In the gap region of tandem cylinders, within the reattachment regime, bi-stability is seen to be cellular. Direct numerical simulations at a Reynolds number of 500, and a gap ratio of 3.0, show that shedding of gap vortices occurs in spanwise cells, with lengths between 0.3 and 2.7 cylinder diameters. These unstable vortex cells tend to be asymmetric with respect to the gap centreline, so that vortices are repeatedly shed from just one gap shear layer for several periods. The unstable cells appear within the basic spanwise cell structure dictated by the three-dimensional instability, and their cell lengths do not exceed those of the basic cells. Unstable cells intermittently become spanwise coherent, and this leads to a significant increase in drag amplitude. The mode change in the gap is associated with low-frequency variation of the reattachment and separation points on the downstream cylinder, causing low-frequency modulation of the vortex formation length.

The instability and vortex shedding in the bottom boundary layer caused by internal solitary waves of depression propagating along a shallow pycnocline of a fluid are computed by finite-volume code in two dimensions. The calculated transition to instability agrees very well with laboratory experiments (Carr et al., Phys. Fluids, vol. 20, issue 6, 2008, 06603) but disagrees with existing computations that give a very conservative instability threshold. The instability boundary expressed by the amplitude depends on the depth $d$ of the pycnocline divided by the water depth $H$, and decays by a factor of 2.2 when $d/H$ is 0.21, and by a factor of 1.6 when $d/H$ is 0.16, and the stratification Reynolds number increases by a factor of 32. The instability occurs at moderate amplitude at large scale. The calculated oscillatory bed shear stress is strong in the wave phase and increases with the scale. Its non-dimensional magnitude at stratification Reynolds number 650 000 is comparable to the turbulent stress that can be extracted from field measurements of internal solitary waves of similar nonlinearity, moving along a pycnocline of similar relative depth.

The two-dimensional stability of vertically sheared inertial oscillations at ocean fronts is explored through a linear stability analysis and nonlinear simulations. Baroclinic effects reduce the minimum frequency of inertia-gravity waves to an extent determined by the balanced Richardson number ${{Ri}}$ of the front. Below a critical value of ${{Ri}}$, which depends on the strength of the inertial shear, the inertial oscillations become unstable to parametric subharmonic instability (PSI) resulting in growing perturbations that oscillate at half the inertial frequency $f$. Since the critical value is always greater than 1, PSI can occur at fronts stable to symmetric instability. Although modest in weak inertial shear, growth rates exceeding $f/2$ can be achieved for inertial shear greater than or equal to the thermal wind shear. Our formulation allows for non-hydrostatic perturbations and can be applied to initially unstratified geostrophic adjustment problems. We find that PSI will almost totally damp the transient oscillations that arise during geostrophic adjustment. The perturbations gain energy at the expense of the inertial oscillations through ageostrophic shear production. The perturbations then themselves become unstable to secondary Kelvin–Helmholtz instabilities creating a pathway by which the inertial oscillations can be dissipated rapidly. In contrast to symmetric and baroclinic instabilities that draw on a front's kinetic or potential energy, PSI acts to increase the energy stored in the balanced front as the convergence and divergence of the eddy-momentum fluxes set up a secondary circulation in the sense to stand up the front.

Self-organization of the vorticity condensate of forced two-dimensional turbulence is examined in analogy with the mixing of a background planetary vorticity gradient in geophysical flows. Starting from the theoretical vorticity profile of the condensate, different scenarios are illustrated by the construction of idealized angular momentum conserving rearrangements of vorticity into a staircase profile similar to the potential vorticity staircase of $\beta$-plane turbulence. Two sets of numerical experiments are then presented that illustrate a similar self-organization of the background vorticity gradient in fully turbulent flows. In the first set of experiments, the flow is initialized with a laminar vortex dipole corresponding to the theoretical condensate vorticity profile. A fluctuation vorticity field is then induced by a stochastic forcing at smaller scales, which induces an azimuthally symmetric self-organization of the laminar flow into distinct annular bands. In the second set of experiments, the flow is initialized from rest with stochastic forcing generating a turbulent inverse energy cascade, out of which emerges the condensate in a self-consistent evolution as the turbulent energy accumulates at the domain scale. A self-organization of the condensate is again observed, giving a distinct annular structure on top of the theoretically predicted condensate profile. A major difference from the potential vorticity staircase of geophysical flows is the emergence in many cases of significantly non-monotonic radial vorticity profiles.

In this study, the transport equation for scalar iso-surface area density ($\varSigma$) in a turbulent, temporally developing mixing layer is examined. Exploring the spatial and temporal evolution of the terms in the $\varSigma$ transport equation is vital to improving our understanding of turbulent flows characterized by distinct interfaces, e.g. the flame surface or the turbulent/non-turbulent interface. Previous work reported by the authors identified that $\varSigma$ exhibits self-similar behaviour consistent with the development of the temporal mixing layer (Blakeley et al., J. Fluid Mech., vol. 951, 2022, A44). Accordingly, each of the terms in the $\varSigma$ transport equation is found to behave in a self-similar manner, though there are notable differences in the self-similar behaviours for each term. Based on the results presented herein, it is suggested that the rate of change of $\varSigma$ ($\partial \varSigma /\partial t$) and the advection term scale with $h\lambda _\varPhi /\Delta U$, where $h$ is the width of the mixing layer, $\lambda _\varPhi$ is the scalar Taylor length scale and $\Delta U$ is the velocity difference. The production and destruction terms are found to scale with an additional factor $({Re}\,Sc)^{1/2}$. In contrast, the molecular diffusion term is found to scale with a factor $({Re}\,Sc)^{-1/2}$ compared to $\partial \varSigma /\partial t$. Importantly, it is found that the difference between the production and destruction terms, or net surface ‘stretch’, scales with the same factor as $\partial \varSigma /\partial t$ and the advection term, which may have a significant impact on how the evolution of $\varSigma$ is understood and modelled in turbulent flows.

Active emulsions can spontaneously form self-propelled droplets or phoretic micropumps. However, it remains unclear how these active systems interact with their self-generated chemical fields, which can lead to emergent chemodynamic phenomena and multistable interfacial flows. Here, we simultaneously measure the flow and chemical concentration fields using dual-channel fluorescence microscopy for active micropumps, i.e. immobilised oil droplets that dynamically solubilise in a supramicellar aqueous surfactant solution. With increasing droplet radius, we observe (i) a migration of vortices from the posterior to the anterior, analogous to a transition from pusher- to puller-type swimmers, (ii) a bistability between dipolar and quadrupolar flows and, eventually, (iii) a transition to multipolar modes. We also investigate the long-time dynamics. Together, our observations suggest that a local build-up of chemical products leads to a saturation of the surface, which controls the propulsion mechanism. These multistable dynamics can be explained by the competing time scales of slow micellar diffusion governing the chemical buildup and faster molecular diffusion powering the underlying transport mechanism. Our results are directly relevant to phoretic micropumps, but also shed light on the interfacial activity dynamics of self-propelled droplets and other active emulsion systems.

A large-scale, fully resolved direct simulation Monte Carlo (DSMC) computation of a non-equilibrium, reactive flow of pure oxygen over a double cone is presented. Under the simulated near-continuum conditions, the computational demands are shown to be significant because of the wide range of length scales that must be resolved. Therefore, robust grid adaption capabilities and efficient parallelization of the Stochastic PArallel Rarefied-gas Time-accurate Analyzer (SPARTA) code that is utilized in this work are essential. The thermochemical and transport collision models were selected for efficiency and simplicity. First-principles data, obtained from the highly accurate direct molecular simulation method, were used to inform the collision models’ parameters. Importantly, because SPARTA implements molecular collision models using collision-specific energies, the resulting macroscopic relaxation rates were evaluated a posteriori via zero-dimensional heat bath simulations. The comparisons of surface properties, namely heat flux and pressure, show very close agreement with previous computational fluid dynamics (CFD) results. Differences with the measurements were found to be similar to the CFD simulations. The unresolved discrepancy with the measurements could be due to inconsistent free stream conditions with the actual experimental data or missing physical phenomena altogether, for example atomic and molecular oxygen electronically excited states, three-dimensional effects, or more complex gas–surface interactions. As shown in this work, the advantages of obtaining a DSMC particle solution for these flows reside in the method's ability to be directly informed from first principles and to seamlessly describe internal energy non-equilibrium for all modes. With the advent of exascale computing and beyond, particle methods will be an increasingly important tool to verify the validity of physical assumptions in reduced-order models via fully resolved, experimental-scale simulations, down to the level of molecular-level distributions.

Near-wall flow simulation remains a central challenge in aerodynamics modelling: Reynolds-averaged Navier–Stokes predictions of separated flows are often inaccurate, and large-eddy simulation (LES) can require prohibitively small near-wall mesh sizes. A deep learning (DL) closure model for LES is developed by introducing untrained neural networks into the governing equations and training in situ for incompressible flows around rectangular prisms at moderate Reynolds numbers. The DL-LES models are trained using adjoint partial differential equation (PDE) optimization methods to match, as closely as possible, direct numerical simulation (DNS) data. They are then evaluated out-of-sample – for aspect ratios, Reynolds numbers and bluff-body geometries not included in the training data – and compared with standard LES models. The DL-LES models outperform these models and are able to achieve accurate LES predictions on a relatively coarse mesh (downsampled from the DNS mesh by factors of four or eight in each Cartesian direction). We study the accuracy of the DL-LES model for predicting the drag coefficient, near-wall and far-field mean flow, and resolved Reynolds stress. A crucial challenge is that the LES quantities of interest are the steady-state flow statistics; for example, a time-averaged velocity component $\langle {u}_i\rangle (x) = \lim _{t \rightarrow \infty } ({1}/{t}) \int _0^t u_i(s,x)\, {\rm d}s$. Calculating the steady-state flow statistics therefore requires simulating the DL-LES equations over a large number of flow times through the domain. It is a non-trivial question whether an unsteady PDE model with a functional form defined by a deep neural network can remain stable and accurate on $t \in [0, \infty )$, especially when trained over comparatively short time intervals. Our results demonstrate that the DL-LES models are accurate and stable over long time horizons, which enables the estimation of the steady-state mean velocity, fluctuations and drag coefficient of turbulent flows around bluff bodies relevant to aerodynamics applications.

We experimentally investigate the transport of liquid by a toroidal bubble that rises vertically and penetrates a horizontal interface between two immiscible liquids. Experiments are conducted with various strengths of vortex circulation in the bubble, and with different liquid densities and viscosities. In contrast to a spherical bubble, a rising toroidal bubble carries a great amount of the lower liquid by virtue of the self-induction of circulating flow. The lower liquid is entrained by the toroidal bubble and forms an ellipsoidal body enclosing the bubble after it penetrates the interface. The downward net force acting on the ellipsoidal body results in the radial contraction of the bubble, reducing the volume of the entrained lower liquid. As the entrained volume decreases, the nearby upper liquid eventually pierces the ellipsoidal body, making the bubble unstable. At this instant, the net force acting on the ellipsoidal body approaches zero, and the volume ratio of the entrained lower liquid and bubble converges to a specific value. For smaller vortex circulation and larger density difference between the liquids, the volume of the entrained lower liquid within the ellipsoidal body becomes smaller and the travel distance of the bubble from the initial interface until it becomes unstable decreases. The effective Froude number, which accounts for both the inertial effect of vortex circulation and the gravitational effect of liquid density difference, is found to characterise the temporal changes in the ring radius, propagation speed and entrained volume.

A flat-plate turbulent boundary layer (TBL) is experimentally subjected to a family of 22 favourable–adverse pressure gradients (FAPGs) using a ceiling panel of variable convex curvature. We define FAPGs as a sequence of streamwise pressure gradients in the order of favourable followed by adverse, similar in sequence to the pressure gradients over the suction side of an airfoil. For the strongest pressure gradient case, the acceleration parameter, $K$, varied spatially from $6 \times 10^{-6}$ to $- 4.8 \times 10^{-6}$. The adverse pressure gradient (APG) region of this configuration is studied using particle image velocimetry in the streamwise–wall-normal plane. The statistics of the APG TBL show that the upstream favourable pressure gradient (FPG) exerts a strong and lasting downstream influence, and that the rapid spatial changes in the pressure gradients imposed cause an internal boundary layer to grow within the TBL for 15 of the cases studied. The internal layer typically occupies 20 $\%$ of the boundary layer thickness and dominates the boundary layer response, containing the peak turbulent production, peak strength and population of vortices, and most of the spectral energy content of the flow. The outer layer, on the other hand, develops in the APG region without considerable changes to the state dictated by the upstream FPG. These trends are in contrast to APG TBLs that originate from a zero pressure gradient region, where the outer/wake region is known to dominate TBL response. The observed changes are quantified across the family of FAPGs imposed.

Ventilated cavitating flows are investigated via direct numerical simulations, using a coupled level set and volume of fluid method to capture the interface between the air and water phases. A ventilated disk cavitator is used to create the cavity and is modelled by a sharp-interface immersed boundary method. The simulation data provide a comprehensive description of the two-phase flow and the air leakage and vortex shedding processes in the cavitating flow. The mean velocity of the air phase suggests the existence of three characteristic flow structures, namely the shear layer (SL), recirculating area (RA) and jet layer (JL). The turbulent kinetic energy (TKE) is concentrated in the JL in the closure region, and streamwise turbulent fluctuations dominate transverse fluctuations in both SL and JL. Budget analyses of the TKE show that the production term causes the TKE to increase in the SL due to the high velocity gradients, and decrease in the JL due to streamwise stretching effects. Air leakage and vortex shedding occur periodically in the closure region, and the one-to-one correspondence between these two processes is confirmed by the velocity and volume fluid spectra results, and the autocorrelation function of the air volume fraction. Moreover, the coherent flow structures are analysed using the spectral proper orthogonal decomposition method. We identify several fine coherent structures, including $SL_{KH}$ induced by the Kelvin–Helmholtz instability, $SL_{out}$ associated with large-scale vortex shedding, $SL_{in}$ associated with small-scale vortex shedding, and $SL_{r}$ associated with upstream turbulent convection. The present study complements previous research by providing detailed descriptions of the turbulent motions associated with the violent mixing of air and water, and the complex interactions between different characteristic structures in cavitating flows.

The water surface response to subcritical turbulent flow over a backward-facing step (BFS) is studied via high-resolution large-eddy simulation (LES). The LES method is validated first using data of previously reported experiments. The LES-predicted water surface is decomposed into different types of gravity waves as well as turbulence-driven forced waves. Analysis of the LES data reveals the interplay between low-frequency large-scale turbulence structures, which are the result of flow separation from the step and reattachment behind the step, and the dynamics of the water surface. The water surface deformation is mainly the result of freely propagating gravity waves and forced waves, owing to turbulence in the form of rollers and/or hairpin vortices. Gravity waves with zero group velocity define the characteristic spatial and temporal scales of the surface deformations at higher frequencies, while large eddies determine their low-frequency modulation. These deformations are mainly confined in lateral bands that propagate downstream following the advection of the near-surface streamwise vortices (rollers) that are shed from the step. Steeper surface waves are observed in regions of negative perturbation velocity gradient and down-welling, downstream of the larger rollers, and are associated with thin isolated regions of high vorticity near the surface. The investigation of such a complex flow has shown that the decomposition of the water surface fluctuations into its different physical components may be used to identify the dynamics of the underlying flow structure.

The dynamics of suspensions of particles has been an active area of research since Einstein first calculated the leading-order correction to the viscosity of a suspension of spherical particles (Einstein, Proc. R. Soc., vol. A102, 1906, pp. 161–179). Since then, researchers have strived to develop an accurate description of the behaviours of suspensions that goes beyond just leading order in the particle volume fraction. Here, we consider the low-Reynolds-number behaviour of a suspension of spherical particles. Working from the Green's functions for the flow due to a single particle, we derive a continuum-level description of the dynamics of suspensions. Our analysis corrects an error in the derivation of these equations in the work of Jackson (Chem. Engng Sci., vol. 52, 1997, pp. 2457–2469) and leads to stable equations of motion for the particles and fluid. In addition, our resulting equations naturally give the sedimentation speed for suspended particles and correct a separate error in the calculation by Batchelor (J. Fluid Mech., vol. 52, 1972, pp. 245–268). Using the pair-correlation function for hard spheres, we are able to compute the sedimentation speed out to seventh order in the volume fraction, which agrees with experimental data up to 30 %–35 %, and also get higher-order corrections to the suspension viscosity, which agree with experiments up to $\sim$15 %. Then, using the pair distribution for spheres in shear flow, we find alterations to both the first and second normal stresses.

When an immiscible oil drop is immersed in a stably stratified ethanol–water mixture, the Marangoni flow on the surface of the drop can experience an oscillatory instability, so that the drop undergoes a transition from levitating to bouncing. The onset of the instability and its mechanisms have been studied previously (Li et al., Phys. Rev. Lett., vol. 126, 2021, 124502; Li et al., J. Fluid Mech., vol. 932, 2022, A11), yet the bouncing motion of the drop itself, which is a completely different problem, has not yet been investigated. Here we study how the bouncing characteristics (jumping height, rising and sinking time) depend on the control parameters (drop radius, stratification strength, drop viscosity). We first record experimentally the bouncing trajectories of drops of different viscosities in different stratifications. Then a simplified dynamical analysis is performed to get the scaling relations of the jumping height and the rising and sinking times. The rising and sinking time scales are found to depend on the drag coefficient $C_D^S$ of the drop in the stratified liquid, which is determined empirically for the current parameter space (Zhang et al., J. Fluid Mech., vol. 875, 2019, 622–656). For low-viscosity (5 cSt) oil drops, the results on the drag coefficient match those from the literature (Yick et al., J. Fluid Mech., vol. 632, 2009, pp. 49–68; Candelier et al., J. Fluid Mech., vol. 749, 2014, pp. 184–200). For high-viscosity (100 cSt) oil drops, the parameter space had not been explored and the drag coefficients are not readily available. Numerical simulations are therefore performed to provide external verification for the drag coefficients, which well match with the experimental results.

The flow in and around a pair of plumes from sources that are vertically and horizontally offset is investigated. An analytical potential flow model is developed using an adapted version of the Milne–Thomson circle theorem to represent the flow due to adjacent circular and point sinks. This approximates the horizontal section through offset plumes, which have differing radii at the same vertical position. The predictions of this model are compared against Reynolds-averaged Navier–Stokes (RANS) simulations of the same system. These yield time-averaged results and so are particularly suitable for investigating the relatively weak entrainment field. Single and double plume results from RANS are also presented to compare with known results. Good agreement is found between the features in the analytical model and in the numerical solutions including the location of the stagnation point between the two plumes.

We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to $W/H=1.2$, while the length-to-height ratio $1/6< L/H<3$ covers a wide range of geometries from thin plates to elongated Ahmed bodies. First, global linear stability analysis yields a series of pitchfork and Hopf bifurcations: (i) at lower Reynolds numbers $Re$, two stationary modes, $A$ and $B$, become unstable, breaking the top/bottom and left/right planar symmetries, respectively; (ii) at larger $Re$, two oscillatory modes become unstable and, again, each mode breaks one of the two symmetries. The critical $Re$ values of these four modes increase with $L/H$, reproducing qualitatively the trend of stationary and oscillatory bifurcations in axisymmetric wakes (e.g. thin disk, sphere and bullet-shaped bodies). Next, a weakly nonlinear analysis based on the two stationary modes $A$ and $B$ yields coupled amplitude equations. For Ahmed bodies, as $Re$ increases, state $(A,0)$ appears first, followed by state $(0,B)$. While there is a range of bistability of those two states, only $(0,B)$ remains stable at larger $Re$, similar to the static wake deflection (across the larger base dimension) observed in the turbulent regime. The bifurcation sequence, including bistability and hysteresis, is validated with fully nonlinear direct numerical simulations, and is shown to be robust to variations in $W$ and $L$ in the range of common Ahmed bodies.

We examine the structure of the continuous circular hydraulic jump and recirculation for a jet impinging on a disk. We use a composite mean-field thin-film approach consisting of subdividing the flow domain into three regions of increasing gravity strength: a developing boundary layer near impact, an intermediate supercritical viscous layer and a region comprising the jump and subcritical flow. Unlike existing models, the approach does not require any empirically or numerically adjusted boundary conditions. We demonstrate that the stress or corner singularity for a film draining at the edge is equivalent to an infinite slope of the film surface, which we impose as the downstream boundary condition. The model is validated against existing experiment and numerical simulation of the boundary-layer and Navier–Stokes equations. We find that the flow in the supercritical region remains insensitive to the change in gravity level but is greatly affected by viscosity. The existence of the jump is not necessarily commensurate with the presence of recirculation, which is strongly dependent on the upstream curvature and steepness of the jump.

Utilizing a fan-stirred chamber and two-dimensional particle image velocimetry, we analyse the modification of homogeneous and isotropic turbulence ($50 \leq Re_\lambda \leq 140$, with supplementary data out to $Re_\lambda = 310$, where $Re_\lambda$ is the longitudinal Taylor Reynolds number) induced by both a non-volatile (water) and a volatile (ethanol) isolated and anchored droplet in the range $(0.3 \leq d/\eta \leq 5.1)$, where $d/\eta$ is the ratio of droplet diameter to the Kolmogorov length scale. The dissipation rate, $\varepsilon$, is calculated via the corrected spatial gradient method, and the resultant fields of both turbulent kinetic energy, $k$, and $\varepsilon$ are presented as spatial heat maps and as shell averages, ${\overline {k_{\Delta r}}}$ and ${\overline {\varepsilon _{\Delta r}}}$, vs the radial coordinate normalized by the droplet radius, $r/R$. The dissipation rate near the water droplet surface may exceed the corresponding unladen flow value by a factor of twenty or more. The normalized radius of recovery, $r^*$, which designates the radial location where ${\overline {k_{\Delta r}}}$ or ${\overline {\varepsilon _{\Delta r}}}$ has returned to within 10 % of the unladen value, is reasonably expressed as $r^* \propto (d/\lambda )^{-C_2}$ in either case, where $\lambda$ is the longitudinal Taylor microscale and $C_2$ is a positive empirical fitting parameter. Recovery of ${\overline {k_{\Delta r}}}$ and ${\overline {\varepsilon _{\Delta r}}}$ may take up to 14 normalized radii when $d/\lambda$ is small. Trend line extrapolation suggests that the attenuation region becomes negligible as $d/\lambda \to 1$. Ethanol, which evaporates up to five times faster than water, induces a much smaller dissipation spike near the surface. The mass ejection phenomenon appears to reduce the strong near-surface damping of the radial root-mean-square component. However, the radius of recovery trend for fields surrounding a volatile ethanol droplet falls directly in line with the non-volatile water droplet data for both $k$ and $\varepsilon$, indicating that droplet vaporization has little effect on the far-field return to isotropy.

This paper discusses how the submergence ratio, defined as the ratio between the flow depth, D, and the height, h, of the solid rigid cylinders forming the array affects flow and turbulence structure inside and around a rectangular array of cylinders placed adjacent to one of the channel sidewalls. As the array becomes submerged, a vertical shear layer develops in between the top face of the array and the free surface, which strongly increases flow three-dimensionality and modifies how the momentum exchange between the array and the surrounding open water regions occurs with respect to the case of an emerged array where only a horizontal shear layer forms as part of the incoming flow approaching the array is deflected laterally. Eddy-resolving simulations are conducted for several values of the solid volume fraction, ϕ, and of the submergence ratio, 1.0 ≤ D/h ≤ 4.0. Similar to the limiting case of an emerged array (D/h = 1.0), the width- and depth-averaged streamwise velocity inside the array reaches a constant value after an initial adjustment region in the submerged-array cases. For D/h ≥ 1.33, the mean normal velocities through the top and side faces of the array do not become equal to zero downstream of the initial adjustment region. The flow inside the array reaches an equilibrium regime where the local flux of fluid leaving the array through its side face is balanced by the local flux of fluid entering the array through its top face. This regime is observed until close to the end of the array. For D/h ≥ 2.0, the horizontal shear layer vortices do not generate successive regions of high and low streamwise velocity and bed friction velocity inside the array, as is observed in the emerged cases. With respect to the emerged case, the size of the shear layer vortices and the shear layer width increase for low submergence ratios before decreasing rapidly for D/h ≥ 1.33. Significant three-dimensional effects are present inside the array and the horizontal shear layer for cases with both emerged and submerged arrays. In the ϕ = 0.08 cases, strong upwelling and downwelling motions are observed inside the array for D/h ≥ 1.33, while the circulation of the streamwise-oriented cell of secondary flow forming close to the lateral face of the array peaks when the submergence ratio is close to 1.33. For constant ϕ, the total streamwise drag force normalized with the height and width of the array increases with increasing submergence ratio. As the array submergence increases, the cylinders near the front of the array contribute less to the total force acting on the cylinders forming the array. For constant D/h, the total streamwise drag force acting on the array increases with ϕ for the submerged and emerged cases.

We experimentally evaluate whether active wall-normal surface deformations are suitable for the targeted control of very-large-scale motions (VLSMs) in a turbulent boundary layer at a friction Reynolds number of $Re_\tau =2600$. Circular surface deformations with a diameter $D$ roughly equal to the boundary layer thickness $\delta$ are generated periodically at a constant amplitude of $0.03\delta$ and at actuation frequencies of $St=0.05$ to 0.20, where $St$ is the Strouhal number based on $D$ and the free stream velocity $U_\infty$. The resulting impact on the flow was captured using high-speed particle image velocimetry and analysed using a triple decomposition. We find that the active surface deformations produce high- and low-speed streamwise velocity fluctuations that are concentrated along the centreline of the actuator. These motions have a negligible impact on the mean velocity profile downstream, i.e. they are truly high and low speed with respect to the unactuated base flow. The motions produced at $St\lesssim 0.1$ are comparable to synthetic VLSMs in terms of their lengths and widths but with a reduced wall-normal extent and rapidly decaying strength. These synthetic motions produce a strong modulation of the turbulence similar to that of the naturally occurring VLSMs. Most notably, we observe that synthetic high-speed motions with magnitudes of the order of $0.05U_\infty$ cause up to a 30 % reduction in turbulence production within the logarithmic layer. The strength and turbulence-modulating characteristics of the synthetic motions appear well suited for targeting the naturally occurring VLSMs locally using a control scheme.