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.

We consider steady surface waves in an infinitely deep two-dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120$^{\circ }$ corner at the crest. The stability of these solutions with respect to coperiodic and subharmonic perturbations is studied, using new matrix-free numerical methods. We provide evidence for a plethora of conjectures on the nature of the instabilities as the steepest wave is approached, especially with regards to the self-similar recurrence of the stability spectrum near the origin of the spectral plane.

The background potential energy (BPE) is the only reservoir that double diffusive instabilities can tap their energy from when developing from an unforced motionless state with no available potential energy (APE). Recently, Middleton and Taylor linked the extraction of BPE into APE to the sign of the diapycnal component of the buoyancy flux, but their criterion can predict only diffusive convection instability, not salt finger instability. Here, we show that the problem can be corrected if the sign of the APE dissipation rate is used instead, making it emerge as the most fundamental criterion for double diffusive instabilities. A theory for the APE dissipation rate for a two-component fluid relative to its single-component counterpart is developed as a function of three parameters: the diffusivity ratio, the density ratio, and a spiciness parameter. The theory correctly predicts the occurrence of both salt finger and diffusive convection instabilities in the laminar unforced regime, while more generally predicting that the APE dissipation rate for a two-component fluid can be enhanced, suppressed, or even have the opposite sign compared to that for a single-component fluid, with important implications for the study of ocean mixing. Because negative APE dissipation can also occur in stably stratified single-component and doubly stable two-component stratified fluids, we speculate that only the thermodynamic theory of exergy can explain its physics; however, this necessitates accepting that APE dissipation is a conversion between APE and the internal energy component of BPE, in contrast to prevailing assumptions.

Recently, subcritical transition to turbulence in the quasi-two-dimensional (quasi-2-D) shear flow with strong linear friction (Camobreco et al., J. Fluid Mech., vol. 963, 2023, R2) has been demonstrated by the 2-D mechanism at $Re = 71\,211$, and the nonlinear Tollmien–Schlichting (TS) waves related to the edge state were approached independently of initial optimal disturbances. For 2-D plane Poiseuille flow, transition to the fully developed turbulence requires that the Reynolds number is several times larger than the critical Reynolds number $Re_c$ (Markeviciute & Kerswell, J. Fluid Mech., vol. 917, 2021, A57). In this paper, we observed the subcritical transitional flow in 2-D plane Poiseuille flow driven by the nonlinear TS waves by both linear and nonlinear optimal disturbances ($Re < Re_c$) with different quantitative edge states. The nonlinear optimal disturbances could trigger the sustained subcritical transitional flow for $Re \geqslant 2400$. The initial energy for nonlinear optimal disturbance is more efficient than the linear optimal disturbance in reaching the subcritical transitional flow for $2400 \leqslant Re \leqslant 5000$. Moreover, the initial energy of linear optimal disturbance is larger than the energy of its edge state. The nonlinear TS waves along the edge state are formed by the nonlinear optimal disturbances to trigger transitional flow, which agrees well with the main conclusions of Camobreco et al. (J. Fluid Mech., vol. 963, 2023, R2), while the required $Re$ of 2-D plane Poiseuille flow is much smaller.

Resistive tearing instabilities are common in fluids that are highly electrically conductive and carry strong currents. We determine the effect of stable stratification on the tearing instability under the Boussinesq approximation. Our results generalise previous work that considered only specific parameter regimes, and we show that the length scale of the fastest-growing mode depends non-monotonically on the stratification strength. We confirm our analytical results by solving the linearised equations numerically, and we discuss whether the instability could operate in the solar tachocline.

Recent years have seen the emergence of new technologies that exploit nanoscale evaporation, ranging from nanoporous membranes for distillation to evaporative cooling in electronics. Despite the increasing depth of fundamental knowledge, there is still a lack of simulation tools capable of capturing the underlying non-equilibrium liquid–vapour phase changes that are critical to these and other such technologies. This work presents a molecular kinetic theory model capable of describing the entire flow field, i.e. the liquid and vapour phases and their interface, while striking a balance between accuracy and computational efficiency. In particular, unlike previous kinetic models based on the isothermal assumption, the proposed model can capture the temperature variations that occur during the evaporation process, yet does not require the computational resources of more complicated mean-field kinetic approaches. We assess the present kinetic model in three test cases: liquid–vapour equilibrium, evaporation into near-vacuum condition, and evaporation into vapour. The results agree well with benchmark solutions, while reducing the simulation time by almost two orders of magnitude on average in the cases studied. The results therefore suggest that this work is a stepping stone towards the development of an accurate and efficient computational approach to optimising the next generation of nanotechnologies based on nanoscale evaporation.

Whether colliding drops will merge with or bounce off each other is critical to numerous processes, and the physics involved is notoriously complex. In particular, experiments show that both sufficiently slow and fast head-on drop collisions lead to merging, but that there is often an intermediate regime in which bouncing is observed; these transitions in behaviour were recently discovered to be surprisingly sensitive to the radius of the drops and the ambient gas pressure. We show here that these transitions between bouncing and merging are governed by nanoscale phenomena; namely, gas-kinetic and disjoining pressure effects. To capture these crucial effects, a novel, open-source computational model is developed for the simulation of colliding drops. The model uses a hybrid approach, based on solving the Navier–Stokes equations in the drop with a lubrication approach for the unconventional physics of the gas film. Our simulations show remarkably good agreement with experiments of head-on collisions and also provide new experimentally verifiable predictions.

A high-resolution numerical simulation of an air–water turbulent upward bubbly flow in a pipe is performed to investigate the turbulence characteristics and bubble interaction with the wall. We consider three bubble equivalent diameters and three total bubble volume fractions. The bulk and bubble Reynolds numbers are $Re_{bulk}= u_{bulk} D/\nu _w = 5300$ and $Re_{bub}= (\langle u_{bub}\rangle - u_{bulk}) d_{eq}/\nu _w = 533\unicode{x2013}1000$, respectively, where $u_{bulk}$ is the water bulk velocity, $\langle u_{bub}\rangle$ is the overall bubble mean velocity, $D$ is the pipe diameter and $\nu _w$ is the water kinematic viscosity. The mean water velocity near the wall significantly increases due to bubble interaction with the wall, and the root-mean-square water velocity fluctuations are proportional to $\bar {\psi }(r)^{0.4}$, where $\bar {\psi } (r)$ is the mean bubble volume fraction. For the cases considered, the bubble-induced turbulence suppresses the shear-induced turbulence and becomes the dominant flow characteristic at all radial locations including near the wall. Rising bubbles near the wall mostly bounce against the wall rather than slide along the wall or hang around the wall without collision. Low-speed streaks observed in the near-wall region in the absence of bubbles nearly disappear due to the bouncing bubbles. These bouncing bubbles generate counter-rotating vortices in their wake, and increase the skin friction by sweeping high-speed water towards the wall. We also suggest an algebraic Reynolds-averaged Navier–Stokes model considering the interaction between shear-induced and bubble-induced turbulence. This model provides accurate predictions for a wide range of liquid bulk Reynolds numbers.

Validating the theoretical work on Rayleigh–Taylor instability (RTI) through experiments with an exceptionally clean and well-characterized initial condition has been a long-standing challenge. Experiments were conducted to study the three-dimensional RTI of an SF$_6$–air interface at moderate Atwood numbers. A novel soap film technique was developed to create a discontinuous gaseous interface with controllable initial conditions. Spectrum analysis revealed that the initial perturbation of the soap film interface is half the size of an entire single-mode perturbation. The correlation between the initial interface perturbation and Atwood numbers was determined. Due to the steep and highly curved feature of the initial soap film interface, the early-time evolution of RTI exhibits significant nonlinearity. In the quasi-steady regime, various potential flow models accurately predict the late-time bubble velocities by considering the channel width as the perturbation wavelength. Differently, the late-time spike velocities are described by these potential flow models using the wavelength of the entire single-mode perturbation. These findings indicate that the bubble evolution is influenced primarily by the spatial constraint imposed by walls, while the spike evolution is influenced mainly by the initial curvature of the spike tip. Consequently, a recent potential flow model was adopted to describe the time-varying amplitude growth induced by RTI. Furthermore, the self-similar growth factors for bubbles and spikes were determined from experiments and compared with existing studies, revealing that a large amplitude in the initial soap film interface promotes the spike development.

Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of counter-rotating monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid transport over large distances. Here, we present a semi-analytical method for finding fully nonlinear modon solutions in a multi-layer quasi-geostrophic model with arbitrarily many layers. Our approach is to reduce the problem to a multi-parameter linear eigenvalue problem which can be solved using numerical techniques from linear algebra. The method is shown to replicate previous results for one- and two-layer models and is applied to a three-layer model to find a solution describing a mid-depth propagating, topographic vortex.

Linear unsteady aerofoil theory, while successfully used for the prediction of unsteady aerofoil lift for many decades, has yet to be proven adequate for predicting the propulsive performance of oscillating aerofoils. In this paper we test the hypothesis that the central shortcoming of linear small-amplitude models, such as the Garrick function, is the failure to account for the flow acceleration caused by aerofoil thrust. A new analytical model is developed by coupling the Garrick function to a cycle-averaged actuator disc model, in a manner analogous to the blade-element momentum theory for wind turbines and propellers. This amounts to assuming the Garrick function to be locally valid and, in combination with a global control volume analysis, enables the prediction of flow acceleration at the aerofoil. The new model is demonstrated to substantially improve the agreement with large-eddy simulations of an aerofoil in combined heave and pitch motion.

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.

An interesting resurrection phenomenon (including the initial complete submersion, subsequent resurfacing and final rebounding) of a superhydrophobic sphere impacting onto a liquid bath was observed in experiments and direct numerical simulations by Galeano-Rios et al. (J. Fluid Mech., vol. 912, 2021, A17). We investigate the mechanisms of the liquid entry for a superhydrophobic cylinder in this paper. The superhydrophobic cylinder, commonly employed as supporting legs for insects and robots at the liquid surface, can exhibit liquid-entry mechanisms different from those observed with the sphere. The direct numerical simulation method is applied to the impact of a two-dimensional (2-D) superhydrophobic cylinder (modelled as a pseudo-solid) onto a liquid bath. We find that for the impacting cylinder the resurrection phenomenon can also exist, and the cylinder can either rebound (get detached from the liquid surface) or stay afloat after resurfacing. The cylinder impact behaviour is classified into four regimes, i.e. floating, bouncing, resurrecting (resurrecting-floating and resurrecting-bouncing) and sinking, dependent on the Weber number and the density ratio of the cylinder to the liquid. For the regimes of floating and bouncing, the force analysis indicates that the form drag dominates the motion of the cylinder in the very beginning of the impact, while subsequently the surface tension force also plays a role with the contact line pinning on the horizontal midline of the cylinder. For the critical states of the highlighted resurrecting regime, our numerical results show that the rising height for the completely submerged cylinder of different density ratios remains nearly unchanged. Accordingly, a relation between the maximum ascending velocity and the density ratio is derived to predict whether the completely submerged cylinder can resurface.