This paper investigates the effects of a light-actuated photosurfactant on the canonical problem of the linear stability of a viscous thread surrounded by a dynamically passive fluid. A model consisting of the Navier–Stokes equations and a set of molar concentration equations is presented that capture light-induced switching between two stable surfactant isomer states, trans and cis. These two states display significantly different interfacial properties, allowing for some external control of the stability behaviour of the thread via incident light. Normal modes are used to generate a generalized eigenvalue problem for the growth rate which is solved with a hybrid analytical and numerical method. The results are validated with appropriate analytical solutions of increasing complexity, beginning with a solution to a clean interface, then analytical solutions for one insoluble surfactant, one soluble surfactant and a special case of two photosurfactants with a spatially uniform undisturbed state. Presenting each of these cases allows for a holistic discussion of the effect of surfactants in general on the stability of a liquid thread. Finally, the numerical solutions in the presence of two photosurfactants that display radially non-uniform undisturbed states are presented, and details of the impact of the illumination on the linear stability of the thread are discussed.

In order to improve the predictive abilities of weather and climate models, it is essential to understand the behaviour of wind stress at the ocean surface. Wind stress is contingent on small-scale interfacial dynamics typically not directly resolved in numerical models. Although skin friction contributes considerably to the total stress up to moderate wind speeds, it is notoriously challenging to measure and predict using physics-based approaches. This work proposes a supervised machine learning (ML) model that estimates the spatial distribution of the skin-friction drag over wind waves using solely wave elevation and wave age, which are relatively easy to acquire. The input–output pairs are high-resolution wave profiles and their corresponding surface viscous stresses collected from laboratory experiments. The ML model is built upon a convolutional neural network architecture that incorporates the Mish nonlinearity as its activation function. Results show that the model can accurately predict the overall distribution of viscous stresses; it captures the peak of viscous stress at/near the crest and its dramatic drop to almost null just past the crest in cases of intermittent airflow separation. The predicted area-aggregate skin friction is also in excellent agreement with the corresponding measurements. The proposed method offers a practical pathway for estimating both local and area-aggregate skin friction and can be easily integrated into existing numerical models for the study of air–sea interactions.

We perform a linear stability analysis of a finite-amplitude plane inertial wave (of frequency $\omega$ in the range $0\le \omega \le f$, where $f$ is the Coriolis frequency) by considering the inviscid evolution of three-dimensional (3-D), small-amplitude, short-wavelength perturbations. Characterizing the base flow plane inertial wave by its non-dimensional amplitude $A$ and the angle $\varPhi$ that its wavevector makes with the horizontal axis, the local stability equations are solved over the entire range of perturbation wavevector orientations. At sufficiently small $A$, 3-D parametric subharmonic instability (PSI) is the only instability mechanism, with the most unstable perturbation wavevector making an angle close to $60^{\circ }$ with the inertial wave plane. In addition, the most unstable perturbation is shear-aligned with the inertial wave in the inertial wave plane. Further, at large $\varPhi$, i.e. $\omega \approx f,$ there exists a wide range of perturbation wavevectors whose growth rate is comparable to the maximum growth rate. As $A$ is increased, theoretical PSI estimates become less relevant in describing the instability characteristics, and the dominant instability transitions to a two-dimensional (2-D) shear-aligned instability, which is shown to be driven by third-order resonance. The transition from 3-D PSI to a 2-D shear-aligned instability is shown to be reasonably captured by two different criteria, one based on the nonlinear time scale in the inertial wave and the other being a Rossby-number-based one.

The evaporation process in porous media typically experiences three main periods, among which the first period, named the constant rate period (CRP), performs most efficiently in removing liquid. We aim to prolong the CRP to very low degrees of saturation (S) and increase its evaporation rate by playing with heterogeneity in wettability and pore size. First, we show that a porous medium with a smaller contact angle at the surface and increasing contact angle towards the inside generally dries out faster compared with that with uniform contact angle. Second, a constant contact angle porous medium with smaller/larger pores in the surface/inside part dries out faster than a medium with uniform pore size. The underlying mechanism is the occurrence of a capillary pressure jump at the border between the two layers accompanied by enhanced capillary pumping, increasing/maintaining the interfacial area in the surface pores. Harnessing the potential of this mechanism, we propose an optimized strategy by combining two heterogeneity effects: increasing contact angle and pore size towards the inside. This strategy is found to be robust both for multilayer and larger systems. In this case, a small drying front first penetrates fast towards the inside and then expands, followed by a horizontal drying front moving back layer by layer to the surface. Quantitatively, compared with evaporation from a homogeneously porous medium with uniform contact angle where CRP stops at $S=0.64$, our optimized design can extend the CRP down to $S=0.12$, and decrease five-fold the drying time needed to reach $S=0.05$.

The synchronisation between rotating turbulent flows in periodic boxes is investigated numerically. The flows are coupled via a master–slave coupling, taking the Fourier modes with wavenumber below a given value $k_m$ as the master modes. It is found that synchronisation happens when $k_m$ exceeds a threshold value $k_c$, and $k_c$ depends strongly on the forcing scheme. In rotating Kolmogorov flows, $k_c\eta$ does not change with rotation in the range of rotation rates considered, $\eta$ being the Kolmogorov length scale. Even though the energy spectrum has a steeper slope, the value of $k_c\eta$ is the same as that found in isotropic turbulence. In flows driven by a forcing term maintaining constant energy injection rate, synchronisation becomes easier when rotation is stronger. Here, $k_c\eta$ decreases with rotation, and it is reduced significantly for strong rotations when the slope of the energy spectrum approaches $-3$. It is shown that the conditional Lyapunov exponent for a given $k_m$ is reduced by rotation in the flows driven by the second type of forcing, but it increases mildly with rotation for the Kolmogorov flows. The local conditional Lyapunov exponents fluctuate more strongly as rotation is increased, although synchronisation occurs as long as the average conditional Lyapunov exponents are negative. We also look for the relationship between $k_c$ and the energy spectra of the Lyapunov vectors. We find that the spectra always seem to peak at approximately $k_c$, and synchronisation fails when the energy spectra of the conditional Lyapunov vectors have a local maximum in the slaved modes.

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ($U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$, where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ($Fr=0.5, 2$) and Prandtl ($Pr=1, 7$) numbers forced so that $Re_{b}=50$, with resolutions up to $30\,240 \times 30\,240 \times 3780$. We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$.

The axially symmetric deformation of a drop in a viscous fluid, under the influence of an externally imposed flow having simultaneous rotating and compressional or extensional components, is addressed. In the previous studies, two families of stationary drop shapes were constructed by simulating the dynamics of drop deformation: stable singly connected shapes with respect to axisymmetric disturbances, and unstable toroidal shapes. These two branches coexist at the same flow conditions, but were not connected. In this study, we obtain a new family of branches of unstable highly deformed stationary drops connecting with the stable flattened shapes and the toroidal ones. We use a method based on classical control theory. The controller is designed for a two-state dynamic model of the system and is employed on a high-order nonlinear dynamic model of the drop deformation. Through this feedback-control-centred approach, an extended collection of unstable stationary solutions is constructed, which spans the range from the loss of stability to the dimpled shapes almost collapsed at the centre. In the latter region, which was never obtained in previous studies, a multiplicity of solutions is identified.

The development of simple, low-order and accurate unsteady aerodynamic models represents a crucial challenge for the design optimisation and control of fluid dynamical systems. In this work, wind tunnel experiments of a pitching NACA 0018 aerofoil conducted at a Reynolds number $Re = 2.8 \times 10^5$ and at different free-stream turbulence intensities are used to identify data-driven nonlinear state-space models relating the time-varying angle of attack of the aerofoil to the lift coefficient. The proposed state-space neural network (SS-NN) modelling technique explores an innovative methodology, which brings the flexibility of artificial neural networks into a classical state-space representation and offers new insights into the construction of reduced-order unsteady aerodynamic models. The work demonstrates that this technique provides accurate predictions of the nonlinear unsteady aerodynamic loads of a pitching aerofoil for a wide variety of angle-of-attack ranges and frequencies of oscillation. Results are compared with a modified version of the Goman–Khrabrov dynamic stall model. It is shown that the SS-NN methodology outperforms the classical semi-empirical dynamic stall models in terms of accuracy, while retaining a fast evaluation time. Additionally, the proposed models are robust to noisy measurements and do not require any pre-processing of the data, thus involving only a limited user interaction. Overall, these features make the SS-NN technique an excellent candidate for the construction of accurate data-driven models from experimental fluid dynamics data, and pave the way for their adoption in applications entailing design optimisation and real-time control of systems involving lift.

The theory of transient growth describes how linear mechanisms can cause temporary amplification of disturbances even when the linearized system is asymptotically stable as defined by its eigenvalues. This growth is traditionally quantified by finding the initial disturbance that generates the maximum response at the peak time of its evolution. However, this can vastly overstate the growth of a real disturbance. In this paper, we introduce a statistical perspective on transient growth that models statistics of the energy amplification of the disturbances. We derive a formula for the mean energy amplification and spatial correlation of the growing disturbance in terms of the spatial correlation of the initial disturbance. The eigendecomposition of the correlation provides the most prevalent structures, which are the statistical analogue of the standard left singular vectors of the evolution operator. We also derive accurate confidence bounds on the growth by approximating the probability density function of the energy. Applying our analysis to Poiseuille flow yields a number of observations. First, the mean energy amplification is often drastically smaller than the maximum. In these cases, it is exceedingly unlikely to achieve near-optimal growth due to the exponential behaviour observed in the probability density function. Second, the characteristic length scale of the initial disturbances has a significant impact on the expected growth, with large-scale initial disturbances growing orders of magnitude more than small-scale ones. Finally, while the optimal growth scales quadratically with Reynolds number, the mean energy amplification scales only linearly for certain reasonable choices of the initial correlation.

We study numerically the microjetting mode obtained when a fluid is injected through a tube submerged in a uniaxial extensional flow. The steady solution to the full nonlinear Navier–Stokes equations is calculated. We obtain the linear global modes determining the linear stability of the steady solution. For sufficiently large outer viscosity, the flow remains stable for infinitely small values of the injected flow rate. This implies that jets with vanishing diameters can be produced regardless of the jet viscosity and outer flow strength. For a sufficiently small inner-to-outer viscosity ratio, the microjetting instability is associated only with the flow near the entrance of the jet. The tapering meniscus stretches and adopts a slender quasiconical shape. Consequently, the cone tip is exposed to an intense outer flow, which stabilizes the flow in the cone–jet transition region. This work presents the first evidence that fluid jets with arbitrarily small diameters can be stably produced via tip streaming. The results are related to those of a droplet in a uniaxial extensional flow with its equator pinned to an infinitely thin ring. The pinning of the equator drastically affects the droplet stability and breakup.

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this third part, we focus on the development of analytical solutions and scaling laws for a benchmark catchment model that models the river flow (runoff) generated during a single rainfall. We demonstrate that for catchments characterised by a shallow impenetrable bedrock, the shallow-water approximation allows a reduction of the governing formulation to a coupled system of one-dimensional time-dependent equations for the surface and subsurface flows. Asymptotic analysis is used to derive semi-analytical solutions for the model. We provide simple asymptotic scaling laws describing the peak flow formation, and demonstrate its accuracy through a comparison with the two-dimensional model developed in Part 2. These scaling laws can be used as an analytical benchmark for assessing the validity of other physical, conceptual or statistical models of catchments.

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this first part, we identify and analyse the key physical parameters that appear in the governing formulations used within hydrodynamic rainfall–runoff models. Such parameters include those related to catchment dimensions, topography, soil and rock properties, rainfall intensities, Manning's coefficients and river channel dimensions. Despite the abundance of research that has produced data sets describing properties of specific river basins, there have been few studies that have investigated the ensemble of typical scaling of key physical properties; these estimates are needed to perform a proper dimensional analysis of rainfall–runoff models. Therefore, in this work, we perform an extensive analysis of the parameters; our results form a benchmark and provide guidance to practitioners on the typical parameter sizes and interdependencies. Crucially, the analysis is presented in a fashion that can be reproduced and extended by other researchers and, wherever possible, uses publicly available data sets for catchments in the UK.

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this second part, we construct a benchmark catchment scenario and investigate the effects of parameters within their typical ranges. Previous research on coupled surface–subsurface models have focused on numerical simulations of site-specific catchments. Here, our focus is broad, emphasising the study of general solutions to the mathematical models, and their dependencies on dimensionless parameters. This study provides a foundation based on the examination of a geometrically simple three-dimensional benchmark scenario. We develop a non-dimensional coupled surface–subsurface model and extract the key dimensionless parameters. Asymptotic methods demonstrate under what conditions the model can be reduced to a two-dimensional form, where the principal groundwater and overland flows occur in the hillslope direction. Numerical solutions provide guidance on the validity of such reductions, and demonstrate the parametric dependencies corresponding to a strong rainfall event.

We study theoretically and experimentally pressure-driven flow between a flat wall and a parallel corrugated wall, a design used widely in microfluidics for low-Reynolds-number mixing and particle separation. In contrast to previous work, which focuses on recirculating helicoidal flows along the microfluidic channel that result from its confining lateral walls, we study the three-dimensional pressure and flow fields and trajectories of tracer particles at the scale of each corrugation. Employing a perturbation approach for small surface roughness, we find that anisotropic pressure gradients generated by the surface corrugations, which are tilted with respect to the applied pressure gradient, drive transverse flows. We measure experimentally the flow fields using particle image velocimetry and quantify the effect of the ratio of the surface wavelength to the channel height on the transverse flows. Further, we track tracer particles moving near the surface structures and observe three-dimensional skewed helical trajectories. Projecting the helical motion to two dimensions reveals oscillatory near-surface motion with an overall drift along the surface corrugations, reminiscent of earlier experimental observations and independent of the secondary helical flows that are induced by confining lateral walls. Finally, we quantify the hydrodynamically induced drift transverse to the mean flow direction as a function of distance to the surface and the wavelength of the surface corrugations.

We describe theoretically ‘electrolubrication’ in liquid mixtures: the phenomenon whereby an electric field applied transverse to the confining surfaces leads to concentration gradients that alter the flow profile significantly. When the more polar liquid is the less viscous one, the stress in the liquid falls on two electric-field-induced thin lubrication layers. The thickness of the lubrication layer depends on the Debye length and the mixture correlation length. For the simple case of two parallel and infinite plates, we calculate explicitly the liquid velocity profile and integrated flux. The maximum liquid velocity and flux can be increased by a factor $\alpha$, of order 10–100 or even more. For a binary mixture of water and a cosolvent, with viscosities $\eta _w$ and $\eta _{cs}$, respectively, $\alpha$ increases monotonically with inter-plate potential $V$ and average ion content, and is large if the ratio $\eta _{cs}/\eta _w$ is large.

The turbulence behaviour of current-dominated pulsating flows has been investigated. Direct numerical simulations have been carried out for Stokes lengths over a range of $l_s^+=5\unicode{x2013}26$, and amplitudes spanning 90 % of the current-dominated regime, about a mean flow of $\overline {Re}=6275$. The results show that the turbulence response in intermediate and low-frequency pulsations is governed by a multistage turbulent–turbulent transition process, which bears a strong similarity to the multistage response of non-periodic acceleration. During the early acceleration period, the flow enters a pretransition stage, in which a new laminar perturbation boundary layer forms at the wall, and the streamwise velocity streaks are stretched. If the low-speed streaks destabilise prior to the deceleration period, then the flow enters a transition stage in which the perturbation boundary layer undergoes a bypass-like transition process. A unique feature of pulsating flows is the ongoing mechanism of turbulence decay, which initiates during the deceleration period and constitutes the main transient turbulence mechanism for much of the cycle. For high-frequency pulsations, the perturbation boundary layer fails to reach the pretransition stage prior to the deceleration period. Instead, the flow alternates between two inertial stages which are characterised by two layers of amplified viscous force; one growing at the wall, and one detached and moving towards the core.

Recent measurements of inertial particles in isotropic turbulence (Hammond & Meng, J. Fluid Mech., vol. 921, 2021, A16) revealed surprising extreme clustering of particles at near-contact separations $(r)$, whereby the radial distribution function, $g(r)$, grows from $O(10)$ to $O(10^3)$ with a $(r/a)^{-6}$ scaling (where $a$ is the particle radius), and a surprising upturn of the mean inward particle-pair relative velocity (MIRV). Hydrodynamic interactions (HIs) were proposed to explain the extreme clustering, but despite predicting the correct scaling $(r/a)^{-6}$, the HI theory underpredicted $g(r)$ by at least two orders of magnitude (Bragg et al., J. Fluid Mech., vol. 933, 2022, A31). To further understand the extreme clustering phenomenon and the relevance of HI, we characterize $g(r)$ and particle-pair kinematics for Stokes numbers $0.07 \leq St \leq 3.68$ in a homogeneous isotropic turbulence chamber using three-dimensional (3-D) particle tracking resolved to near–contact. A drift–diffusion equation governing $g(r)$ is presented to investigate the kinematic mechanisms of particle pairs. Measurements in all 24 conditions show that when $r/a\lessapprox 20$, extreme clustering consistently occurs, scaling as $g(r) \sim (r/a)^{-k}$ with $4.5 \leq k \leq 7.6$, which increases with $St$. Here $g(r)$ varies with $St$, particle size, density and polydispersity in ways that HI cannot explain. The extreme clustering region features an inward drift contributed by particle-pair turbophoresis and an inward radial relative acceleration. The latter indicates an interparticle attractive force at these separations that HI also cannot explain. The MIRV turns upward when approaching the extreme clustering region, opposite to direct numerical simulation predictions. These observations further support our previous assessment that extreme clustering arises from particle–particle interactions, but HI is not the main mechanism.

The current study investigates the global linear stability of a two-layer channel flow with a train of solid particles flowing near the liquid–liquid interface. Three different mechanisms of instability (shear, interfacial and migration modes) are identified, and their interactions are examined. The interfacial instability, associated with the viscosity jump at the liquid–liquid interface, is found to be coupled to the migration of the particle. The stability of the flow configuration is evaluated for various governing parameters, including fluid viscosities and flow rate ratios, particle position, inter-particle distance, and Reynolds and capillary numbers. Our numerical results are compared with the particle-free flow configuration, indicating that the presence of the particle in the more viscous fluid promotes the destabilization of the interface. Remarkably, under certain flow parameters, the presence of the particle stabilizes the interface when flowing in the less viscous liquid. The impact of particles is more significant as the capillary number increases or the Reynolds number decreases.

Subgrid-scale (SGS) modelling is formulated using a local transport of spectral kinetic energy estimated by a wavelet multiresolution analysis. Using a spectrally and spatially local decomposition by wavelet, the unresolved inter-scale energy transfer and modelled SGS dissipation are evaluated to enforce explicitly and optimally their balance a priori over a range of large-eddy simulation (LES) filter widths. The formulation determines SGS model constants that optimally describe the spectral energy balance between the resolved and unresolved scales at a given cutoff scale. The formulation is tested for incompressible homogeneous isotropic turbulence (HIT). One-parameter Smagorinsky- and Vreman-type eddy-viscosity closures are optimised for their model constants. The algorithm discovers the theoretical prediction of Lilly (The representation of small-scale turbulence in numerical simulation experiments. In Proceedings of the IBM Scientific Computing Symposium on Environmental Sciences, pp. 195–210) at a filter cutoff scale in the inertial subrange, whereas the discovered constants deviate from the theoretical value at other cutoff scales so that the spectral optimum is achieved. The dynamic Smagorinsky model used a posteriori shows a suboptimal behaviour at filter scales larger than those in the inertial subrange. A two-parameter Clark-type closure model is optimised. The optimised constants provide evidence that the nonlinear gradient model of Clark et al. (J. Fluid Mech., vol. 91, issue 1, 1979, pp. 1–16) is prone to numerical instability due to its model form, and combining the pure gradient model with a dissipative model such as the classic Smagorinsky model enhances numerical stability but the standard mixed model is not optimal in terms of spectral energy transfer. A posteriori analysis shows that the optimised SGS models produce accurate LES results.

The relationships between characteristic large-scale wake structures appearing behind a free-stream-aligned circular cylinder are investigated and discussed from the velocity field obtained by wind tunnel tests. The tests were conducted under a supportless condition using a magnetic suspension and balance system and stereo PIV measurements at a Reynolds number of $3.46\times 10^4$. The velocity fields were analysed with a modal decomposition combining azimuthal Fourier decomposition and proper orthogonal decomposition. The wake behind the free-stream-aligned circular cylinder with three different fineness ratios of 1.0, 1.5 and 2.0 was investigated, and the wake structures in a non-reattaching flow formed by the cylinder at a fineness ratio of 1.0 are mainly discussed in the present study. Four characteristic large-scale wake structures of the recirculation bubble pumping, azimuthal shear mode, large-scale vortex shedding and streaks are identified and mainly focused on in the present study. The state of the vortex shedding is classified into three: anticlockwise/clockwise circular and flapping patterns. Each state has a relationship with the azimuthal shear mode and it tends to appear when the state is circular. Furthermore, from the analysis of the relationship between modes, the recirculation bubble pumping is found to be related to the vortex shedding position in the radial direction and the strength of the streaks. Particularly, analysis of causality shows that the recirculation bubble pumping is affected by them in the low-frequency range.