The most common method to characterize the electrical response of a nanofluidic system is through its steady-state current–voltage response. In Part 1, we demonstrated that this current–voltage response depends on the geometry, the layout of the surface charge and the effects of advection. We demonstrated that each configuration has a unique steady-state signature. Here, we will elucidate the behaviour of the time-transient response. Similar to the steady-state response, we will show that each configuration has its own unique time-transient signature when subjected to electroosmotic instability. We show that bipolar systems behave differently than unipolar systems. In unipolar systems, the instability appears only at one end of the system. In contrast, in bipolar systems the instability will either appear on both sides of the nanochannel or not at all. If it does appear on both sides, the instability will eventually vanish on one or both sides of the system. In Part 1, these phenomena were explained using steady-state considerations of the behaviour of the fluxes. Here, we will examine the time-transient behaviour to reveal the governing principles that are, on the one hand, not so different from unipolar systems and, on the other hand, remarkably different.

The steady-state current–voltage response of ion-selective systems varies as the number of ion-selective components is varied. For the highly investigated unipolar system, including only one ion-selective component, it has been shown that above a supercritical voltage, an electroosmotic instability is triggered, leading to overlimiting currents. In contrast, the effects of this instability on the current–voltage response of the second most common system of a bipolar system, including two oppositely charged permselective regions, have yet to be reported. Using numerical simulations, we investigate the steady-state electrical response of bipolar systems as we vary the ratio of the charge within the two oppositely charged regions. The responses are divided into those with an internal symmetry related to the surface charge and those without. In contrast to the unipolar systems, bipolar systems with the internal symmetry do not exhibit overlimiting currents and their steady-state response is identical to the convectionless steady-state response. In contrast, the systems without the internal symmetry exhibit much more complicated behaviour. For positive voltages, they have overlimiting currents, while for negative voltages, they do not have overlimiting currents. Our findings contribute to a more profound understanding of the behaviour of the current–voltage response in bipolar systems.

Motivated by flow interactions in schooling biological swimmers as well as in unmanned underwater vehicle fleets, we investigate the flow past two identical 6 : 1 ellipses using two-dimensional simulations at Reynolds numbers of $\mathcal {O}(10^3)$. When both ellipses move at the same velocity, overall drag reductions of 10 %–20 % can be achieved in staggered formations, with the strongest drag reductions occurring at the smallest lateral distances. In side-by-side configurations, the drag on both bodies increases by 10 %–20 %. Lift coefficients are repulsive and up to four times larger than the total drag coefficients. During overtaking manoeuvres, increasing the relative speed of the overtaking ellipse predominantly affects the forces on the overtaken ellipse. The mean drag force on the overtaken ellipse increases with increasing speed difference. Mean lift forces during the overtaking manoeuvre are repulsive for both bodies; as the speed difference increases, the repulsive force increases on the overtaken body and decreases on the overtaking body. Overall, these results highlight that the lateral forces in hydrodynamic interactions between bodies in formation dominate the hydrodynamic interactions. Further, the results indicate that future work is needed to investigate how viscous and three-dimensional effects change the lateral forces between side-by-side submerged bodies.

Superhydrophobic (SHPo) surfaces can capture a thin layer of air called a plastron under water to reduce skin friction. Although a ~30 % drag reduction has been recently reported with longitudinal micro-trench SHPo surfaces under a boat and in a towing tank, the results lacked the consistency to establish a clear trend. Designed based on Yu et al. (J. Fluid Mech, vol. 962, 2023, A9), this work develops and tests a series of high-performance SHPo surface coupons that can sustain a pinned plastron underneath a passenger motorboat revamped to reach 14 knots. Importantly, plastrons in a pinned state, not just their existence, are confirmed during flow experiments for the first time. All the drag-reduction data measured on different longitudinal micro-trenches are found to collapse if plotted against slip length in wall units. In comparison, aligned posts and transverse trenches show less and little drag reduction, respectively, confirming the adverse effect of the spanwise slip in turbulent flows. This report not only verifies SHPo surfaces can provide a consistent drag reduction at high speeds in open sea but also shows that one may predict the amount of drag reduction in turbulent flows using the physical slip length obtained for Stokes flows.

Thwaites (Aeronaut. Q., vol. 1, 1949, pp. 245–280) developed an approximate method for determining the evolution of laminar boundary layers. The approximation follows from an assumption that the growth of a laminar boundary layer in the presence of pressure gradients could be parameterized solely as a function of the Holstein–Bohlen flow parameter, thus reducing the von Kármán momentum integral to a first-order ordinary differential equation. This method is useful for the analysis of laminar flows, and in computational potential flow solvers to account for the viscous effects. In this work, an approximate method for determining the momentum thickness of a two-dimensional, turbulent boundary layer is proposed following Thwaites’ work. It is shown that the method provides good estimates of the momentum thickness for multiple boundary layers, including both favourable and adverse pressure gradient effects, up to the point of separation. In the limit of high Reynolds numbers, it is possible to derive a criterion for the onset of separation from the proposed model, which is shown to be in agreement with prior empirical observations (Alber, 9th Aerospace Sciences Meeting, 1971). The sensitivity of the separation location with respect to upstream perturbations is also analysed through this model for the NASA/Boeing speed bump and the transonic Bachalo–Johnson bump.

Hydroelectric turbine designers need to know the damping coefficient of a turbine blade to assess its longevity. Damping is difficult to simulate numerically. Current flow-added damping evaluation methods involve solving Reynolds-averaged Navier–Stokes simulations, which are numerically expensive and complex. This paper presents a new, simple and fast method to evaluate the added damping coefficient of a standalone and straight hydrofoil using NASTRAN's multiple modules. Using the vacuum and resting fluid natural frequencies, a proportionality matrix is implemented into NASTRAN's flutter solution using the added virtual mass incremental factor to evaluate the added damping adequately. The methodology is validated against experimental and numerical data from previously published articles and presents good agreement with existing results.

Indoor ventilation is underutilized for the control of exposure to infectious pathogens. Occupancy restrictions during the pandemic showed the acute need to control detailed airflow patterns, particularly in heavily occupied spaces, such as lecture halls or offices, and not just to focus on air changes. Displacement ventilation is increasingly considered a viable energy efficient approach. However, control of airflow patterns from displacement ventilation requires us to understand them first. The challenge in doing so is that, on the one hand, detailed numerical simulations – such as direct numerical simulations (DNSs) – enable the most accurate assessment of the flow, but they are computationally prohibitively costly, thus impractical. On the other hand, large eddy simulations (LES) use parametrizations instead of explicitly capturing small-scale flow processes critical to capturing the inhomogeneous mixing and fluid–boundary interactions. Moreover, their use for generalizable insights requires extensive validation against experiments or already validated gold-standard DNSs. In this study, we start to address this challenge by employing efficient monotonically integrated LES (MILES) to simulate airflows in large-scale geometries and benchmark against relevant gold-standard DNSs. We discuss the validity and limitations of MILES. Via its application to a lecture hall, we showcase its emerging potential as an assessment tool for indoor air mixing heterogeneity.

This study presents a direct numerical simulation that investigates the transport mechanisms of sand particles in the neutrally stable atmospheric Ekman boundary layer (AEBL). The simulation models the AEBL in a half-channel flow, taking into account the Earth's rotation and adding a Coriolis term to the Navier–Stokes equations. The Lagrangian point-particle method with one-way coupling is used to track the sand particles. The main objective is to examine the impact of gravity and particle Stokes number on the sand particle dynamics. The results indicate that gravity has a significant effect on large-size sand particles, as seen in the mean and root-mean-square sand velocity profiles. The slip velocity profiles of sand particles relative to the surrounding air show that larger particles experience higher drag forces in the viscous sublayer, which hinders their forward movement. This effect is also amplified by gravity. Furthermore, the mean profiles of the streamwise and spanwise slip velocities exhibit distinct demarcations of the viscous sublayer, buffer layer and log-law region. The spatial and temporal Voronoï analysis reveals that gravity increases the clustering level of sand particles in the entire turbulent Ekman layer and reduces the time for the change of the Voronoï volume, particularly for large-size particles.

Benthic macroalgae (including brown macroalgae or kelp) constitute one of the largest contributors to coastal primary production, but their ability to store and sequester carbon remains uncertain. Here, we use a numerical model of the flow/kelp interactions to study how tidal currents interact with an idealised numerical model of a giant kelp (Macrocystis pyrifera) forest, intending to better understand the potential for kelp growth in nutrient-limited conditions and the export of important tracers such as dissolved organic carbon. We calibrate and test our model using observations of currents within and surrounding a kelp forest in Southern California. By varying the density of kelp in our model, we find that there is a kelp density that maximises the export of tracer released from the kelp forest. Since the tracer advection/diffusion equation is linear with respect to the tracer concentration, the same kelp density corresponds to the maximum uptake for a tracer with a constant far-field concentration. The density at which this maximum occurs coincides with the density typical of natural kelp forests, where kelp growth may be limited by the uptake of dissolved nutrients from the surrounding water. Additionally, the drag induced on the tidal currents by the kelp forest results in a mean circulation through the kelp forest and a mean displacement of the kelp forest canopy.

The stirring and mixing of heat and momentum in the ocean surface boundary layer (OSBL) are dominated by 1 to 10 km fluid flows – too small to be resolved in global and regional ocean models. Instead, these processes are parametrized. Two main parametrizations include vertical mixing by surface-forced metre-scale turbulence and overturning by kilometre-scale submesoscale frontal flows and instabilities. In present models, these distinct parametrizations are implemented in tandem, yet ignore meaningful interactions between these two scales that may influence net turbulent fluxes. Using a large-eddy simulation of frontal spin down resolving processes at both scales, this work diagnoses submesoscale and surface-forced turbulence impacts that are the foundation of OSBL parametrizations, following a traditional understanding of these flows. It is shown that frontal circulations act to suppress the vertical buoyancy flux by surface forced turbulence, and that this suppression is not represented by traditional boundary layer turbulence theory. A main result of this work is that current OSBL parametrizations excessively mix buoyancy and overestimate turbulence dissipation rates in the presence of lateral flows. These interactions have a direct influence on the upper ocean potential vorticity and energy budgets with implications for global upper ocean budgets and circulation.

We experimentally investigate the flow through a hollow cube, with an indoor ground-level passive scalar source, immersed in a rough-wall turbulent boundary layer inside a water tunnel. The focus is on characterizing scalar transport within the cube, through simultaneous scalar and flow measurements using planar laser-induced fluorescence and particle image velocimetry. To understand the role of window positioning, three cube configurations, labelled as ‘centre’, ‘up-down’ and ‘down-up’, distinguished by window positions at the upstream and downstream ends, are studied. Varying window position alters the flow characteristics within the cube, resulting in differences in scalar concentration and distribution. The steady-state concentration is highest for ‘centre’, followed by ‘up-down’ and ‘down-up’ configurations. Regarding the scalar distribution, ‘centre’ showed accumulation near the top and bottom walls, while ‘up-down’ and ‘down-up’ exhibited scalar buildup in the lower and upper half of the cube, respectively. The flow patterns and scalar transport mechanisms remained consistent across different Reynolds numbers ($Re=U_{Ref}H/\nu = 20\ 000$, 35 000, 50 000) for each configuration; $U_{Ref}=$ incoming flow velocity at cube height ($H$), and $\nu =\,$ kinematic viscosity of water. The analysis is extended by revising the classical box model, accounting for practical complexities such as non-perfect mixing. Our results can help better understand and model indoor–outdoor pollutant exchange in complex urban environments.

Hollow fibre membrane bioreactors provide a fast and efficient method for engineering functional tissue for use in medical treatments. Flow is utilised to overcome mass transport limitations by perfusing a nutrient-rich culture medium through the fibre lumen, which can then transport along the fibre lumen or across the porous membrane wall. Cells seeded at the outer membrane wall consume the nutrient and subsequently produce waste metabolites, which are transported away through an external extra-capillary space (ECS) along with excess nutrient. We present and investigate a two-dimensional axisymmetric model for fluid flow and solute transport through a single-fibre bioreactor configuration, with cells seeded to the external fibre wall. Fluid flow is modelled by steady lubrication and Darcy equations, which are coupled to the solute transport problem modelled by a system of advection–diffusion equations, supplemented with a reaction term to model the cell layer. Our model analysis reveals how spatially varying wall permeability distributions can be utilised to provide uniform nutrient delivery to a spatially uniform, homogeneous cell population. We also reveal how maximising the transmural pressure drop across the membrane wall is the dominant mechanism for waste removal rather than traditional experimental methods of flushing the ECS.

Breaking waves aerate seawater surfaces and form whitecaps in the open ocean. The aerated surface area, or whitecap coverage, has been used to macroscopically parametrize air–sea momentum and gas exchange. However, the microscopic mechanisms of the generation, evolution and attenuation of surface bubbles in whitecaps remain poorly understood. In this study, we examined the size distributions and size-dependent lifetimes of surface bubbles generated by water sheet entry and air injection on a porous plate during the clustering, coalescing and bursting processes, depending on surfactant concentrations and bubble mobility. Mechanisms of coalescence through film thinning of adjacent bubble walls owing to the inter-bubble attraction and Marangoni forces experimentally described the surfactant-dependent bubble growth, finally achieving bubble bursting, which were statistically characterized in a population balance analysis. Lagrangian bubble lifetimes were described by the Weibull distribution, providing that surfactant in seawater extended the probabilistic survival periods of surface bubbles two times longer than those of clean bubbles.

The Reynolds-averaged Navier–Stokes (RANS) models depend on empirical constants to close the Reynolds stress terms. The empirical constants were obtained using experiments conducted at low Reynolds numbers several decades ago. In this paper, we revisit the turbulent viscosity parameter $C_\mu$, based on the stress–intensity ratio $c^2 = {|\overline {uw}|}/{k}$. Here, $\overline {|uw|}$ and $k$ are the absolute values of the Reynolds stress and turbulent kinetic energy, respectively. Through a priori comparisons, we find that the currently accepted value of $C_\mu = 0.09$ does not agree with the latest direct numerical simulation (DNS) and experimental datasets of wall-bounded turbulent planar flows. Therefore, a new value is suggested by averaging $c^2$ in the equilibrium region, where the production ($\mathcal {P}$) of $k$ is within 10 % of the dissipation rate ($\epsilon$), and consequently, $c^4 \approx C_\mu$. We evaluate flows up to friction Reynolds number $Re_\tau \approx 10\,000$ and find that with increasing $Re_\tau$, $C_\mu$ approaches a value of 0.06, which is almost 50 % lower than the prevalent value of 0.09. Finally, we perform an a priori test with the new (proposed) value of $C_\mu = 0.06$ to show that the estimated turbulent viscosity $\nu _T$ for wall-bounded flows is in much closer agreement with the exact (DNS) values than when $\nu _T$ is estimated using $C_\mu = 0.09$.

This manuscript mainly explores the characteristics of turbulence quantities in the wake of tall building clusters of different array size ($N$) and building spacing ($W_S$) arranged in an aligned and regular grid in the flow direction. Velocity fields are measured in a wind tunnel using three-dimensional laser Doppler anemometry. Results show a delayed recovery of $u_{rms}$ and $v_{rms}$ (defined as the root-mean-square of the streamwise and lateral velocities, respectively) in the wake flow compared with the mean flow. Based on the turbulent fluctuations, the extents of the near-, transition- and far-wake regions in Mishra et al. (Boundary-Layer Meteorol., vol. 189, 2023, pp. 1–25) are revisited. In the near wake, we observe a significant reduction in $u_{rms}$ and $v_{rms}$ in the wake of a $4\times 4$ cluster compared with that of a single building. In the transition region, the turbulence intensity magnitudes within the cluster reduce to below their free-stream counterpart; this reduction is associated with the slowly varying nature of the normalised wake deficit in the streamwise direction. The recovery of the root mean square in the far-wake region is observed for $x \geq 2.5W_A$ (where $W_A$ is the width of the cluster), with the mutual interaction of the wakes formed behind the individual buildings reducing with an increase in $W_S$, resulting in a faster recovery of the turbulent fluctuations. Finally, wavelet analysis suggests the existence of multi-scale vortex-shedding frequencies downwind of tall building clusters.

This paper focuses on simulating turbulent flow over propagating waves by solving the full Navier–Stokes equations in a moving frame. A careful comparison of flow statistics with previous experimental and numerical results demonstrates, to some extent, the rationality of simplifying wind waves as turbulent flow over moving wave boundaries. The phase-averaging method is then applied to investigate the momentum and energy transfers between turbulent wind and waves propagating at slow, intermediate and fast speeds. The results suggest that the dominant mechanism for producing Reynolds shear stress (RSS) and turbulent kinetic energy (TKE) is related to the wave age. Slow waves produce RSS and TKE similar to a two-dimensional shear turbulence. However, a fast wave enhances the streamwise Reynolds normal stress, the windward side's negative RSS and the gradient of both streamwise and vertical velocities, leading to additional RSS and TKE productions that can be ignored under the slow wave regimes. A strengthening wave–turbulence exchange is also found for fast waves. The intermediate wave can be regarded as a transitional condition determining this change.

This paper describes the scientific features of an innovative technique to mass-produce monolayers of hexagonal close-packed structures (HCP) of particles (280–1100 nm). Our technique differs from a continuous roll-to-roll Langmuir–Blodgett (LB) process. It consists of a thin liquid film flowing down an inclined plane channel, the ramp, and entraining deposited particles floating on its surface to form a compact monolayer. Vertical sidewalls limit the entire flow. The main benefits of this technique in comparison with a standard LB process are a gentler push on the floating particles during the assembly and the prospect of better flexibility and scalability in the design of industrial applications. Our disruptive approach presents new control parameters and surprising but challenging hydraulic phenomena due to the flowing liquid. This paper investigates the hydrodynamics of this new LB-type design theoretically and experimentally. We propose an original theoretical prediction of the thickness of the liquid film flowing down the ramp without or with particles on its surface, including within the hydraulic jump region separating the liquid film whose surface is free of particles and the liquid film whose surface is particle-loaded. The experimental determinations of the film thickness obtained by a confocal chromatic technique and moiré topography agree well with our model. In addition, Bragg diffraction topography and false colour topography allow the HCP structure of the compact monolayer of particles to be quantified.

Microstructured surfaces with pillar arrays are widely used to control the wetting morphology and spreading dynamics of droplets. In both simulations and experiments, it is shown that fabricating the surface with various microstructures is a very effective method for achieving the desired symmetry of the moving contact line. However, the method for characterizing miscellaneous pillar-arrayed microstructured surfaces is still insufficient. This paper presents the configurational entropy to characterize the microstructured surfaces with pillar arrays. By calculating the configurational entropy of pillar-arrayed microstructured surfaces, the relationship between the configurational entropy and the wetting morphology of droplets is obtained. For pillar-arrayed microstructured surfaces with the configurational entropy S > 0, the droplet wetting morphology may be much more complex than those with S = 0. The relationship is found to be consistent with the previous results. Furthermore, the wetting dynamics has been analysed. This study may be useful to understand the mechanism of droplet wetting on pillar-arrayed microstructured surfaces and provide insights for the design and manufacture of microstructured surfaces.

The shoaling of large-amplitude internal waves in the coastal ocean yields a consistent mechanism for both horizontal and vertical transport of material, momentum and energy. This review surveys recent numerical, field and laboratory work on the details of this transport. A particular focus is made on the two issues of how boundary-layer processes are modified during shoaling, and the development of spanwise structure, especially in the trapped cores that form during shoaling. Numerical challenges, including gaps in existing parametrizations are identified using pseudospectral simulations on the laboratory scale. A number of challenges for future work, for simulations, parametrizations and laboratory and field measurements are laid out.

Underwater explosions are inherently complex and unique physical phenomena markedly distinct from those occurring above the surface. This distinctiveness is primarily attributed to the relatively incompressible nature of water, which fundamentally alters the propagation and impact of shock waves. The study of underwater explosions is paramount in applications such as underwater demolitions for construction and salvage operations. These applications require a comprehensive understanding in order to mitigate the disturbances’ impact on marine structures and ecosystems. Studying underwater explosions and their mitigation encompasses various disciplines, including fluid mechanics, materials science and structural engineering. The work reviewed in this study contributes significantly to enhancing safety measures in marine structures by providing critical insights into the behaviour of structures under extreme conditions. This includes understanding the behaviour of gas bubbles formed by explosions, the transmission of shock waves through different media and the resultant forces exerted on structures submerged in water. Consequently, this review is meant to aid in designing robust and resilient marine systems capable of withstanding severe loading conditions caused by underwater explosions by providing key engineering considerations. The continuous evolution of this research area is essential for advancing maritime technology, ensuring the safety of undersea operations and protecting marine environments from the adverse effects of extreme subaqueous loadings.