Electrophoretic characterization of nano- and micro-metre scaled bubbles and drops is increasingly important in environmental and health sciences. Despite more than a hundred years of study, the interpretation of bubble electrophoresis data remains an unresolved fundamental problem that bridges fluid mechanics and interfacial science. This paper examines, from a theoretical perspective, how the electrophoretic mobility of small drops and bubbles responds to the interfacial kinetic-exchange rate and interfacial-charge mobility: factors that have been largely overlooked, but which provide new insights on the interpretation of $\zeta$-potentials, which are routinely used to assess surface charge density. A variety of outcomes are demonstrated, each reflecting subtle balances of hydrodynamic and electrical forces, modulated by interfacial thermodynamics and transport. Among the findings is that irreversibly bound charge with low interfacial mobility furnishes rigid-sphere behaviour; whereas interfacial charge with high mobility produces the characteristically high electrophoretic mobilities of non-conducting, uniformly charged fluid spheres. Outcomes are more complex when drops and bubbles have interfacial charge that seeks local equilibrium with the immediately adjacent electrolyte. For example, the present model shows that interfacial-charge mobility regularizes the singular behaviour predicted by theories for fluid spheres bearing high, perfectly uniform surface charge.

The instantaneous structure of a turbulent boundary layer (TBL) subjected to freestream turbulence (FST) is investigated at several streamwise locations downstream of an active turbulence-generating grid. Using planar particle image velocimetry, three grid sequences are tested at four streamwise locations with FST intensities up to 10.9 %. A low-turbulence reference case is included for comparison. A novel method is proposed to separate the instantaneous TBL and FST flows by identifying a distinct interface for each realisation using probability density functions of the vorticity field. Two alternative approaches are used to define the interfaces, based on either constant velocity contour lines or constant vorticity magnitude contour lines. The former is found to highlight the momentum events in the velocity fields, whereas the latter outlines the vortical features of the flow. Regardless of the interface choice, when faced with FST, the interface moves closer to the wall on average, and its location fluctuates more. When FST is present, the shear and mean spanwise vorticity magnitudes increase on the TBL side of the interface. Uniform momentum zones (UMZs) beneath the velocity interfaces are identified. In the presence of FST, UMZs located closer to the wall appear to be compressed, resulting in fewer identified UMZs. Moving downstream, the FST intensity decays while the TBL develops. As a result, many characteristics of the TBL recover to an undisturbed state, with the interface moving away from the wall, vorticity and turbulent fluctuations returning to their natural state undisturbed by FST and the number of detected UMZs increasing.

We demonstrate the first successful non-invasive stabilisation of nonlinear travelling waves in a straight cylindrical pipe using time-delayed feedback control working in various symmetric subspaces. By using an approximate linear stability analysis and by analysing the frequency-domain effect of the control using transfer functions, we find that solutions with well-separated unstable eigenfrequencies can have narrow windows of stabilising time delays. To mitigate this issue we employ a ‘multiple time-delayed feedback’ approach, where several control terms are included to attenuate a broad range of unstable eigenfrequencies. We implement a gradient descent method to dynamically adjust the gain functions in order to reduce the need for tuning a high-dimensional parameter space. This results in a novel control method where the properties of the target state are not needed in advance, and speculative guesses can result in robust stabilisation. This enables travelling waves to be stabilised from generic turbulent states and unknown travelling waves to be obtained in highly symmetric subspaces.

It is widely believed that statistical closure theories for dynamical systems provide statistics equivalent to those of the governing dynamical equations from which the former are derived. Here, we demonstrate counterexamples in the context of the widely used mean-field quasi-linear approximation applied to both deterministic and stochastic two-dimensional fluid dynamical systems. We compare statistics of numerical simulations of a quasi-linear model (QL) with statistics obtained by direct statistical simulation via a cumulant expansion closed at second order (CE2). We observe that although CE2 is an exact statistical closure for QL dynamics, its predictions can disagree with the statistics of the QL solution for identical parameter values. These disagreements are attributed to instabilities, which we term rank instabilities, of the second cumulant dynamics within CE2 that are unavailable in the QL equations.

In this work, the stability and transition to turbulence over blunt flat plates with different leading-edge radii are investigated computationally. The benchmark experimental work for comparative studies is conducted by Borovoy et al. (AIAA J., vol. 60, 2022, pp. 497–507). The freestream Mach number is 5, the unit Reynolds number is $6\times 10^7$ m$^{-1}$, and the maximum nose-tip radius 3 mm exceeds the experimental reversal value. High-resolution numerical simulation and stability analysis are performed. Three-dimensional broadband perturbation is added on the far field boundary to initiate the transition. The highlight of this work is that the complete physical process is considered, including the three-dimensional receptivity, linear and nonlinear instabilities, and transition. The experimental reversal phenomenon is reproduced favourably in the numerical simulation for the first time. Linear stability analysis shows that unstable first and second modes are absent in the blunt-plate flows owing to the presence of the entropy layer, although these modes are evident in the sharp-leading-edge case. Therefore, the transition on the blunt plate is due to non-modal instabilities. Numerical results for all the blunt-plate cases reveal the formation of streamwise streaky structures downstream of the nose (stage I) and then the presence of intermittent turbulent spots in the transitional region (stage II). In stage I, a preferential spanwise wavelength approximately 0.9 mm is selected for all the nose-tip radii, and low-frequency components are dominant. In stage II, high-frequency secondary instabilities appear to grow, which participate in the eventual breakdown. By contrast, leading-edge streaks are not remarkable in the sharp-leading-edge case, where transition is induced by oblique first and Mack second modes. The transition reversal beyond the critical nose-tip radius arises from an increasing magnitude of the streaky response in the early stage, while the transition mechanism stays similar qualitatively.

Liouville-type theorems for the steady incompressible Navier–Stokes system are investigated for solutions in a three-dimensional (3-D) slab with either no-slip boundary conditions or periodic boundary conditions. When the no-slip boundary conditions are prescribed, we prove that any bounded solution is trivial if it is axisymmetric or $ru^r$ is bounded, and that general 3-D solutions must be Poiseuille flows when the velocity is not big in $L^\infty$ space. When the periodic boundary conditions are imposed on the slab boundaries, we prove that the bounded solutions must be constant vectors if either the swirl or radial velocity is independent of the angular variable, or $ru^r$ decays to zero as $r$ tends to infinity. The proofs are based on the fundamental structure of the equations and energy estimates. The key technique is to establish a Saint-Venant type estimate that characterizes the growth of the Dirichlet integral of non-trivial solutions.

In the present research, the effect of streamwise finlets on the coherent structures of a turbulent boundary layer and their relation with pressure fluctuations and trailing-edge noise is investigated experimentally over a NACA0018 airfoil. A synthetic measurement is performed using time-resolved particle image velocimetry, wall-pressure transducers and a far-field microphone. The finlets induce strong momentum transport within the boundary layer, leading to the formation of a detached shear layer and backward flow separation. A strong velocity deficit is produced close to the wall. The instantaneous flow organisation reveals the formation of hairpin-like vortices on top of the finlets and spanwise rollers in the near-wall separation bubble. The newly generated vortices disrupt the turbulent coherent structures of the untreated case remarkably. An overall lift-up process of the unsteady turbulent structures is produced, bringing the most energetic turbulent structures away from the wall and reducing the near-wall shear stress. The spatial and temporal relation between instantaneous unsteady flow features and wall-pressure fluctuations is analysed quantitatively. A notable reduction of the correlation and coherence intensity in the mid- and high-frequency bands is achieved due to the modification of the turbulent structures. The former frequency ranges agree with that of the pressure fluctuations and far-field noise suppression, revealing the noise-reduction mechanisms.

The lattice Boltzmann method has become a popular tool for simulating complex flows, including incompressible turbulent flows; however, as an artificial compressibility method, it can generate spurious pressure oscillations whose impact on the statistics of incompressible turbulence has not been systematically examined. In this work, we propose a theoretical approach to analyse the origin of compressibility-induced oscillations (CIOs) and explore ways to suppress or remove them. We begin by decomposing the velocity field and pressure field each into the solenoidal component and the compressive component, and then study the evolution of these two components analytically and numerically. The analysis yields an evolution equation of the mean-square pressure fluctuation which reveals several coupling effects of the two components. The evolution equation suggests that increasing the bulk-to-shear viscosity ratio can suppress CIOs, which is confirmed by numerical simulations. Furthermore, based on the derived evolution equation and data from the simulation, a model is developed to predict the long-term behaviours of the mean-square pressure fluctuations. In the case of decaying turbulence in a periodic domain, we show that the Helmholtz–Hodge decomposition can be used to obtain the solenoidal components reflecting the true evolution of incompressible turbulent flow, from the mesoscopic artificial compressibility approach. The study provides general theoretical guidelines to understand, suppress and even remove CIOs in other related pseudo-compressibility methods.

Sea ice is a mushy layer, a porous material whose properties depend on the relative proportions of solid and liquid. The growth of sea ice is governed by heat transfer through the ice together with appropriate boundary conditions at the interfaces with the atmosphere and ocean. The salinity of sea ice has a major effect on its thermal properties so might naïvely be expected to have a major effect on its growth rate. However, previous studies observed a low sensitivity throughout the winter growth season. The goal of this study is to identify the controlling physical mechanisms that explain this observation. We develop a simplified quasi-static framework by applying a similarity transformation to the underlying heat equation and neglecting the explicit time dependence. We find three key processes controlling the sensitivity of growth rate to salinity. First, the trade-off between thermal conductivity and (latent) heat capacity leads to low sensitivity to salinity even at moderately high salinity and brine volume fraction. Second, the feedback on the temperature profile reduces the sensitivity relative to models that assume a linear profile, such as zero-layer Semtner models. Third, thicker ice has the opposite sensitivity of growth rate to salinity compared with thinner ice, sensitivities that counteract each other as the ice grows. Beyond its use in diagnosing these sensitivities, we show that the quasi-static approach offers a valuable sea-ice model of intermediate complexity between zero-layer Semtner models and full partial-differential-equation-based models such as Maykut–Untersteiner/Bitz–Lipscomb and mushy-layer models.

In this experimental and numerical study, we revisit the question of the onset of the elastic regime in viscoelastic pinch-off. This is relevant to all modern filament thinning techniques, which aim to measure the extensional properties of low-viscosity polymer solutions. Examples are the slow retraction method (SRM) for capillary breakup extensional rheometry (CaBER), or the dripping method, in which a drop detaches from a nozzle. As part of these techniques, a stable liquid bridge is brought slowly to its stability threshold, where capillary-driven thinning starts. This thinning slows down dramatically at a critical radius $h_1$, marking the onset of the elasto-capillary regime, characterised by a filament of nearly uniform radius. While a theoretical scaling exists for this transition in the case of the classical step-strain CaBER protocol, where polymer chains stretch without relaxing during the fast plate separation, we show that this theory is not necessarily valid for a slow protocol such as the SRM. In that case, polymer chains start stretching (beyond their equilibrium coiled configuration) only when the bridge thinning rate becomes comparable to the inverse of their relaxation time. We derive a universal scaling for $h_1$, valid for both low- and high-viscosity polymer solutions. This scaling is validated by CaBER experiments with a slow plate separation protocol using different polymer solutions, plate diameters and sample volumes, as well as by numerical simulations using the FENE-P model.

We investigate flame–acoustic interactions in a turbulent combustor during the state of intermittency before the onset of thermoacoustic instability using complex networks. Experiments are performed in a turbulent bluff-body stabilised dump combustor where the inlet airflow rate is varied quasi-statically and continuously. We construct a natural visibility graph from the local heat release rate fluctuations ($\dot {q}'$) at each location. Comparing the average degree during epochs of high- and low-amplitude acoustic pressure oscillations ($p'$) during the state of intermittency, we detect frequency modulation in $\dot {q}'$. Through this approach, we discover unique spatial patterns of cross-variable coupling between the frequency of $\dot {q}'$ and the amplitude of $p'$. The frequency of $\dot {q}'$ increases in regions of flame anchoring owing to high-frequency excitation of the flow and flame during epochs of high-amplitude $p'$ dynamics. However, the frequency of $\dot {q}'$ decreases in regions associated with flame-front distortions by large coherent vortices. In experiments with continuously varying airflow rates, the spatial pattern of frequency modulation varies with an increase in the average amplitude of $p'$ owing to an increase in the epochs of periodic $p'$ dynamics and the size of vortices forming in the flow. Dynamic shifts in the location of flame anchoring induce low-frequency fluctuations in $\dot {q}'$ during very-high-amplitude intermittent $p'$ dynamics. Our approach using conditional natural visibility graphs thus reveals the spatial pattern of amplitude-frequency coupling between the co-evolving flame and the acoustic field dynamics in turbulent reacting flows.

Ocean turbulence at meso- and submesocales affects the propagation of surface waves through refraction and scattering, inducing spatial modulations in significant wave height (SWH). We develop a theoretical framework that relates these modulations to the current that induces them. We exploit the asymptotic smallness of the ratio of typical current speed to wave group speed to derive a linear map – the U2H map – between surface current velocity and SWH anomaly. The U2H map is a convolution, non-local in space, expressible as a product in Fourier space by a factor independent of the magnitude of the wavenumber vector. Analytic expressions of the U2H map show how the SWH responds differently to the vortical and divergent parts of the current, and how the anisotropy of the wave spectrum is key to large current-induced SWH anomalies. We implement the U2H map numerically and test its predictions against WAVEWATCH III numerical simulations for both idealised and realistic current configurations.

Although both butterflies and dragonflies are four-winged insects, their wing geometries and kinematics differ significantly. Butterflies have a much narrower gap between their forewing and hindwing than dragonflies. While previous research has extensively investigated the forewing–hindwing interactions in dragonfly flight, this work focuses on their interactions in butterfly flight. The interactions are studied based on numerical simulations of the Navier–Stokes equations around a butterfly-inspired flapping wing with an adjustable slot, representing the narrow gap between the forewing and hindwing. The slot is controlled by a dihedral angle between the forewing and hindwing. The lift coefficients of wings with different slot sizes and locations are investigated in detail. The results show that the forewing–hindwing interactions can significantly enhance the lift if the slot is properly configured. When the slot is configured by elevating the forewing at a 10-degree dihedral angle relative to the hindwing during flapping flight, the wing generates over 20 % more lift than the model without a slot. The streamwise ram effect and tip-vortex capture are shown to be responsible for the lift enhancement by using a lift decomposition formula. The streamwise ram effect reduces the streamwise velocity beneath the forewing, decreasing the negative vortex lift associated with spanwise vorticity. The tip-vortex capture enhances the positive vortex lift associated with streamwise vorticity when the hindwing captures the tip vortex shedding from the forewing.

Small-scale shear layers arising from the turbulent motion of viscoelastic fluids are investigated through direct numerical simulations of statistically steady, homogeneous isotropic turbulence in a fluid described by the FENE-P model. These shear layers are identified via a triple decomposition of the velocity gradient tensor. The viscoelastic effects are examined through the Weissenberg number ($Wi$), representing the ratio of the longest polymer relaxation time scale to the Kolmogorov time scale. The mean flow around these shear layers is analysed within a local reference frame that characterises shear orientation. In both Newtonian and viscoelastic turbulence, shear layers appear in a straining flow, featuring stretching in the shear vorticity direction and compression in the layer normal direction. Polymer stresses are markedly influenced by the shear and strain, which enhance kinetic energy dissipation due to the polymers. The shear layers in viscoelastic turbulence exhibit a high aspect ratio, undergoing significant characteristic changes once $Wi$ exceeds approximately 2. As $Wi$ increases, the extensive strain weakens, diminishing vortex stretching. This change coincides with an imbalance between extension and compression in the straining flow. In the shear layer, the interaction between vorticity and polymer stress causes the destruction and production of enstrophy at low and high $Wi$ values, respectively. Enstrophy production at high $Wi$ is induced by normal polymer stress oriented along the shear flow, associated with the diminished extensive strain. The $Wi$-dependent behaviour of these shear layers aligns with the overall flow characteristics, underscoring their pivotal roles in vorticity dynamics and kinetic energy dissipation in viscoelastic turbulence.

Experiments on microfluidic core–annular flows demonstrated a transition from a continuous core jet to core-fluid drops and slugs separated by the annular fluid films/slugs due to absolute instability. The flows in the higher-generation airways could be modelled as core–annular flow with the laminar core airflow and annular airway surface liquid (ASL). Thus, if an absolute instability exists in the higher-generation airways, then it could lead to ASL film/slug-induced airway closure, necessitating the present study. Taking cues from previous studies, we derive an evolution equation using the lubrication approximation. The analysis, using the dispersion relation obtained from the evolution equation, predicts the existence of the critical capillary number $Ca_c$ such that, for $Ca < Ca_c$, the flow will be absolutely unstable for vanishing Reynolds number $Re$. The parameter $Ca_c$ exhibits the scaling as $Ca_c \sim (1-H)^2/\mu _r$, where $1-H$ is the dimensionless thickness of the ASL, and $\mu _r$ is the ratio of the air viscosity to the ASL viscosity. In agreement with the experimental observations, for a healthy lung, the analysis predicts absolute instability triggered airway closure only at the end of expiration during a breathing cycle. For a diseased lung, the ASL thickness and viscosity drastically increase the possibility of absolutely unstable flow and, thus, airway closure. Increasing inertial effect (i.e. $Re$) exacerbates airway closure by curtailing the convectively unstable region. Similarly, the ASL shear thinning widens the absolute instability parametric region. Thus, the present analysis demonstrates a pathway for airway closure in the higher-generation airways due to absolute instability.