely swimming foils in a stable side-by-side formation show efficiency and speed enhancements of up to 9 % and 15 %, respectively. These newfound schooling performance and stability characteristics suggest that fluid-mediated equilibria may play a role in the control strategies of schooling fish and fish-inspired robots.

Direct numerical simulation is performed for flow separation over a bump in a turbulent channel. Comparisons are made between a smooth bump and one where the lee side is covered with replicas of shark denticles – dermal scales that consist of a slender base (the neck) and a wide top (the crown). As flow over the bump is under an adverse pressure gradient (APG), a reverse pore flow is formed in the porous cavity region underneath the crowns of the denticle array. Remarkable thrust is generated by the reverse pore flow as denticle necks accelerate the fluid passing between them in the upstream direction. Several geometrical features of shark denticles, including some that had not previously been considered hydrodynamically functional, are identified to form the two-layer denticle structure that enables and sustains the reverse pore flow and thrust generation. The reverse pore flow is activated by the APG before massive flow detachment. The results indicate a proactive, on-demand drag reduction mechanism that leverages and transforms the APG into a favourable outcome.

The effects of the evolution of vortices on the aeroacoustics generated by a hovering wing are numerically investigated by using a hybrid method of an immersed boundary–finite difference method for the three-dimensional incompressible flows and a simplified model based on the Ffowcs Williams-Hawkings acoustic analogy. A low-aspect-ratio ($AR=1.5$) rectangular wing at low Reynolds ($Re=1000$) and Mach ($M=0.04$) numbers is investigated. Based on the simplified model, the far-field acoustics is shown to be dominated by the time derivative of the pressure on the wing surface. Results show that vortical structure evolution in the flow fields, which is described by the divergence of the convection term of the incompressible Navier–Stokes equations in a body-fixed reference frame, determines the time derivative of the surface pressure and effectively the far-field acoustics. It dominates over the centrifugal acceleration and Coriolis acceleration terms in determining the time derivative of the surface pressure. The position of the vortex is also found to affect the time derivative of the surface pressure. A scaling analysis reveals that the vortex acoustic source is scaled with the cube of the flapping frequency.

Spanwise vortex instability and the growth of secondary hairpin-like vortical structures in the wake of an oscillating foil are investigated numerically at Reynolds number 8000 in a range of chord-based Strouhal number ($0.32 \le St_c \le 0.56$). The phase-offset ($\phi$) between the heaving and pitching motion is $\phi = 90^\circ$. The wake at the lowest $St_c$ (0.32) is characterized by a single system of streamwise hairpin-like structures that evolve from the core vorticity outflux of the secondary leading edge vortex (LEV) over the foil boundary. The primary LEV features spanwise dislocations, but it does not reveal substantial changes advecting downstream. Increasing $St_c$ beyond 0.32 reveals that the transition in spanwise instability characterizes the deformation of primary LEV cores, which subsequently transforms to hairpin-like secondary structures. At higher $St_c$, stronger trailing edge vortices (TEVs) grow in close proximity to the primary LEVs, which contributes to an enhanced localized vortex compression and tilting near dislocations. This phenomenon amplifies the undulation amplitude of primary LEVs, eventually leading to vortex tearing. The larger circulation of TEVs with increasing $St_c$ provides an additional explanation for an accelerated vortex compression that coincides with a faster transition of spanwise LEV instability to secondary hairpin-like structures in the wake.

Although the interaction between microswimmers and walls during near-wall swimming has been extensively studied, the effect of microswimmer shapes and slip boundary conditions on the dynamic characteristics of near-wall microswimmers has received less attention. In this study, elliptical microswimmer models have been developed with various aspect ratios based on circular microswimmers. The lattice Boltzmann method has been used for the numerical simulation of the dynamic behaviour of microswimmers near walls. Under slip boundary conditions, the escape or capture of microswimmers by the walls is influenced by the swimming Reynolds number (Res), wall slip length (ls) and the aspect ratio (Cab) of a microswimmer. Changes in the Cab value of a microswimmer considerably affect its swimming state, especially for puller-type microswimmers. The tendency of pullers to be captured by the wall increases with increasing Cab. Moreover, changes in ls within the slip boundary condition of a puller can induce a transition in its movement state from a wall oscillation state to a stable sliding state and eventually to a wall lock-up state, a process influenced by the Cab value of the puller. Pusher-type microswimmers show a considerably increased tendency to escape from walls with increasing Cab and no wall lock-up state is observed, which is opposite to the case of pullers. Pushers and pullers show an increased tendency to be captured by the wall with increasing initial swimming angle of the microswimmer. The findings of this study enhance our understanding of the swimming patterns of natural microswimmers near walls and are of substantial importance for the design of artificial microswimmers and microfluidic devices.

Flow control of a low-aspect-ratio flat-plate heaving wing at an average angle of attack of $10^{\circ }$ by a steady-blowing jet is numerically studied by using a feedback immersed boundary–lattice Boltzmann method. Blowing jets at the leading edge, mid-chord and trailing edge are considered. The wing enjoys the highest lift production with the trailing-edge downstream blowing jet, which improves the average lift by 50.0 % at $Re = 1000$ and 22.9 % at $Re = 5000$ through the enhancement of the tip vortex circulation caused by the increase in the mass flux of the shear layer at the wing tips. This increase in mass flux decreases as $Re$ increases from 1000 to 5000 due to its self-limiting mechanism. A mid-chord vertical blowing jet induces a middle vortex which enhances the lift production but the enhancement is smaller than that of trailing-edge downstream blowing jet. Other jet arrangements do not significantly increase the lift coefficient, but the mid-chord upstream blowing jet experiences a significant reduction in the drag coefficient, leading to an increase of 50.6 % in the average lift-to-drag ratio. The effectiveness of the flow control is not significantly affected by the aspect ratio.

Flying insects exhibit remarkable capabilities in coordinating their olfactory sensory system and flapping wings during odour plume-tracking flights. While observations have indicated that their flapping wing motion can ‘sniff’ up the incoming plumes for better odour sampling range, how flapping motion impacts the odour concentration field around the antennae is unknown. Here, we reconstruct the body and wing kinematics of a forwards-flying butterfly based on high-speed images. Using an in-house computational fluid dynamics solver, we simulate the unsteady flow field and odourant transport process by solving the Navier–Stokes and odourant advection-diffusion equations. Our results show that, during flapping flight, the interaction between wing leading-edge vortices and antenna vortices strengthens the circulation of antenna vortices by over two-fold compared with cases without flapping motion, leading to a significant increase in odour intensity fluctuation along the antennae. Specifically, the interaction between the wings and antennae amplifies odour intensity fluctuations on the antennae by up to 8.4 fold. This enhancement is critical in preventing odour fatigue during odour-tracking flights. Further analysis reveals that this interaction is influenced by the inter-antennal angle. Adjusting this angle allows insects to balance between resistance to odour fatigue and the breadth of odour sampling. Narrower inter-antennal angles enhance fatigue resistance, while wider angles extend the sampling range but reduce resistance. Additionally, our findings suggest that while the flexibility of the wings and the thorax's pitching motion in butterflies do influence odour fluctuation, their impact is relatively secondary to that of the wing–antenna interaction.

Numerous flying and swimming creatures use the ground effect to boost their propulsive performance, with the ‘ground’ referring to either a solid boundary or a free surface. While our knowledge of how a solid boundary affects biolocomotion is relatively comprehensive, the ground effect of a free surface is not fully understood. To address this limitation, we conduct a numerical investigation on the propulsion performance of a flapping plate under a free surface, subject to a range of control parameters. When the Froude number ($Fr$) is very low (i.e. little surface deformation), the effects of a free surface are similar to those of a solid boundary, with enhanced thrust and input power but little change in efficiency. However, as $Fr$ increases (i.e. more surface deformation), our results reveal an optimal $Fr$ of approximately 0.6, where the free surface induces a more streamlined flow around the flapping plate, effectively reducing the added mass. This results in a significant decrease in input power and greatly enhanced efficiency.

During stroke reversals, insect wings interact with their own wake flow from the preceding half-stroke, resulting in an unsteady aerodynamic mechanism known as ‘wing–wake interaction’ or ‘wake capture’. To better elucidate this mechanism, we numerically solved the incompressible Navier–Stokes equations at Reynolds numbers $10^2$ and $10^3$. Simulations were conducted for wing planforms defined using the beta function distribution with varying aspect ratios ($AR=2\unicode{x2013}6$) and radial centroid locations ($\hat {r}_1=0.4\unicode{x2013}0.6$), whilst employing representative normal hovering kinematics. The wake development from the considered flapping wing planforms was investigated, and the wake capture contribution to aerodynamic force production was quantified by comparing the force generation between the fifth and first stroke cycles at multiple sections along the wingspan. Our results revealed that on the inboard wing region experiencing an attached leading-edge vortex (LEV) structure, wing–wake interaction is dominated by an unsteady downwash effect, resulting in a reduction in local force production. However, in regions closer to the wingtip experiencing detachment of the LEV, wing–wake interaction is dominated by an unsteady upwash effect, leading to an increase in local force production. Consequently, the global wake capture force production is controlled by the extent of LEV detachment, which primarily increases with the increase of wing aspect ratio. This suggests that for normal hovering flapping wings, the typical loss in translational force production due to wingtip stall is partially mitigated by wake capture effects.

Understanding the propulsion of a swimmer in a large group of individuals holds the key to unravelling the intriguing dynamics of active matter collective motion. Here, we develop a two-dimensional (2-D) self-assembled rotor, powered by bacterial flagella. At a water–air interface, the average direction of rotation of a rotor is fixed. When the chiral rotor is put into a 2-D bacterial suspension, we examine the average and fluctuation of the angular velocity of the rotor. Remarkably, the average angular velocity of a rotor is found to increase up to 3 times when the density of surrounding bacterial suspension increases and the increase is nonlinear. In a dense suspension of bacteria, the existence of a rotor disrupts vortices in the surrounding active turbulence, and the acceleration of the rotor is independent of the activity level of the surrounding free bacteria. The nonlinear acceleration thus results from hydrodynamic interaction with surrounding crowdedness that can be quantitatively explained by hydrodynamic simulation. The simultaneity between the acceleration of rotor and free bacteria in active turbulence suggests that crowding-induced acceleration may promote the onset of instability. The result will inspire new active-matter-based microfluidic devices with improved transport properties.

Single-flagellated bacteria are ubiquitous in nature. They exhibit various swimming modes using their flagella to explore complex surroundings such as soil and porous polymer networks. Some single-flagellated bacteria swim with two distinct modes, one with the flagellum extended away from its body and another with the flagellum wrapped around it. The wrapped mode has been observed when bacteria swim under tight confinements or in highly viscous polymeric melts. In this study we investigate the hydrodynamics of these two modes inside a circular pipe. We find that the wrapped mode is slower than the extended mode in bulk but more efficient under strong confinement due to a hydrodynamic increase of its flagellum translation–rotation coupling and an Archimedes’ screw-like configuration that helps to move the fluid along the pipe.

We present evidence revealing that an object with specific properties can exhibit multiple stable falling postures at low Reynolds numbers. By scrutinizing the force equilibrium relationship of a fixed object at various attack angles and Reynolds numbers, we introduce a methodology that can obtain the stable falling postures of the object. This method saves computational resources and more intuitively presents the results in the full parameter domain. Our findings are substantiated by free-fall tests conducted through both physical experiments and numerical simulations, which validate the existence of multiple stable solutions in accordance with the interpolation results obtained with fixed objects. Additionally, we quantify the abundance and distribution patterns of stable falling postures for a diverse range of representative shapes. This discovery highlights the existence of multiple stable solutions that are universally present across objects of different shapes. The implications of this research extend to the design, stability control and trajectory prediction of all free and controlled flights in both air and water.

Chiral fluids – such as fluids under rotation or a magnetic field as well as synthetic and biological active fluids – flow in a different way than ordinary ones. Due to symmetries broken at the microscopic level, chiral fluids may have asymmetric stress and viscosity tensors, for example giving rise to a hydrostatic torque or non-dissipative (odd) and parity-violating viscosities. In this article, we investigate the motion of rigid bodies in such an anisotropic fluid in the incompressible Stokes regime through the mobility matrix, which encodes the response of a solid body to forces and torques. We demonstrate how the form of the mobility matrix, which is usually determined by particle geometry, can be analogously controlled by the symmetries of the fluid. By computing the mobility matrix for simple shapes in a three-dimensional (3-D) anisotropic chiral fluid, we predict counterintuitive phenomena such as motion at an angle to the direction of applied forces and spinning under the force of gravity.

We present experiments on oscillating hydrofoils undergoing combined heaving and pitching motions, paying particular attention to connections between propulsive efficiency and coherent wake features extracted using modal analysis. Time-averaged forces and particle image velocimetry measurements of the flow field downstream of the foil are presented for a Reynolds number of $Re=11\times 10^3$ and Strouhal numbers in the range $St=0.16\unicode{x2013}0.35$. These conditions produce 2S and 2P wake patterns, as well as a near-momentumless wake structure. A triple decomposition using the optimized dynamic mode decomposition method is employed to identify dominant modal components (or coherent structures) in the wake. These structures can be connected to wake instabilities predicted using spatial stability analyses. Examining the modal components of the wake provides insightful explanations into the transition from drag to thrust production, and conditions that lead to peak propulsive efficiency. In particular, we find modes that correspond to the primary vortex development in the wakes. Other modal components capture elements of bluff body shedding at Strouhal numbers below the optimum for peak propulsive efficiency and characteristics of separation for Strouhal numbers higher than the optimum.

Microorganisms are ubiquitous in nature and technology. They inhabit diverse environments, ranging from small river tributaries and lakes, to oceans, as well as wastewater treatment plants and food manufacturing. In many of these environments, microorganisms coexist with settling particles. Here, we investigate the effects of microbial activity (swimming E. coli) on the settling dynamics of passive colloidal particles using particle tracking methods. Our results reveal the existence of two distinct regimes in the correlation length scale ($L_u$) and the effective diffusivity of the colloidal particles ($D_{eff}$), with increasing bacterial concentration ($\phi _b$). At low $\phi _b$, the parameters $L_u$ and $D_{eff}$ increase monotonically with increasing $\phi _b$. Beyond critical $\phi _b$, a second regime is found where both $D_{eff}$ and $L_u$ are independent of $\phi _b$. We demonstrate that the transition between these regimes is characterized by the emergence of bioconvection. We use experimentally measured particle-scale quantities $L_u$ and $D_{eff}$ to predict the critical bacterial concentration for the diffusion–bioconvection transition.

Insects flip their wings around each stroke reversal and may enhance lift in the early stage of a half-stroke. The possible lift-enhancing mechanism of this rapid wing rotation and its strong connection with wake vortices are still underexplored, especially when unsteady leading-edge vortex (LEV) behaviours occur. Here, we numerically studied the lift generation and underlying vorticity dynamics during the rapid rotation of a low aspect ratio flapping wing at a Reynolds number (${\textit {Re}}$) of 1500. Our findings prove that when the outboard LEV breaks down, an advanced rotation can still enhance the lift in the early stage of a half-stroke, which originates from an interaction with the breakdown vortex in the outboard region. This interaction, named the breakdown-vortex jet mechanism, results in a jet and thus a higher pressure on the upwind surface, including a stronger wingtip suction force on the leeward surface. Although the stable LEV within the mid-span retains its growth and location during an advanced rotation, it can be detrimental to lift enhancement as it moves underneath the wing. Therefore, for a flapping wing at ${\textit {Re}}\sim 10^3$, the interactions with stable and breakdown leading-edge vortices lead to the single-vortex suction and breakdown-vortex jet mechanisms, respectively. In other words, the contribution of wing–wake interaction depends on the spanwise location. The current work also implies the importance of wing kinematics to this wing–wake interaction in flapping wings, and provides an alternative perspective for understanding this complex flow phenomenon at ${\textit {Re}}\sim 10^3$.

Birds employ rapid pitch-up motions close to the ground for different purposes: perching birds use this motion to decelerate and come to a complete stop while hunting birds, such as bald eagles, employ it to catch prey and swiftly fly away. Motivated by these observations, our study investigates how natural flyers accomplish diverse flying objectives by rapidly pitching their wings while decelerating near ground. We conducted experimental and analytical investigations focusing on rapidly pitching plates during deceleration in close proximity to the ground to explore the impact of ground proximity on the unsteady dynamics. Initially, we executed synchronous pitch-up motion, where both pitching and deceleration have the same motion duration, at different ground heights. Experimental results demonstrate that as the pitching wing approaches the ground, the instantaneous lift increases by approximately $38\,\%$ compared with a far-from-ground case, while the initial peak drag force remains relatively unchanged. Our analytical model conforms to this trend, predicting an increase in lift force as the wing approaches the ground, indicating enhanced added mass and circulatory lift force due to the ground effect. Next, we examined asynchronous pitch-up motion cases, where rapid pitching motions were initiated at different stages of deceleration. The results reveal that initiating the wing pitch early in the deceleration leads to the formation of larger counter-rotating vortices at the early stage of the manoeuvre. These vortices generate stronger dipole jets that orient backward in the later stages of the manoeuvre after impinging with the ground surface, which hunting birds utilize to accelerate after catching prey. Conversely, when the wing pitch is delayed, smaller vortices form, but their growth is postponed until late in the manoeuvre. This delayed vortex growth produces lift and drag force at the end phase of the manoeuvre that facilitates a smooth landing or perching. Thus, through strategic tuning of a rapid pitch-up motion with deceleration, natural flyers, such as birds, achieve diverse flying objectives.