The effect of single perforations and their location on the drag and reconfiguration of flexible plates was explored through laboratory experiments and direct numerical simulations. The plates were subjected to uniform flows with negligible turbulence, and the perforations had a square cross-section resulting in a low porosity ratio of $\gamma \approx 0.028$. Rigid plates with and without perforations and flexible plates without perforations served as the baseline cases. The perforated plates exhibited distinct jets through the openings in the wake, significantly impacting the aerodynamic force and plate deformation. The velocity and position of the centre jet velocity in relation to downwind distance were influenced by both the incoming flow and the location of the perforations. The centre jet velocity profiles were normalized using an effective velocity and corrected perforation half-width, revealing their dependence on these factors. A simple first-order formulation was developed to predict the change in drag for various perforated plates under a wide range of incoming velocities. This formulation was supported by numerical simulations across a wider range of Cauchy number to confirm the proposed model and separate the effect of the Cauchy and Reynolds numbers. The results of this study may inform the design of flexible structures, define effective porosity and serve as an initial step towards modelling the complex interaction between flow and structures with low porosity.

Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically investigated. Here, we fill this gap by identifying and exploring the complete parameter space associated with periodic deformations in the context of a one-dimensional model problem. We use large-deformation poroelasticity to consider a wide range of loading periods and amplitudes. We identify two distinct mechanical regimes, distinguished by whether the loading period is slow or fast relative to the characteristic poroelastic timescale. We develop analytical solutions for slow loading at any amplitude and for infinitesimal amplitude at any period. We use these analytical solutions and a full numerical solution to explore the localisation of the deformation near the permeable boundary as the period decreases and the emergence of nonlinear effects as the amplitude increases. We show that large deformations lead to asymmetry between the loading and unloading phases of each cycle in terms of the distributions of porosity and fluid flux.

The collision of binary droplets plays a key role in several industrial, chemical and biological processes. In these processes, the quality of the desired outcome is strongly dependent on the mixing of the liquid droplets as they collide in mid-air. In this work, multiphase direct numerical simulations based on the volume-of-fluid method have been used to investigate the process of mixing and analyse the effects of parameters such as injection velocity, timing and collision angles. The evolution of mixing due to convection and irreversible diffusive processes has been quantified by means of the segregation parameter. To synthesise the outcome of a collision, the impact parameter has been redefined to account for the collision of non-spherical droplets. It has been found that the optimal mixing does not occur for symmetric head-on collisions, but rather at moderately asymmetrical configurations. This behaviour has been explained by analysing the velocity gradient tensor. It has been demonstrated that by breaking the symmetry, the local topology of the flow is altered and the resulting convective flows increase the contact area between the liquids, thereby augmenting the mixing process. However, it was also observed that lateral misalignment transforms the initial kinetic energy into the spinning of the merged droplets, thus preventing an enhanced mixing.

Many geological layers include cross bedding, which leads to different values for permeability along and across the bedding planes. We explore how such cross bedding impacts buoyancy-driven flow through an inclined aquifer. For each bedding angle and ratio of the permeability along and across the bedding, a free buoyancy-driven plume rises at a particular angle to the horizontal. If the angle of inclination of the aquifer to the horizontal is smaller than this angle, then the plume rises along the upper boundary, otherwise, somewhat surprisingly, the buoyant plume rises along the lower boundary of the aquifer. We present new laboratory experiments to support these predictions. We also test a model for the effective permeabilities which control the speed and the rate of spread of the plume along one or other boundary of the aquifer. We consider the impact of our results for modelling geological storage of ${\rm CO}_2$ or aquifer thermal energy storage.

This study experimentally investigates the influence of structural damping on the transverse flow-induced vibration (FIV) of an elastically mounted thin elliptical cylinder. The cylinder tested has an elliptical ratio of $\varepsilon = b/a = 5$, where $a$ and $b$ are the streamwise and cross-flow dimensions, respectively, and a mass ratio (i.e. the total oscillating mass/the displaced fluid mass) of $17.4$. The FIV response was characterised over a reduced velocity range of $2.30 \leq U^* = U/(\,{{f_{{nw}}}} b) \leq 10.00$ (corresponding to a Reynolds number range of $300 \leq \textit {Re} =(U b)/\nu \leq 1300$) and a structural damping ratio range of $3.62\times 10^{-3}\leq \zeta \leq 1.87\times 10^{-1}$. Here, $U$ is the free stream velocity, ${{f_{{nw}}}}$ is the natural frequency of the system in quiescent fluid (water) and $\nu$ is the kinematic viscosity of the fluid. The FIV response was characterised by four wake–body synchronisation regimes (defined as the matching of the dominant fluid forcing and oscillation frequencies, and labelled regime I, regime II, regime III and the hyper branch) and a desynchronisation region, with the hyper branch representing a high amplitude regime not observed for a circular cylinder. Interestingly, the major vortex shedding mode was predominately two single opposite-signed vortices shed per body vibration cycle. Moreover, hydrogen-bubble-based flow visualisations revealed a secondary vortex street forming in the elongated shear layers associated with largest-scale vibration amplitudes ($A^* = A/b$ up to $7.7$) in the hyper branch and regime II. As the structural damping ratio was increased beyond $1.92 \times 10^{-2}$, the hyper branch was found to be suppressed. The results have potential ramifications for the efficient extraction of energy from free-flowing water sources, which has become increasingly topical over the last decade.

Because the Navier–Stokes equations are dissipative, the long-time dynamics of a flow in state space are expected to collapse onto a manifold whose dimension may be much lower than the dimension required for a resolved simulation. On this manifold, the state of the system can be exactly described in a coordinate system parameterising the manifold. Describing the system in this low-dimensional coordinate system allows for much faster simulations and analysis. We show, for turbulent Couette flow, that this description of the dynamics is possible using a data-driven manifold dynamics modelling method. This approach consists of an autoencoder to find a low-dimensional manifold coordinate system and a set of ordinary differential equations defined by a neural network. Specifically, we apply this method to minimal flow unit turbulent plane Couette flow at $Re=400$, where a fully resolved solutions requires ${O}(10^5)$ degrees of freedom. Using only data from this simulation we build models with fewer than $20$ degrees of freedom that quantitatively capture key characteristics of the flow, including the streak breakdown and regeneration cycle. At short times, the models track the true trajectory for multiple Lyapunov times and, at long times, the models capture the Reynolds stress and the energy balance. For comparison, we show that the models outperform POD-Galerkin models with $\sim$2000 degrees of freedom. Finally, we compute unstable periodic orbits from the models. Many of these closely resemble previously computed orbits for the full system; in addition, we find nine orbits that correspond to previously unknown solutions in the full system.

Based on a generalized local Kolmogorov–Hill equation expressing the evolution of kinetic energy integrated over spheres of size $\ell$ in the inertial range of fluid turbulence, we examine a possible definition of entropy and entropy generation for turbulence. Its measurement from direct numerical simulations in isotropic turbulence leads to confirmation of the validity of the fluctuation relation (FR) from non-equilibrium thermodynamics in the inertial range of turbulent flows. Specifically, the ratio of probability densities of forward and inverse cascade at scale $\ell$ is shown to follow exponential behaviour with the entropy generation rate if the latter is defined by including an appropriately defined notion of ‘temperature of turbulence’ proportional to the kinetic energy at scale $\ell$.

Except in the trivial case of spatially uniform flow, the advection–diffusion operator of a passive scalar tracer is linear and non-self-adjoint. In this study, we exploit the linearity of the governing equation and present an analytical eigenfunction approach for computing solutions to the advection–diffusion equation in two dimensions given arbitrary initial conditions, and when the advecting flow field at any given time is a plane parallel shear flow. Our analysis illuminates the specific role that the non-self-adjointness of the linear operator plays in the solution behaviour, and highlights the multiscale nature of the scalar mixing problem given the explicit dependence of the eigenvalue–eigenfunction pairs on a multiscale parameter $q=2{\rm i}k\,{\textit {Pe}}$, where $k$ is the non-dimensional wavenumber of the tracer in the streamwise direction, and ${\textit {Pe}}$ is the Péclet number. We complement our theoretical discussion on the spectra of the operator by computing solutions and analysing the effect of shear flow width on the scale-dependent scalar decay of tracer variance, and characterize the distinct self-similar dispersive processes that arise from the shear flow dispersion of an arbitrarily compact tracer concentration. Finally, we discuss limitations of the present approach and future directions.

To get an insight into the dynamics of the oceanic surface boundary layer we develop an asymptotic model of the nonlinear dynamics of linearly decaying three-dimensional long-wave perturbations in weakly stratified boundary-layer flows. Although in nature the free-surface boundary layers in the ocean are often weakly stratified due to solar radiation and air entrainment caused by wave breaking, weak stratification has been invariably ignored. Here, we consider an idealized hydrodynamic model, where finite-amplitude three-dimensional perturbations propagate in a horizontally uniform unidirectional weakly stratified shear flow confined to a boundary layer adjacent to the water surface. Perturbations satisfy the no-stress boundary condition at the surface. They are assumed to be long compared with the boundary-layer thickness. Such perturbations have not been studied even in a linear setting. By exploiting the assumed smallness of nonlinearity, wavenumber, viscosity and the Richardson number, on applying triple-deck asymptotic scheme and multiple-scale expansion, we derive in the distinguished limit a novel essentially two-dimensional nonlinear evolution equation, which is the main result of the work. The equation represents a generalization of the two-dimensional Benjamin–Ono equation modified by the explicit account of viscous effects and new dispersion due to weak stratification. It describes perturbation dependence on horizontal coordinates and time, while its vertical structure, to leading order, is given by an explicit analytical solution of the linear boundary value problem. It shows the principal importance of weak stratification for three-dimensional perturbations.

The quasigeostrophic shallow-water system on the mid-latitude $\beta$ plane with weak, small-scale turbulent forcing is explored in the limit of large energy. Forcing is weak in the sense that the energy input rate relative to the energy of the flow is very small, of the order of $10^{-5}$–$10^{-10}$, and the potential vorticity assumes an approximate staircase structure. The flow has large energy in the sense that the jet spacing is equal to the domain width so that no further jet mergers can occur. Quasi-stationary numerical experiments, in which the energy grows linearly, reveal late-time quasi-steady, translating solutions comprising a single jet and vortex dipole, with details of the jet-vortex configuration depending on the deformation radius. At a smaller deformation radius the jet may traverse the entire domain in the $y$ direction one or more times, giving a jet orientation that is predominantly north–south, rather than the usual east–west orientation characteristic of $\beta$-plane jets at lower energy. In these meandering cases, a mode number is proposed that quantifies the degree of meandering relative to the vortices. Besides the steadily translating solutions, topological changes in the jet-vortex structure are identified that occur via a transient interaction of a meandering jet with a vortex. At high energy, these give rise to apparently periodic solutions of the system; at low energy, before a single, domain-wide jet is established, they indicate that jet merger may occur through more complicated processes than the simple merging of neighbouring jets.

Linear models, based on stochastically forced linearized equations, are deployed for spectral linear stochastic estimation (SLSE) of the velocity and temperature fluctuations in compressible turbulent channel flows with a bulk Mach number of 1.5. Through comparison with the direct numerical simulation (DNS) data, an eddy-viscosity-enhanced model (eLNS) outperforms the one not enhanced (LNS) in computing the coherence and amplitude ratio of streamwise velocity at different wall-normal heights, but they both largely deviate from DNS regarding the temperature prediction. For further investigation, the eigenspectra and pseudospectra of the linear operators are scrutinized. The eddy viscosity is shown to stabilize the eigenmodes and decrease the non-normality of the vortical modes. Consequently, the relative importance of acoustic and entropy modes increases, and they can contribute 20 % to 55 % of the response growth, which is not supported by DNS. Hence, it is an intrinsic defect of the eLNS model introduced by turbulence modelling. After a procedure of cospectrum decomposition, the contributions of acoustic and entropy components are filtered out. The resulting SLSE quantities for velocity, temperature and their coupling are basically agreeable with DNS, demonstrating that the coherent temperature fluctuation is dominated by advection and other vortical motions, instead of the compressibility effects. Moreover, a parameter study of Reynolds and Mach numbers (from 0.3 to 4) is conducted. The semi-local units are shown to well collapse the velocity SLSE quantities to the incompressible case for streamwise-elongated structures of high coherence.

Turbulent flows over canopies of rigid filaments with different densities are studied using direct numerical simulations at moderate Reynolds numbers $Re_\tau \approx 550\unicode{x2013}1000$. The canopies have heights $h^+\approx 110\unicode{x2013}220$, and are used as an instance of obstructing substrate for the assessment of outer-layer similarity. We show that conventional methods used to determine the zero-plane displacement $\Delta y$ can be at odds with proper outer-layer similarity and may not be applicable for flows at moderate $Re_\tau$. Instead, we determine $\Delta y$ and the length and velocity scales that recover outer-layer similarity by minimising the difference between the smooth-wall and canopy diagnostic function everywhere above the roughness sublayer, not just in the logarithmic layer. In addition, we explore the possibility of the zero-plane displacement and the friction velocity being set independently, but find that outer-layer similarity is recovered more consistently when they are coupled. We observe that although the Kármán constant, $\kappa$ may not have smooth-wall-like values, the flow statistics are smooth-wall-like in the logarithmic layer and above if the surface effect is limited within the near-wall region. This suggests a modified outer-layer similarity, where $\kappa$ is not 0.39, but turbulence is otherwise smooth-wall-like. When the canopy is dense, the flow above the tips is essentially smooth-wall-like, with smooth-wall-like $\kappa \approx 0.39$ and origin essentially at the tip plane. For canopies with intermediate density, the overlying flow perceives a deeper zero-plane displacement into the canopy, which is consistent with observations reported by previous studies, but exhibits a lower Kármán constant, $\kappa \approx 0.34\unicode{x2013}0.36$. For sparse canopies, $\kappa$ tends back to its smooth-wall value, and the zero-plane displacement height is at the canopy bed. For all canopies studied, the decrease in $\kappa$ never exceeds $15\,\%$, which is significantly less than that obtained in some previous works using conventional methods to assess outer-layer similarity.

We investigate the role of pressure, via its Hessian tensor ${\boldsymbol {H}}$, on amplification of vorticity and strain-rate and contrast it with other inviscid nonlinear mechanisms. Results are obtained from direct numerical simulations of isotropic turbulence with Taylor-scale Reynolds number in the range 140–1300. Decomposing ${\boldsymbol {H}}$ into local isotropic (${\boldsymbol {H}}^{I}$) and non-local deviatoric (${\boldsymbol {H}}^{D}$) components reveals that ${\boldsymbol {H}}^{I}$ depletes vortex stretching, whereas ${\boldsymbol {H}}^{D}$ enables it, with the former slightly stronger. The resulting inhibition is significantly weaker than the nonlinear mechanism which always enables vortex stretching. However, in regions of intense vorticity, identified using conditional statistics, contribution from ${\boldsymbol {H}}$ prevails over nonlinearity, leading to overall depletion of vortex stretching. We also observe near-perfect alignment between vorticity and the eigenvector of ${\boldsymbol {H}}$ corresponding to the smallest eigenvalue, which conforms with well-known vortex-tubes. We discuss the connection between this depletion, essentially due to (local) ${\boldsymbol {H}}^{I}$, and recently identified self-attenuation mechanism (Buaria et al., Nat. Commun., vol. 11, 2020, p. 5852), whereby intense vorticity is locally attenuated through inviscid effects. In contrast, the influence of ${\boldsymbol {H}}$ on strain-amplification is weak. It opposes strain self-amplification, together with vortex stretching, but its effect is much weaker than vortex stretching. Correspondingly, the eigenvectors of strain and ${\boldsymbol {H}}$ do not exhibit any strong alignments. For all results, the dependence on Reynolds number is very weak. In addition to the fundamental insights, our work provides useful data and validation benchmarks for future modelling endeavours, for instance in Lagrangian modelling of velocity gradient dynamics, where conditional ${\boldsymbol {H}}$ is explicitly modelled.

This article presents a theoretical modelling framework for the previously unconsidered case of turbulent wall plumes that detrain continually with height in stably stratified environments. Built upon the classic turbulent plume model, our approach incorporates turbulent detrainment with a variable coefficient of detrainment. Based on a linear constitutive relationship between the ratio of the detrainment to entrainment coefficients and the ambient buoyancy gradient, it is found that for linear ambient stratifications, a dynamic quasi-equilibrium region, characterised by a near invariant local plume Richardson number, is achieved, downstream of which this equilibrium rapidly breaks down. With increasing ambient buoyancy gradient, while the plume becomes increasingly slender with weaker vertical motions, the level at which the plume breaks down to form a horizontal intrusion first decreases and then increases. Moreover, distinct from classic purely entraining plumes, a detraining wall plume can swell within the pre-equilibrium adjustment stage provided the local Richardson number is sufficiently low $({Ri\ll 6})$, behaviour which is in accordance with observations made in filling-box experiments.

A series of laboratory experiments are reported in which a continuous stream of bubbles rise from a small source at the base of a tank of water. Using different nozzles, bubble sizes $d$ ranging from 1.2 to 11.6 mm were produced for a number of gas volume fluxes, $Q_b$, ranging between 1.1 and $21.1\times 10^{-6}\ {\rm m}^3\ {\rm s}^{-1}$. Within a small distance from the source, the slip speed of these bubbles exceeds the speed of the equivalent single-phase plume with the same buoyancy flux, leading to formation of what we refer to as the ‘slip plume’ regime. Through a combination of high-speed photography, coupled with flow visualisation in the plume and the ambient fluid using dye, we find that the bubble speed and the fluid speed remain nearly constant with height, with the maximum fluid speed being of order $0.30\pm 0.03$ of the bubble speed. Using the filling box method, we also find that the net fluid volume flux in the slip plume increases linearly with distance from the source at a rate $Q_l = \lambda Bz/v_s^2$, where $B$ is the buoyancy flux of the gas, $v_s$ the rise speed of the gas bubbles, $z$ the distance above the source and $\lambda$ is a constant related to the dimensionless volume of fluid in the wake of each bubble. This slip-dominated flow regime can be understood in terms of kinetic energy imparted to the fluid as the bubbles rise and release potential energy. Further experiments with particle-laden plumes illustrate similar scalings for the volume flux in a particle-driven slip plume once the slip speed of the particles exceeds the bulk speed of the equivalent single-phase buoyant plume with the same buoyancy flux. Near the source the slip speed may be smaller than the plume speed, and the flow follows the classical model for a turbulent buoyant plume, with the transition to the slip regime occurring at a distance $z^*\approx (32\pm 5)\lambda ^{3/2} B/v_s^3$ from the source, where the dimensionless parameter $\lambda$ relates to the dimensionless volume of the fluid wake, which we find varies with the Reynolds number of the particles.

We consider the dynamics of a set of reduced equations describing the evolution of a magnetised, rotating stably stratified fluid layer, atop a stagnant dense, perfectly conducting layer. We consider two closely related models. In the first, the layer has, above it, relatively light fluid where the magnetic pressure is much larger than the gas pressure, and the magnetic field is largely force-free. In the second model, the magnetic field is constrained to lie within the dynamical layer by the implementation of a model diffusion operator for the magnetic field. The model derivation proceeds by assuming that the horizontal velocity and the horizontal magnetic field are independent of the vertical coordinate, whilst the vertical components in the layer have a linear dependence on height. The full system comprises evolution equations for the magnetic field, horizontal velocity and height field together with a linear elliptic equation for the vertically integrated non-hydrostatic pressure. In the magneto-hydrostatic limit, these equations simplify to equations of shallow-water type. Numerical solutions for both models are provided for the fiducial case of a Gaussian vortex interacting with a magnetic field. The solutions are shown to differ negligibly. We investigate how the interaction of the vortex changes in response to the magnetic Reynolds number ${Rm}$, the Rossby deformation radius $L_D$, and a Coriolis buoyancy frequency ratio $f/N$ measuring the significance of non-hydrostatic effects. The magneto-hydrostatic limit corresponds to $f/N\to 0$.

Previous mathematical models of quasi-steady turbulent plumes and fountains have described the flow that results from a prescribed input of buoyancy. We offer a new perspective by asking, what input of buoyancy would give rise to a plume, or fountain, with given properties? Addressing this question by means of an analytical framework, we take a first step toward enabling a plume with specific characteristics, i.e. a synthetic plume, to be designed. We develop analytical solutions to the conservation equations that describe four kinds of turbulent flow: axisymmetric plume, starting fountain, line plume and wall plume. Crucially, our solutions do not require the buoyancy distribution to be specified, whether this be the source or off-source distribution. Key to our approach, we specify a function for the volume flux, $Q=f(z)$, and take advantage of the weak coupling between the conservation equations to uniquely express general solutions in terms of $f$. We show that any analytic function $f$ can form the basis for a set of solutions for the fluxes, local variables and local Richardson number, though $f/({\rm d}f/{\rm d}z)>0$ is a necessary condition for physically realistic solutions. As an example of plume synthesis, we show that an axisymmetric plume can have an invariant radius if there is an exponentially increasing input of buoyancy to the plume centreline. We also consider how plume synthesis could be achieved practically.

We report on an experimental study of a device comprising an array of submerged, inverted and periodic cylindrical pendula (resonators), whose objective is the attenuation of surface gravity waves. The idea is inspired by the concept of metamaterials, i.e. engineered structures designed to interact with waves and manipulate their propagation properties. The study is performed in a wave flume where waves are excited in a wide range of frequencies. We explore various configurations of the device, calculating the transmitted, reflected and dissipated energy of the waves. If the incoming wave frequencies are sufficiently close to the natural frequency of the pendula, we find a considerable wave attenuation effect. This behaviour is enhanced by the number of resonators in the array. Moreover, the device is also capable of reflecting the energy of selected frequencies of the incoming waves. These frequencies, predicted by a generalized Bragg scattering mechanism, depend on the spacing between the resonators. The presented results show promise for the development of an environmentally sustainable device for mitigating waves in coastal zones.

Perturbed rapidly rotating flows are dominated by inertial oscillations, with restricted group velocity directions, due to the restorative nature of the Coriolis force. In containers with some boundaries oblique to the rotation axis, the inertial oscillations may focus upon reflections, whereby their energy increases whilst their wavelength decreases and their trajectories focus onto attractor regions. In a linear inviscid setting, these attractors are Delta-like distributions. The linear inviscid setting is obtained formally by setting both Ekman number ${E}$ (ratio of inertial to viscous time scales) and Rossby number ${Ro}$ (non-dimensional amplitude of the forcing that drives the inertial oscillations) to zero. These settings raise fundamental questions, in particular concerning the nature of energy dissipation in the vanishing Ekman number regime. Here, we consider a simple container geometry, a rectangular cuboid, in which the direction of the rotation axis is oblique to four of its walls, subject to librational forcing (small-amplitude harmonic oscillations of the rotation rate). This geometry allows for accurate and efficient direct numerical simulations of the three-dimensional incompressible Navier–Stokes equations with no-slip boundary conditions using a spectral-Galerkin spatial discretisation along with a third-order temporal discretisation. Solutions with Ekman and Rossby numbers as small as ${E}={Ro}=10^{-8}$ reveal many details of how the inertial oscillations focus, at the libration frequency considered, onto attractors, and how the focusing leads to increased localised nonlinear and dissipative processes as ${E}$ and ${Ro}$ are reduced. Even for extremely small forcing amplitudes, nonlinear effects have important dynamic consequences for the attractors.

In the present work, we study the flow field around, and forces acting on, a circular cylinder with an attached flexible splitter plate/flap. Two cases of flap length ($L/D$), namely, $L/D = 5$ and $L/D = 2$ have been investigated focusing on the effect of variations in flap flexural rigidity, $EI$. We find that for a range of $EI$ and Reynolds numbers $Re = UD/\nu$, a non-dimensional bending stiffness $K^{\ast }=EI/((1/2)\rho U^2 L^3)$ collapses flap motion and forces on the system well, as long as $Re>5000$. In the $L/D = 5$ flap case, two periodic flap deformation regimes in the form of travelling waves are identified (modes I and II), with mode I occurring at $K^{\ast } \approx 1.5\times 10^{-3}$ and mode II at lower $K^{\ast }$ values ($K^{\ast }<3\times 10^{-5}$). In the $L/D = 2$ flap case, we find a richer set of flapping modes (modes A, B, C and D) that are differentiated by their flapping characteristics (symmetric/asymmetric and amplitude). Force measurements show that the largest drag reduction occurs in mode I ($L/D = 5$) and mode C ($L/D = 2$), which also correspond to the lowest lift and wake fluctuations, with the mode C wake fluctuations being lower than even the rigid splitter plate case. In contrast, the highest fluctuating lift, in both $L/D$ cases, occurs at higher $K^{\ast }$, when the wake frequency is close to the first structural bending mode frequency of the flap. The observed rich range of flap/splitter plate dynamics could be useful for applications such as drag reduction, vibration suppression, reduction of wake fluctuations and energy harvesting.