Electro-osmotic flow (EOF) in nanochannels exhibits a puzzling non-monotonic dependence on salt concentration, which contrasts with observations in microchannels and remains not fully understood. In this work, we address this phenomenon through a theoretical investigation of EOF in $\mathrm{pH}$-regulated channels. New analytical approximations for electrostatic potential, EOF profile and electro-osmotic mobility beyond the Debye–Hückel limit are derived through asymptotic analysis. Our findings reveal that the surface electrostatic potential is independent of the channel size only when the half-channel size exceeds the Gouy–Chapman length. In contrast, surface ionization and net charge distribution play more crucial roles in EOF at the nanoscale, as they govern both the magnitude and the spatial distribution of the Coulomb driving force. As salt concentration increases, EOF velocity initially rises due to enhanced surface ionization, followed by a decline attributed to increased wall shear stress. This work provides key insights for EOF applications in nanofluidics and biomedical devices, and deepens the understanding of electrokinetic phenomena influenced by $\mathrm{pH}$-regulation effects.

We consider the flow of a volume $\mathcal {V} = q t^\alpha$ of viscous fluid injected into a gap $H$ between two horizontal plates ($q$ and $\alpha$ are positive constants, $t$ is time). When the viscosity of the displaced fluid is negligible, the injected fluid forms a slug in contact with both plates connected (at a moving grounding line) to a gravity current (GC) with a downward-inclined interface. Hutchinson et al. (J. Fluid Mech., 598, 2023, pp. A4–1–13) considered a constant source ($\alpha = 1$) of Newtonian fluid at the center of an axisymmetric gap; the flow, governed by the parameter $J$ (the height ratio of the unconfined GC to $H$), admits a similarity solution. Here, the self-similar flow theory is (a) extended to rectangular geometry and power-law fluids, and (b) simplified. Similarity appears when $\alpha = n/(n+1)$ (two-dimensional) and $\alpha = 2n/(n+1)$ (axisymmetric), with propagation $\sim t^\beta$, where $\beta /\alpha = 1$ and $1/2$, respectively, and $n-1$ is the power of the shear in the viscosity law ($n=1$ for Newtonian fluid). The flow is governed by a single parameter $J$, representing the above-mentioned ratio. For small $J$, the GC is mostly unconfined; for large $J$, almost all the injected fluid is in contact with both boundaries of the gap. For given geometry and $n$, we solve one ordinary differential equation (ODE) for the reduced thickness over the reduced length $0\lt y \leqslant 1$, with a singular-regular condition at $y=1$. The details of the confined GC, functions of $J$, follow by simple formulae.

Elastoinertial turbulence (EIT) is a chaotic state that emerges in the flows of dilute polymer solutions. Direct numerical simulation (DNS) of EIT is highly computationally expensive due to the need to resolve the multiscale nature of the system. While DNS of two-dimensional (2-D) EIT typically requires $O(10^6)$ degrees of freedom, we demonstrate here that a data-driven modelling framework allows for the construction of an accurate model with 50 degrees of freedom. We achieve a low-dimensional representation of the full state by first applying a viscoelastic variant of proper orthogonal decomposition to DNS results, and then using an autoencoder. The dynamics of this low-dimensional representation is learned using the neural ordinary differential equation (NODE) method, which approximates the vector field for the reduced dynamics as a neural network. The resulting low-dimensional data-driven model effectively captures short-time dynamics over the span of one correlation time, as well as long-time dynamics, particularly the self-similar, nested travelling wave structure of 2-D EIT in the parameter range considered.

Explaining fast magnetic reconnection in electrically conducting plasmas has been a theoretical challenge in plasma physics since its first description by Eugene N. Parker. In recent years, the observed reconnection rate has been shown by numerical simulations to be explained by the plasmoid instability that appears in highly conductive plasmas. In this work, by studying numerically the Orszag–Tang vortex, we show that the plasmoid instability is very sensitive to the numerical resolution used. It is shown that well-resolved runs display no plasmoid instability even at Lundquist numbers as large as $5\times 10^5$ achieved at resolutions of $32\,768^2$ grid points. On the contrary, in simulations that are under-resolved below a threshold, the plasmoid instability manifests itself with the formation of larger plasmoids the larger the under-resolving is. The present results thus emphasize the importance of performing convergence tests in numerical simulations and suggest that further investigations on the nonlinear evolution of the plasmoid instability are required.

We investigate viscous dissipation in linear flows driven by small-amplitude longitudinal librations in rotating fluid spheres focusing on the rapid rotation regime applicable to planets. Viscous coupling can resonate with inertial modes in the bulk of the fluid when the frequency of the forcing is within the range $(0,2\Omega _0)$, where $\Omega _0$ is the mean angular velocity of the sphere. We solve the linearised equations of motion with a semi-spectral numerical method and with an asymptotic expansion exploiting the small Ekman number, $E$, which quantifies the strength of viscous forces relative to the Coriolis force. Our results confirm that the dominant contribution to the dissipation occurs in the Ekman boundary layer with leading-order scaling $E^{1/2}$. When the forcing frequency coincides with that of an inertial mode, dissipation is reduced by as much as 9 % compared with boundary layer theory alone. The percentage-wise reduction is independent of $E$ and the frequency width of the reduction envelope scales as $E^{1/2}$. At non-resonant frequencies conic shear layers develop in the bulk interior and, together with the Ekman layer bulge at critical latitude, slightly enhance dissipation. We confirm critical latitude bulge and shear layer contributions to the overall dissipation scale as $E^{4/5}$ and $E^{6/5}$ respectively, becoming negligible compared with dissipation in the main boundary layer as $E\rightarrow 0$. The frequencies at which the dissipation enhancement from critical latitude effects is maximised are displaced from the inviscid limit periodic orbit frequencies by a factor that scales with $E^{0.23}$.

In this paper, the reflection of shock waves with downstream expansion fan interference in two-dimensional, inviscid flow is investigated, including steady Mach reflection (MR) and the unsteady transition process from regular reflection (RR) to MR. A threshold for the configuration based on non-dimensional wedge length is proposed. The analytical model for the steady MR and RR$\rightarrow$MR transition process is established based on the classical shock and expansion wave relations, whose prediction agrees well with results obtained through inviscid numerical simulation. It is found that the expansion fan interference significantly influences the steady flow patterns, especially the height of the Mach stem and the shape of the slip line. The interaction accelerates the formation of the sonic throat, stabilizing the flow structure rapidly, and results in generally small Mach stem heights. The exposure of the triple point to the expansion fan eliminates the inflection point on the slip line, whose slope increases smoothly. The interaction further affects the time evolution of the Mach stem during the multiple-interaction stage of the RR$\rightarrow$MR transition process. It appears that the modifications come from the curvature of the incident shock brought by the wave interference. During the multiple-interaction stage, the triple point moves upstream along the curved incident shock, where the incident shock angle changes according to the curvature, resulting in the variation of the evolution velocity.

This article explores how a submerged elastic plate, clamped at one edge, interacts with water waves. Submerged elastic plates have been considered as potentially effective design elements in the development of wave energy harvesters but their behaviour in a wave field remains largely unexplored, especially experimentally. Positioned at a fixed depth in a wave tank, the flexible plate demonstrates significant wave reflection capabilities, a characteristic absent in rigid plates of identical dimensions. The experiments thus reveal that plate motion is crucial for wave reflection. Sufficiently steep waves are shown to induce a change in the mean position of the plate, with the trailing edge reaching the free surface in some cases. This configuration change is found to be particularly efficient to break water waves. These findings contribute to understanding the potential of elastic plates for wave energy harvesting and wave attenuation scenarios.

The Liebau effect generates a net flow without the need for valves. For the Liebau effect pumping phenomenon to occur, the pump must have specific characteristics. It needs tubes with different elastic properties and an actuator to provide energy to the fluid. The actuator periodically compresses the more flexible element. Furthermore, asymmetry is a crucial factor that differentiates between two pumping mechanisms: impedance pumping and asymmetric pumping. In this work, a model based on the fluid dynamics of an asymmetric valveless pump under resonant conditions is proposed to determine which parameters influence the pumped flow rate. Experimental work is used to validate the model, after which each of the parameters involved in the pump performance is dimensionlessly analysed. This highlights the most significant parameters influencing the pump performance such as the actuator period, length tube ratio and tube diameters. The results point out ways to increase a valveless asymmetric pump’s net-propelled flow rate, which has exciting applications in fields such as biomedicine. The model also allows for predicting the resonance period, a fundamental operating parameter for asymmetric pumping.

The intrinsic uncertainty of fluid properties, including the equation-of-state, viscosity and thermal conductivity, on boundary layer stability has scarcely been addressed. When a fluid is operating in the vicinity of the Widom line (defined as the maximum of isobaric specific heat) in supercritical state, its properties exhibit highly non-ideal behavior, which is an ongoing research field leading to refined and more accurate fluid property databases. Upon crossing the Widom line, new mechanisms of flow instability emerge, feasibly leading to changes in dominating modes that yield turbulence. The present work investigates the sensitivity of three-dimensional boundary layer modal instability to these intrinsic uncertainties in fluid properties. The uncertainty, regardless of its source and the fluid regimes, gives rise to distortions of all profiles that constitute the inputs of the stability operator. The effect of these distortions on flow stability is measured by sensitivity coefficients, which are formulated with the adjoint operator and validated against linear modal stability analysis. The results are presented for carbon dioxide at a representative supercritical pressure of approximately 80 bar. The sensitivity to different inputs of the stability operator across various thermodynamic regimes shows an immense range of sensitivity amplitude. A balancing relationship between the density gradient and its perturbation leads to a quadratic effect across the Widom line, provoking significant sensitivity to distortions of the second derivative of the pressure with respect to the density, $\partial ^2 p/\partial \rho ^2$. From an application-oriented point of view, one important question is whether the correct baseflow profiles can be meaningfully analysed by the simplified ideal-fluid model. The integrated modal disturbance growth – the N factor calculated with different partly idealised models – indicates that the answer depends strongly on the thermodynamic regime investigated.

The dynamics of small-scale structures in free-surface turbulence is crucial to large-scale phenomena in natural and industrial environments. Here, we conduct experiments on the quasi-flat free surface of a zero-mean-flow turbulent water tank over the Reynolds number range $Re_{\lambda } = 207$–312. By seeding microscopic floating particles at high concentrations, the fine scales of the flow and the velocity-gradient tensor are resolved. A kinematic relation is derived expressing the contribution of surface divergence and vorticity to the dissipation rate. The probability density functions of divergence, vorticity and strain rate collapse once normalised by the Kolmogorov scales. Their magnitude displays strong intermittency and follows chi-square distributions with power-law tails at small values. The topology of high-intensity events and two-point statistics indicate that the surface divergence is characterised by dissipative spatial and temporal scales, while the high-vorticity and high-strain-rate regions are larger, long-lived, concurrent and elongated. The second-order velocity structure functions obey the classic Kolmogorov scaling in the inertial range when the dissipation rate on the surface is considered, with a different numerical constant than in three-dimensional turbulence. The cross-correlation among divergence, vorticity and strain rate indicates that the surface-attached vortices are strengthened during downwellings and diffuse when those dissipate. Sources (sinks) in the surface velocity fields are associated with strong (weak) surface-parallel stretching and compression along perpendicular directions. The floating particles cluster over spatial and temporal scales larger than those of the sinks. These results demonstrate that, compared with three-dimensional turbulence, in free-surface turbulence the energetic scales leave a stronger imprint on the small-scale quantities.

The present study aims to provide an understanding of the influence of an afterbody on the flow-induced vibration (FIV) of cylinders. This is achieved through experimental and numerical investigations into the FIV response of a reverse-D-cross-section cylinder of aspect ratio $AR=5$. By carefully monitoring the point of flow separation to show it always occurs at the sharp top and bottom edges and never further upstream, it is demonstrated that vortex-induced vibration (VIV) can occur without an afterbody. However, for other aspect ratios, an afterbody does play a crucial role in determining the type of fluid forces responsible for sustaining VIV from low to moderate Reynolds numbers in the range $100$–$4700$. For a cylinder without an afterbody, it is found that the viscous force originating from the presence of strong compact vortices forming close to the leeward side of the cylinder is responsible for sustaining strong transverse vibration. In contrast, for a cylinder with an afterbody, the dominant force component depends on the size of the afterbody. In cylinders with a small afterbody, such as a reverse-D semi-circular cylinder, the viscous force dominates, while in cylinders with a larger afterbody such as a circular cylinder, the pressure force dominates.

Skin-friction drag reduction (DR) in a turbulent boundary layer (TBL) using plasma-generated streamwise vortices (PGSVs) is governed by plasma-induced spanwise wall-jet velocity $W$, the distance $L$ between the positive electrodes of two adjacent plasma actuators (PAs) and the friction Reynolds number $Re_\tau$. It is found experimentally that DR increases logarithmically with the growing maximum spanwise mean velocity $\overline {W}_{max}^+$ but decreases with rising $L^+$ and $Re_\tau$, where superscript ‘+’ denotes normalization by the inner scales. It is further found from theoretical and empirical scaling analyses that the dimensionless drag variation $\Delta F = g_1 (\overline {W}_{max}^+, L^+, {Re_\tau })$ may be reduced to $\Delta F = g_2 (\xi )$, where $g_1$ and $g_2$ are different functions and the scaling factor $\xi = [k_{2} \log _{10} (k_{1} \overline {W}_{max }^{+} ) ] / (L^{+} Re_{\tau } )$ ($k_{2}$ and $k_{1}$ are constants) is physically the circulation of the PGSVs. Discussion is conducted based on $\Delta F = g_2 (\xi )$, which provides important insight into the physics of TBL control based on PAs.

A collection of secondary instability calculations in streaky boundary layers is presented. The data are retrieved from well-resolved numerical simulations of boundary layers forced by free-stream turbulence (FST), considering different geometries and FST conditions. The stability calculations are performed before streak breakdown, taking place at various $Rey_x$ the Reynolds number based on the streamwise coordinate. Despite the rich streak population of various sizes, it is found that breaking streaks have similar aspect ratios, independently of the streamwise position where they appear. This suggests that wider streaks will break down further downstream than thinner ones, making the appearance of secondary instabilities somewhat independent of the streak’s wavelength. Moreover, the large difference in the integral length scale among the simulations suggests that this aspect ratio is also independent of the FST scales. An explanation for this behaviour is provided by showing that these breaking streaks are in the range of perturbations that can experience maximum transient growth according to optimal disturbance theory. This could explain why, at a given streamwise position, there is a narrow spanwise wavelength range where streak breakdown is more likely to occur.

When a droplet impacts onto a superheated liquid pool, vapour generation and drainage within the gas cushion play a crucial role in postponing or even preventing contact between the droplet and the pool surface. Through direct numerical simulations, we closely examine the transient dynamics of vapour flow confined within the thin film, with a particular focus on the minimum thickness of this film under a range of impact conditions. Our numerical findings manifest the significant influence of evaporation on the vertical motion of the liquid–vapour interface, revealing how the minimum film thickness evolves in response to variations in impact velocity and degree of superheat. In our numerical simulations, we have identified two distinct evolution laws for the minimum film thickness, corresponding to moderate and high superheat regimes, respectively. These regimes are differentiated by the dominance of evaporation effects within the vapour film during the early falling stage. Subsequently, we establish scaling relations to characterize these regimes by carefully balancing inertial, pressure and evaporation effects within the thin vapour film. Furthermore, we observe that the vapour pressure eventually reaches equilibrium with the rapid increase in capillary pressure at the spreading front, thereby controlling the minimum thickness of the vapour layer in both moderate and high superheat regimes. We derive self-similar solutions based on this equilibrium, and the predicted minimum film thickness aligns remarkably well with our numerical results. This provides compelling evidence that evaporation alone is insufficient to prevent droplet–pool coalescence.

In this work, we investigate the mixing of active scalars in two dimensions by the stirring action of stochastically generated weak shock waves. We use Fourier pseudospectral direct numerical simulations of the interaction of shock waves with two non-reacting species to analyse the mixing dynamics for different Atwood numbers (At). Unlike passive scalars, the presence of density gradients in active scalars alters the molecular diffusion term and makes the species diffusion nonlinear, introducing a concentration gradient-driven term and a density gradient-driven nonlinear dissipation term in the concentration evolution equation. We show that the direction of concentration gradient causes the interface across which molecular diffusion occurs to expand outwards or inwards, even without any stirring action. Shock waves enhance the mixing process by increasing the perimeter of the interface and by sustaining concentration gradients. Negative Atwood number mixtures sustain concentration gradients for a longer time than positive Atwood number mixtures due to the so-called nonlinear dissipation terms. We estimate the time until that when the action of stirring is dominant over molecular mixing. We also highlight the role of baroclinicity in increasing the interface perimeter in the stirring dominant regime. We compare the stirring effect of shock waves on mixing of passive scalars with active scalars and show that the vorticity generated by baroclinicity is responsible for the folding and stretching of the interface in the case of active scalars. We conclude by showing that lighter mixtures with denser inhomogeneities ($At\lt 0$) take a longer time to homogenise than the denser mixtures with lighter inhomogeneities ($At\gt 0$).

Dust storms are a unique form of high-Reynolds-number particle-laden turbulence associated with intense electrical activity. Using a wavelet-based analysis method on field measurement data, Zhang et al. (2023 J. Fluid Mech. 963, A15) found that wind velocity intermittency intensifies during dust storms, but it is weaker than both dust concentration and electric field. However, the linear and nonlinear multifield coupling characteristics, which significantly influence particle transport and turbulence modulation, remain poorly understood. To address this issue, we obtained high-fidelity datasets of wind velocity, dust concentration, and electric field at the Qingtu Lake Observation Array. By extending the wavelet-based data analysis method, we investigated localised linear and quadratic nonlinear coupling characteristics in strong turbulence–particle–electrostatics coupling regimes. Our findings reveal that linear coupling behaviour is largely dominated by the multifield intermittent components. At small scales, due to very high intermittency, no strong phase synchronisation can be formed, and the interphase linear coupling is weak and notably intermittent. At larger scales, however, perfect phase synchronisation emerges, and dust concentration and electric field exhibit strong, non-intermittent linear coupling, suggesting that large-scale coherent structures play a dominant role in driving the coupling. Importantly, the multifield spectra show well-developed $-1$ and $-5/3$ power-law regions, but the spectral breakpoints for dust concentration and electric field are two decades lower than that for streamwise wind velocity. This difference is due to the broader range and stronger intensity of quadratic nonlinear coupling in dust concentration and electric field, which leads to the broadening of Kolmogorov’s $-5/3$ power-law spectrum.

We perform direct numerical simulations of turbulent channel flows. Secondary motions are produced by applying a streamwise-homogeneous, spanwise-heterogeneous roughness pattern of spanwise period $\Lambda _s$ to the walls of the channel; their time evolution is observed. Notice that, owing to the geometry, the secondary motions are streamwise-invariant at any instant of time, so that no spatial development is seen. Once the secondary motions reach a statistically steady state, the roughness pattern is suddenly removed, so that the secondary motions decay. The time needed for the secondary motions to vanish is then measured; in doing so, we distinguish between the streamwise-momentum pathways and the cross-sectional circulatory motions that compose the secondary motions. Larger values of $\Lambda _s$ are generally associated with a longer time scale for the decay of the momentum pathways, although this might not hold true for $\Lambda _s/h\gt 4$ (where $h$ is the channel half-height). The value of such a time scale for the circulatory motions, instead, saturates for $\Lambda _s/h \geqslant 2$; this may be related to the observed spatial confinement of said circulatory motions. For specific values of $\Lambda _s$ ($2 \leqslant \Lambda _s/h \leqslant 4$), the volume-averaged energy associated with the momentum pathways undergoes an unexpected transient growth with respect to its value at the beginning of the decay. This might indicate that structures of such a specific size are able to self-sustain as postulated by Townsend (The Structure of Turbulent Shear Flow, 2nd edition, 1976, ch. 7.19); the evidence we gather in this respect is however inconclusive. Finally, the present data suggest that most of the energy of the momentum pathways is produced by the circulatory motions transporting the mean (spanwise-averaged) velocity.

Cilia perform various functions, including sensing, locomotion, generation of fluid flows and mass transport, serving to underpin a vast range of biological and ecological processes. However, analysis of the mass transport typically fails to resolve the near-field dynamics around individual cilia, and therefore overlooks the intricate role of power/recovery strokes of ciliary motion. Selvan et al. (2023, Phys. Rev. Fluids 8, 123103) observed that the flow field due to a point torque (i.e. a rotlet) accurately resolves both the near- and far-field characteristics of a single cilium’s flow in a semi-infinite domain. In this paper, we calculate the mass transport between a no-slip boundary and an adjacent fluid, as a model system for nutrient exchange with ciliated tissues. We develop a Langevin model in the presence of a point torque (i.e. a single cilium) to examine the nutrient flux from a localised surface source. This microscopic transport model is validated using a macroscopic continuum model, which directly solves the advection–diffusion equation. Our findings reveal that the flow induced by a point torque can enhance the particles’ transport, depending on their diffusivity and the magnitude of the point torque. Additionally, the average mass transport affected by a single cilium can be enhanced or diminished by the presence of an externally imposed linear shear flow, with a strong dependence on the alignment of the cilium. Taken together, this framework serves as a useful minimal model for examining the average nutrient exchange between ciliated tissues and fluid environments.

Inertia–gravity waves are scattered by background flows as a result of Doppler shift by a non-uniform velocity. In the Wentzel–Kramers–Brillouin regime, the scattering process reduces to a diffusion in spectral space. Other inhomogeneities that the waves encounter, such as density variations, also cause scattering and spectral diffusion. We generalise the spectral diffusion equation to account for these inhomogeneities. We apply the result to a rotating shallow-water system, for which height inhomogeneities arise from velocity inhomogeneities through geostrophy, and to the Boussinesq system for which buoyancy inhomogeneities arise similarly. We compare the contributions that height and buoyancy variations make to the spectral diffusion with the contribution of the Doppler shift. In both systems, we find regimes where all contributions are significant. We support our findings with exact solutions of the diffusion equation and with ray tracing simulations in the shallow-water case.

Particle image velocimetry is used to study the control of swirl momentum, delivered through an orifice formed by a physically rotating tube of finite length, relevant to the evolution of vortex rings produced at a Reynolds number ${Re}\approx 1000$ based on the average discharge velocity, for swirl numbers ${S} \in [0, 1]$. Experiments without discharge, reinforced with complimentary numerical predictions, reveal the presence of an intriguing secondary flow pattern in the rotating tube, preventing attainment of a solid-body-like swirl distribution. Nevertheless, it is found that fully established rings produced in this way, following discharge once conditions in the tube have reached a steady state, exhibit similar characteristics to rings formed by an otherwise solid-body rotating initial condition as explored computationally by Ortega-Chavez et al. (2023, J. Fluid Mech. 967, A16). Namely, opposite-signed vorticity forms due to vortex tilting, which subsequently interacts with the ring, promoting vorticity cancellation and vortex ring breakdown. A key feature of the experimental work is that partially established vortex rings, produced before a steady-state rotating tube condition is reached, show unique characteristics. Their creation, a short time after the onset of tube rotation: (i) facilitates more efficient delivery of swirl momentum to the vortex core area; (ii) maintains a low level of swirl in the ring bubble’s central region which would otherwise promote the formation of opposite-signed vorticity and vortex breakdown.