Spectral turbulence models commonly used in the design and certification of wind turbines have only been validated at heights up to 70 m in the atmosphere, but many offshore wind turbines now operate at heights above 150 m. Moreover, there is a lack of measurement data on the spatial structure of turbulence at such heights in the marine atmospheric boundary layer (MBL). Consequently, it is uncertain whether these turbulence models are valid for the design of tall offshore wind turbines. To fill this gap, we present measurements of one-point auto-spectra and two-point spectral coherence at heights of 150–250 m and lateral separations up to 241 m providing lateral coherence of turbulence in the MBL that has never been measured before for these heights and separations. Five light detection and ranging (lidar) instruments were deployed on the west coast of Denmark, and we reconstructed the along-wind and cross-wind components at the lidar beam intersection points. The measurements were compared with the theoretical predictions of auto-spectra and lateral coherence from the Mann model and its extension, the Syed–Mann model. The latter models turbulence down to frequencies of 1 h$^{-1}$ through the $-5/3$ scaling observed in the mesoscale range. The results show that the Mann model did not compare well with the measurements under stable and near-neutral conditions. On the other hand, the Syed–Mann model predicted the lateral coherence for a range of different conditions. However, the lateral coherence was under predicted in about $8\,\%$ of the data, possibly due to gravity waves. We believe that the high coherence from mesoscale turbulence at these heights can influence the loads on floating wind turbines and large offshore wind farms.

We experimentally investigate the structure and evolution of planar, inertia-dominated intrusions from a constant source into linearly stratified ambients that are either quiescent or uniformly flowing. The source is either a negatively buoyant plume or a diffuser at the level of neutral buoyancy. The intrusions generated by plumes in a quiescent ambient form self-similar wedges, with constant thickness at the source $(2.5\pm 0.3)\sqrt {Q/N}$ and the wedge lengthening in time $t$ as $(0.32\pm 0.03)\sqrt {\textit{NQ}}\,t$, where $N$ is the buoyancy frequency, and $Q$ is the areal supply rate. In a flowing ambient, the intrusions remain self-similar with the same functional dependence on parameters. However, they become increasingly asymmetric as the ambient flow speed increases, and for speeds greater than approximately $0.3\sqrt {\textit{NQ}}$, there is no upstream propagation. Intrusions generated by diffusers are structurally different and not clearly self-similar. Immediately adjacent to the source, they thicken significantly through a turbulent, entraining hydraulic jump. Beyond this is a gently thinning region that lengthens over time. Ahead of this is a more rapidly tapering nose. Both the area of these intrusions and the front positions increase as power laws in time, with exponents between $0.6$ and $0.7$. With an ambient flow, this overall structure persists with asymmetry. We compare our experimental observations for plume-generated intrusions with predictions from the intrusive shallow-water model of Ungarish (2005, J. Fluid Mech., vol. 535, pp. 287–323). The model explains some of the observed behaviours, but does not provide an accurate description of the thickness profiles.

The interaction of an object with an unsteady flow is non-trivial and is still far from being fully understood. When an aerofoil or hydrofoil, for example, undergoes time-dependent motion, nonlinear flow phenomena such as dynamic stall can emerge. The present work experimentally investigates the interaction between a hydrofoil and surface gravity waves. The waves impose periodic fluctuations of the velocity magnitude and orientation, causing a steadily translating hydrofoil to be susceptible to dynamic stall at large wave forcing amplitudes. Simultaneous measurement of both the forces acting on the hydrofoil and the flow around it by means of particle image velocimetry (PIV) are performed, to properly characterise the hydrofoil–wave interaction. In an attempt at alleviating the impact of the flow unsteadiness via passive flow control, a bio-inspired tubercle geometry is applied along the hydrofoil leading edge. This geometry is known to delay stall in steady cases but has scarcely been studied in unsteady flow conditions. The vortex structures associated with dynamic stall are identified, and their trajectories, dimension and strength characterised. This analysis is performed for both straight- and tubercled-leading-edge geometries, with tubercles found to qualitatively modify the flow behaviour during dynamic stall. In contrast to previous studies, direct measurements of lift do not evidence any strong modification by tubercles. Drag-driven horizontal force fluctuations, however, which have not previously been measured in this context, are found to be strongly attenuated. This decrease is quantified and a physical model based on the flow observations is finally proposed.

In the decay region around the centreline of three qualitatively different turbulent plane wakes, the turbulence is non-homogeneous and two-point turbulent diffusion counteracts the turbulence cascade all the way down to scales smaller than the Taylor length. It is found that the sum of the inter-space transfer rate and the horizontal part of the inter-scale transfer rate of horizontal two-point turbulent kinetic energy is approximately proportional to the turbulence dissipation rate in the inertial range with a constant of proportionality between $-0.6$ and $-1$ depending on wake and location within the wake, except at the near-field edge of the decay region.

An experimental investigation of separation bubble shaped control bumps for oblique shock wave–boundary-layer interactions was performed in two supersonic wind tunnel facilities at Mach 2.5 and 2, with incident shock deflection angles of $8^\circ$ and $12^\circ$, respectively, and momentum thickness Reynolds numbers of approximately $1.5 \times 10^4$. Shock control bumps were designed to replicate the time-averaged separation bubble shape, and were placed onto the floor in the separation location. This resulted in almost complete elimination of flow separation. There was also a marked improvement in the downstream boundary-layer state. A low-frequency bubble breathing oscillation was identified in the baseline interaction using high-speed shadowgraphy and particle image velocimetry measurements. This oscillation was strongly suppressed in the controlled interactions. Velocity fluctuations in the downstream boundary layer were also significantly reduced. We propose that the key mechanism by which flow separation is eliminated is by breaking down the overall pressure rise into smaller steps, each of which is below the separation threshold. A key feature is the bump crest expansion fan, located near to where the incident shock terminates, which negates the shock induced pressure jump. Thus, the precise bump geometry is critical for control efficacy and should be designed to manage these pressure rise steps as well as the expansion fan strength and location with respect to the incident shock wave. The length of the bump faces must also be sufficiently long for the boundary layer to recover between successive adverse pressure jumps.

The high-Rayleigh-number asymptotic behaviour of three-dimensional steady exact coherent states (ECS) in Rayleigh–Bénard convection is studied. The steady square and hexagonal convection cell states, whose horizontal scales are optimised to maximise Nusselt number, persist into the Rayleigh-number regime where a clear asymptotic trend emerges. A detailed asymptotic analysis of the governing equations reinforces that this trend persists in the limit of infinite Rayleigh number, with the corresponding Nusselt number following the classical scaling to leading order. The optimised Nusselt number of the three-dimensional ECS far exceeds that of the two-dimensional roll solutions, which are believed to bound currently available experimental and simulation results, reaching nearly twice the typical experimental values. This is an interesting result from an applied perspective, although our solutions are unstable at high Rayleigh numbers.

Triply periodic minimal surfaces (TPMS)-based media (a type of metamaterial) are defined by mathematical expressions, which are amenable to additive manufacturing, and are finding increasing practical applications owing to their porous nature. We present experimental pressure drop measurements for a range of velocities spanning laminar to turbulent regimes for three TPMS geometries – gyroid, primitive and body-centred cubic (BCC) – with different porosity, unit cell length and surface finish. Dimensional Darcy and Forchheimer permeabilities are estimated via quadratic fitting for the gyroid geometry, which closely resembles random packed porous media. Subsequently, the non-dimensional drag (${\kern-0.5pt}f$) is plotted against Reynolds number ($Re$) yielding distinct curves for each case. The lack of collapse stems from varying definitions of pore diameter, complicating comparisons across porous media (not just TPMS). Therefore, a method is developed to estimate an equivalent hydraulic diameter $d_{{H\hbox{-}\textit{equ}}}$ from pressure drop data by matching the laminar drag $f$ of packed spheres via the Ergun equation, allowing the collapse of all porous media $f-Re$ curves in the laminar regime. The value of $d_{ {H\hbox{-}\textit{equ}}}$ is related to the ‘true’ Darcy permeability defined strictly in the linear regime (unlike permeability from quadratic fitting). We observe an approximate linear relationship between the $d_{ {H\hbox{-}\textit{equ}}}$ and the hydraulic diameter for self-similar TPMS configurations. The common basis of $d_{ {H\hbox{-}\textit{equ}}}$ allows intercomparison of TPMS geometries, and shows that BCC achieves significant drag reduction compared with packed spheres in the turbulent regime partially because of their open tube-like structure, whereas some configurations show drag increase. Although gyroid can be represented using the traditional quadratic drag law, primitive and BCC show an increase in $f$ with increasing $Re$ immediately before transitioning to fully turbulent regime – akin to rough-wall pipe flows, likely owing to their periodic streamwise elongated open structures.

A linear theory for unsteady aerodynamic effects of the actuator line method (ALM) is developed. This theory is validated using two-dimensional ALM simulations, where we compute the unsteady lift generated by the plunging and pitching motion of a thin aerofoil in uniform flow, comparing the results with Theodorsen’s theory. This comparison elucidates the underlying characteristics and limitations of ALM when applied to unsteady aerodynamics. Numerical simulations were conducted across a range of chord lengths and oscillation frequencies. Comparison of ALM results with theoretical predictions shows consistent accuracy, with all Gaussian parameter choices yielding accurate results at low reduced frequencies. Furthermore, the study indicates that selecting a width parameter ratio of $\varepsilon /c$ (the Gaussian width parameter over the chord length) between 0.33 and 0.4 in ALM yields the closest alignment with analytical results across a broader frequency range. Additionally, a proper definition of angle of attack for a pitching aerofoil is shown to be important for accurate computations. These findings offer valuable guidance for the application of ALM in unsteady aerodynamics and aeroelasticity.

We investigate the influence of shear-thinning and viscoelasticity on turbulent drag reduction in lubricated channel flow – a configuration where a thin lubricating layer of non-Newtonian fluid facilitates the transport of a primary Newtonian fluid. Direct numerical simulations are performed in a channel flow driven by a constant mean pressure gradient at a reference shear Reynolds number $\textit{Re}_\tau = 300$. The interface between the two fluid layers is characterised by Weber number $\textit{We} = 0.5$. The fluids are assumed to have matched densities. In addition to a single-phase reference case, we analyse four configurations: a Newtonian lubrication layer, a shear-thinning Carreau fluid layer, a shear-thinning and viscoelastic FENE-P fluid layer, and a purely viscoelastic FENE-CR fluid layer. Consistent with previous findings (Roccon et al. 2019, J. Fluid Mech., vol. 863, R1), surface tension is found to induce significant drag reduction across all cases. Surprisingly, variations in the lubricating layer viscosity do not yield noticeable drag-reducing effects: the Carreau fluid, despite its lower apparent viscosity, behaves similarly to the Newtonian case. In contrast, viscoelastic effects lead to a further reduction in drag, with both the FENE-P and FENE-CR fluids demonstrating enhanced drag-reducing capabilities.

This study investigates the wake dynamics of a wall-mounted square cylinder with an aspect ratio of 2, subjected to varying inflow turbulence intensities, employing high-fidelity large-eddy simulation complemented by spectral proper orthogonal decomposition. The simulations are conducted at a Reynolds number of 43 000. A synthetic momentum source term is integrated within the Navier–Stokes equations to generate turbulence consistent with the von Kármán spectrum. Four inflow cases, comprising an undisturbed inflow and three disturbed inflows with turbulence intensities of 10 %, 20 % and 30 %, are examined to elucidate their impact on vortex shedding, shear-layer behaviours and coherent structures. Results demonstrate that increased turbulence intensity significantly modifies vortex coherence, suppresses recirculation regions, promotes earlier shear-layer reattachment on the top surface and leads to reattachment of the shear layer on the side surface. Spectral proper orthogonal decomposition analysis, conducted on 17 orthogonal planes in the streamwise (x), wall-normal (y) and spanwise (z) directions, reveals two dominant energetic frequencies: a primary vortex-shedding frequency around a Strouhal number of 0.084, and a secondary high frequency associated with Kelvin–Helmholtz instabilities. The imposed turbulence effectively redistributes spectral energy, diminishing the coherence and altering the spatial organisation of vortical structures. These findings enhance fundamental understanding of turbulent wake dynamics and flow–structure interactions in bluff-body flows.

Fully resolved three-dimensional simulations of planar gravity currents are conducted to investigate the influence of imposed spanwise perturbations on flow evolution and mixing at two Reynolds numbers ($ \textit{Re}=3450$ and 10 000). The initial perturbations consist of sinusoidal waves with a varying number of repeating waves, $k_y$, with simulations spanning $0 \leqslant k_y \leqslant 8$. At low-$ \textit{Re} $, cases with perturbations ($k_y \gt 0$) exhibit a more rapid breakdown of spanwise coherence compared with the unperturbed case ($k_y = 0$), although the resulting structures retain spatial periodicity and remain relatively ordered. This earlier disruption leads to greater front propagation distances beyond the self-similar inertial phase compared with the unperturbed case. Notably, imposed perturbations exhibit minimal influence on the flow transition; all cases follow the slumping velocity reported in the literature, with the transition into the inertial phase occurring at comparable times across different $k_y$ values at both $ \textit{Re} $. The increased propagation speed is accompanied by reduced mixing efficiency due to the premature disruption of coherent Kelvin–Helmholtz (K–H) billows, which play a key role in maintaining multi-scale mixing. At high-$ \textit{Re} $, the influence of initial spanwise perturbations diminishes, as three-dimensional turbulence induces a more chaotic, fine-scale breakdown of spanwise coherence across all $k_y$ cases, overriding the effects of the initial perturbations. Consequently, the dominant stirring mechanism shifts from K–H billows to vortices within the current head. Nevertheless, the unperturbed case maintains comparatively higher mixing efficiency at both low- and high-$ \textit{Re} $. This is attributed to the persistence of recognisable K–H billow structures, which, despite undergoing chaotic breakdown at high-$ \textit{Re} $, still contribute to effective stirring by stretching and folding the density interface. These results highlight the dual role of K–H billows: they promote efficient mixing, yet the enhanced mixing reduces the density difference between the current and the ambient fluid, weakening buoyancy and slowing front propagation despite stronger stirring. These findings are supported by consistent trends in streamwise density distribution and ‘local’ energy exchange analyses.

In many electrochemical systems, variations in fluid density due to salinity gradients are unavoidable, leading to solutally driven Rayleigh–Bénard convection (RBC). In this study, we perform direct numerical simulations and theoretical analyses of two-dimensional solutal convection near perfectly cation-selective membranes by incorporating buoyancy and electrostatic forces into the Navier–Stokes and Poisson–Nernst–Planck equations. When electroconvection (EC) is negligible, we observe a flow reversal of large-scale circulation (LSC) in salt-driven RBC within a square-cavity electrochemical system, triggered by the periodic reconfiguration of corner vortices. Furthermore, we found that the competition between RBC and EC determines the dominant flow pattern. The buoyancy-driven convection and the LSC are suppressed at sufficiently strong EC flow, leading to a transition from buoyancy-driven flow to electrically driven flow. Consequently, the flow structures into a pair of EC vortices, driven by strong electric field forces within the extended space charge layer. Using Grossmann–Lohse theory, we derive a critical scaling law that describes the flow pattern selection, governed by the combined effects of the Rayleigh number, voltage difference and hydrodynamic coupling coefficient. Our work presents a novel approach to controlling flow patterns, distinct from existing strategies in thermally driven RBC.

The acoustically excited vibrations of a micrometric object in a viscous liquid induce a net fluid flow known as microstreaming. This phenomenon can be harnessed for a variety of microscale applications, including particle transport, fluid mixing and the propulsion of micro-swimmers. Acoustic propulsion holds significant promise for in vivo manipulation due to its inherent biocompatibility and remote actuation capability, eliminating the need for an onboard energy source. However, designing steerable swimmers powered by vibrating tails requires a detailed understanding of the relationship between the input acoustic signal and the resulting streaming flow. In this paper, we characterise experimentally and model the microstreaming generated by a vertically standing micro-cantilever attached to a vibrating plate, as a function of the excitation frequency. Significant streaming is observed only at specific frequencies corresponding to the vibration modes of the support, which both translate and bend the cantilever. Computations based on a two-dimensional semi-analytical model enable quantitative predictions of the in-plane streaming flow structure and velocity magnitude, using as input the cantilever’s vibration profile, fully characterised by laser Doppler vibrometry. In particular, comparison between experiments and simulations allows us to rationalise the frequency-dependent emergence of dipolar, circular and elliptical streaming patterns, which are respectively induced by rectilinear, circular and elliptical translations of the cantilever. This analysis also explains the prevalence of elliptical streaming structures observed in our system. Beyond advancing our fundamental understanding of streaming generated by vibrating slender bodies, these results highlight the potential for frequency-based control of micro-swimmers through predictable, mode-specific flow responses.

Recent work (Raufaste et al. 2022 Soft Matter, vol. 18, p. 4944) studied the dynamics of a soap film in the shape of an unstable minimal surface whose evolution is governed in part by the frictional forces associated with surface Plateau border (SPB) motion. In this note, we study a variant of this problem in which a half-catenoid bounded by a wire loop and a fluid bath axisymmetrically surrounds a cylindrical rod with a radius equal to the neck of the critical catenoid given by the wire loop. When the half-catenoid is brought just beyond the point of instability, the film touches the cylinder and separates from the bath, creating an SPB that is dragged upwards along the rod by the now unstable soap film, and asymptotically relaxes to a new stable annular minimal surface. For this free-boundary problem involving an unstable initial condition, we find the dynamics by balancing the capillary force of successive unstable minimal surfaces spanning the SPB and the wire loop with the frictional force associated with the moving SPB. We find good agreement between theory and experiment using the frictional force $f\sim \textit{Ca}^{2/3}$ given by Bretherton’s law, where $ \textit{Ca} $ is the capillary number.

We study the behaviour of a thin fluid filament (a rivulet) flowing in an air-filled Hele-Shaw cell. Transverse and longitudinal deformations can propagate on this rivulet, although both are linearly attenuated in the parameter range we use. On this seemingly simple system, we impose an external acoustic forcing, homogeneous in space and harmonic in time. When the forcing amplitude exceeds a given threshold, the rivulet responds nonlinearly, adopting a peculiar pattern. We investigate the dance’ of the rivulet both experimentally using spatiotemporal measurements, and theoretically using a model based on depth-averaged Navier–Stokes equations. The instability is due to a three-wave resonant interaction between waves along the rivulet, the resonance condition fixing the pattern wavelength. Although the forcing is additive, the amplification of transverse and longitudinal waves is effectively parametric, being mediated by the linear response of the system to the homogeneous forcing. Our model successfully explains the mode selection and phase-locking between the waves, it notably allows us to predict the frequency dependence of the instability threshold. The dominant spatiotemporal features of the generated pattern are understood through a multiple-scale analysis.

In this work we present a framework to explain the prediction of the velocity fluctuation at a certain wall-normal distance from wall measurements with a deep-learning model. For this purpose, we apply the deep-SHAP (deep Shapley additive explanations) method to explain the velocity fluctuation prediction in wall-parallel planes in a turbulent open channel at a friction Reynolds number ${\textit{Re}}_\tau =180$. The explainable-deep-learning methodology comprises two stages. The first stage consists of training the estimator. In this case, the velocity fluctuation at a wall-normal distance of 15 wall units is predicted from the wall-shear stress and wall-pressure. In the second stage, the deep-SHAP algorithm is applied to estimate the impact each single grid point has on the output. This analysis calculates an importance field, and then, correlates the high-importance regions calculated through the deep-SHAP algorithm with the wall-pressure and wall-shear stress distributions. The grid points are then clustered to define structures according to their importance. We find that the high-importance clusters exhibit large pressure and shear-stress fluctuations, although generally not corresponding to the highest intensities in the input datasets. Their typical values averaged among these clusters are equal to one to two times their standard deviation and are associated with streak-like regions. These high-importance clusters present a size between 20 and 120 wall units, corresponding to approximately 100 and 600 $\unicode{x03BC} \textrm {m}$ for the case of a commercial aircraft.

This study conducted theoretical analysis and direct numerical simulations (DNS) of vertical natural convection in a two-dimensional cavity filled with porous media, where the imposed temperature gradient is oriented perpendicular to the direction of gravity. Three regimes characterised by distinct flow states and the angle $\theta$ of the isothermal layer are identified. In the steady regime I with $\theta \approx \pi /2$, the flow is weak and heat transfer is dominated by conduction. In the transitional regime II with rapidly increasing $\theta$, kinetic and thermal boundary layers gradually develop. In the turbulent regime III with $\theta \approx 0$, clear boundary layers arise and turbulent thermal convection prevails. Corresponding to these flow states, theoretical analysis is performed to derive the scaling laws of the Nusselt number $\textit{Nu}-1\sim Ra_{D}^{\gamma _1 }\textit{Pr}^{\eta _1}$ and Reynolds number $\textit{Re}\sim Ra_{D}^{\gamma _2 }\textit{Pr}^{\eta _2}$ with respect to Rayleigh–Darcy number $Ra_D$ and Prandtl number $\textit{Pr}$. We derive $(\gamma _1,\gamma _2,\eta _1,\eta _2)=(2,1,0,-1)$ for the steady regime and $(1/3,4/9,0,-2/3)$ for the turbulent regime. All theoretical scaling exponents in these two regimes are validated by DNS results. Furthermore, we find that the influence of the Darcy number $Da$ becomes almost negligible when it is sufficiently small. Unified models for $\textit{Pr}=1$ are proposed to integrate the three regimes and are applicable across a broad range of $\phi$ and $Ra_D$, which are satisfactorily verified by DNS results. The unified models provide a predictive framework for heat transport and flow intensity in porous-medium thermal convection, thereby offering practical values for thermal engineering applications.