Flows over a disc are studied in a wind tunnel over incidence angles between $0^\circ \text { and }36^\circ$, a Reynolds number of $2.7 \times 10^4$ and rotational speed ratios of $0\unicode{x2013}10$. Smoke-wire visualization, particle image velocimetry and hot-film anemometry are employed. Two vortex shedding modes originating from the upstream surface of the disc are observed. The first is dominant at incidence angles up to ${\sim }21^\circ$. Beyond $21^\circ$, the second mode dominates. It appears as a soliton on the vortices and has a shedding frequency nearly twice that of the first at the highest incidence angle. The Strouhal number monotonically increases with incidence angle from approximately 0.2 to 0.4. Spectral analysis of the hot-film measurements confirms the findings from flow visualization experiments. Flows over the spinning disc generally mimic the stationary disc flows; however, centrifugal forces lead to cross-stream instability features that may be attributed to spiral wave instabilities intrinsic to the boundary layers in rotating flows. Velocity measurements are used to construct streamline patterns to compare with the smoke streaklines. The unsteadiness of the flows results in large variances. Mean strain rates are extracted from velocity data, where the fixed disc case at normal incidence compares well with theoretical predictions. The unsteady boundary layer thickness over the fixed disc, however, is approximately twice that predicted by theory for steady flow, stemming from the dominance of large unsteady vortices. Limited comparisons are made of the Strouhal numbers from experiments and numerical calculations in the literature.

The formation mechanism for the stopping vortex ring (SVR) and its effects on the development of starting jets have been systematically investigated. The radial inward flow near the nozzle exit, arising from the pressure difference caused by the deceleration of starting jets, is considered to be the main contributing factor to the formation of the SVR. The formation process can generally be divided into (i) the rapid accumulation stage ($t_d^*\leq 1$) and (ii) the development stage ($t_d^*>1$), where $t_d^*$ is the formation time defined by the duration of the deceleration stage. For starting jets with different $(L/D)_d$, the final circulation value and circulation growth rate of the SVR can be scaled by $[(L/D)_d]^{-0.5}$ and $[(L/D)_d]^{-1.5}$, respectively. Here $(L/D)_d$ represents the stroke ratio during the deceleration stage. Analysing the temporal evolution of fluid parcels in the vicinity of the nozzle exit reveals that SVR entrains fluid from both inside and outside of the nozzle. Additionally, the influence of the SVR on the leading vortex ring and the trailing jet has been examined, with particular attention to its effects on the propulsive performance of the starting jet. The SVR affects the profiles of axial velocity and gauge pressure at the nozzle exit, thereby enhancing the generation of total thrust during the deceleration stage. Analysis has shown that depending on the deceleration rate, SVR can enhance the average velocity thrust by at least $10\,\%$ and compensate for up to a $60\,\%$ reduction in pressure thrust due to deceleration.

Three-dimensional vortex dynamics around two pitching foils arranged in side-by-side (parallel) configurations is numerically examined at a range of separation (gap) distances ($0.5c \leqslant y^* \leqslant 1.5c$). In-phase ($\phi =0$) and out-of-phase ($\phi ={\rm \pi}$) motions are considered for Strouhal numbers of $0.3$ and $0.5$ at a Reynolds number of $8000$. In this work, we show that the foil proximity effect, defined as the influence of one foil on the flow characteristics around the other, induces a spanwise instability in the braids of trailing-edge vortices (TEVs) during their roll-up. This is a newly identified instability that manifests itself in the form of secondary vortical structures with opposite circulation compared with the TEVs formed on the foils, which leads to the formation of double necking on the braids of the TEVs. We provide quantitative evidence linking the formation of these secondary structures to the braid instability. The first neck merges with the TEV, while the second neck detaches from the braid region and moves downstream independently. As the foil proximity effect intensifies (spacing between the foils decreases), secondary vortical structures, as well as the necks, become more prominent, leading to the emergence of three-dimensional wake features. Lastly, the influence of kinematics of the foils on three-dimensionality of the wake is investigated. At higher Strouhal numbers, broader regions of high strain are developed near the trailing edge, associated with the detachment of stronger structures from the braids of TEVs. The characterized instability demonstrates consistent properties for in-phase and out-of-phase motions, albeit with specific differences in dynamics of leading-edge vortices.

Turbulent flow around curved tandem cylinders has been studied for the first time, by means of direct numerical simulation. The convex configuration was used, with a nominal gap ratio of $L/D = 3$ and a Reynolds number of 3900. Along the span, the flow regimes vary from alternating overshoot/reattachment to co-shedding. Three distinct Strouhal numbers coexist in the flow that are tied directly to different tandem cylinder flow regimes. This result differs substantially from convex curved tandem cylinders at a transitional Reynolds number, where only a single dominant frequency is found. All regimes exhibit some degree of instability, so that the flow can be considered multistable. A mode switch from alternating overshoot/reattachment to symmetric reattachment is found. Complex interactions are observed between the primary instability, the shear layer instability and the flow mode alterations. As opposed to previous investigations with single and tandem straight cylinders in the subcritical flow regime, our results indicate that there may be direct feedback from the primary instability to the shear layer instability. The downdraft region in the gap exhibits slow meandering, and may travel upstream and amplify the shear layer instability, causing early transition in the gap shear layer. This downdraft is governed by the slow modulations of the vortex formation region in the lower gap, meaning that the vortex dynamics of this region may indirectly influence the shear layer instability higher up in the gap.

Meandering designates the main manifestation of unsteady vortex dynamics observed in experiments. This study has the twofold objective to (i) develop a theoretical model describing vortex meandering and (ii) conduct a quantitative and objective evaluation of the model against experimental data. Based on an analogy with Brownian motion, we derive the theoretical model in the framework of linear response theory. Taking the form of a Langevin equation, our model explains meandering as the competition between external excitation by free-stream perturbations, counteracted by stabilising intrinsic vortex dynamics. As such, it contains the previous approaches to explaining the phenomenon as limiting cases, and clearly highlights their shortcomings. The statistical identification of characteristic regularities in experimental data as well as the assessment of their consistency with theoretical models are important problems in physics. For samples obtained from finite-length records of correlated data, these statistical characteristics are not unique and may show spurious behaviour merely induced by the finiteness of the sample. Statistical inference provides a systematic and quantitative methodology to objectively assess the reproducibility of statistical characteristics and to evaluate their consistency with theoretical models. Their systematic application to the analysis of vortex meandering has not been done before and provides statistical evidence for our proposed Brownian-motion-like model. That is, experimental vortex meandering constitutes the manifestation of a stationary Gauss–Markov random process, which implies that the dynamics admits an ergodic probability measure.

Nonlinear steady solutions of the barotropic quasi-geostrophic equation in basins, gulfs and channels on a $\beta$-plane are presented. The domains are rectangular with arbitrary aspect ratios. The two-dimensional solutions assume a linear relationship between the potential vorticity $q$ and the stream function $\psi$. The sign of the slope in the linear $q\unicode{x2013}\psi$ relationship defines two broad sets of solutions. For a positive slope, the solutions in a closed basin correspond to the inertial gyres derived by Fofonoff in 1954. The negative slope solutions consist of normal modes that can be resonant. For gulfs and channels, the conditions at the open boundaries are almost arbitrary flows entering or leaving the domain. Such conditions allow a great variety of solutions in the interior, characterised mainly by arrays of vortices with alternate signs. Several examples are presented and discussed.

Rotating Rayleigh–Bénard convection denotes the convection between a warm plate and a cold plate in a rotating environment. It is a classic model for understanding convective vortices in the atmosphere and ocean. The influence of background rotation on fluid inertia breaks the symmetry between cyclones and anticyclones. Such a symmetry breaking could be represented by vorticity skewness, which still lacks a systematic theory. Rapidly rotating convection with stress-free boundaries and unit Prandtl number is a convenient starting point. The investigation starts from the convective onset stage, where the vortices grow stationarily. Asymptotic analysis shows that the volumetric vorticity skewness $S$ is produced by the interaction between the $n=0,1$ and $n=1,2$ vertical eigenmodes. The $n=0$ (barotropic) mode contributes positively to $S$ mainly by stretching the vertical relative vorticity, an ageostrophic effect. The $n=2$ mode makes a minor negative contribution to $S$ by preferentially intensifying the outflow over the inflow, a non-hydrostatic effect. The theory predicts $S$ to be proportional to the global Rossby number defined with the volumetric standard deviation of vorticity, ${Ro_g}$. The proportional factor does not depend on the Rayleigh and Ekman numbers, agreeing with direct numerical simulations. Then the system enters the equilibrium stage. The stretching of vertical vorticity still contributes to $S$ dominantly. At ${Ro_g}\gtrsim 0.5$, the emergent unsteady flow significantly suppresses the asymmetry between the inflow and outflow strength, and weakens its influence on $S$.

This research investigates the wake–foil interactions between two oscillating foils in a tandem configuration undergoing energy harvesting kinematics. Oscillating foils have been shown to extract hydrokinetic energy from free-stream flows through a combination of periodic heave and pitch motions, at relatively higher amplitudes and lower reduced frequency than thrust generating foils. When placed in tandem, the wake–foil interactions can govern the energy harvesting efficiency of the system due to a reduced relative flow velocity in combination with a structured and coherent wake of vortices shed from the high amplitude flapping of upstream foils. This work utilizes simulations of two tandem foils to parameterize and model the energy harvesting performance as a function of array configuration and foil kinematics. Once the wake of the leading foil has been fully parameterized, the placement, phase angle and kinematic stroke of the second foil is utilized to estimate the time-dependent power curve. The algorithm predicts the power of the second foil through the mean and unsteady wake characteristics, including the direct impingement of a vortex with the trailing foil.

The asymmetric instability in two streamwise orthogonal planes for three-dimensional flow-induced vibration (FIV) of an elastically mounted cube at a moderate Reynolds number of 300 is numerically investigated in this paper. The full-order computational fluid dynamics method, data-driven stability analysis via the eigensystem realization algorithm and the selective frequency damping method and total dynamic mode decomposition (TDMD) are applied here to explore this problem. Due to the unsteady non-axisymmetric wakefield formed for flow passing a stationary cube, the FIV response was found to exhibit separate structural stability and oscillations (including lock-in and galloping behaviour) in the two different streamwise orthogonal planes while the body is released. The initial kinetic energy accompanying the release of the cube could destabilize the above-mentioned structural stability. The observed FIV asymmetric instability is verified by the root trajectory of the structural mode obtained via data-driven stability analysis. The stability of the structural modes dominates regardless of whether the structural response oscillates significantly in various (reduced) velocity ranges. Further TDMD analysis on the wake structure, accompanied by the time–frequency spectrum of time-history structural displacements, suggested that the present FIV unit with galloping behaviour is dominated by the combination of the shifted base-flow mode, structure modes and several harmonics of the wake mode.

In this work we investigate the spatio-temporal nature of various coherent modes present in a wind turbine wake using a combination of new particle image velocimetry experiments and data from Biswas & Buxton (J. Fluid Mech., vol. 979, 2024, A34). A multiscale triple decomposition of the acquired velocity field is sought to extract the coherent modes and, thereafter, the energy exchanges to and from them are studied using the multiscale triple decomposed coherent kinetic energy budgets developed by Baj & Buxton (Phys. Rev. Fluids, vol. 2, 2017, 114607). Different frequencies forming the tip vortex system (such as the blade passing frequency, turbine's rotational frequency and their harmonics) are found to be energised by different sources such as production from the mean flow or nonlinear triadic interaction or both, similar to the primary, secondary or the mixed modes discussed in Biswas et al. (J. Fluid Mech., vol. 941, 2022, A36). The tip vortex system forms a complex network of nonlinear triadic energy transfers, the nature and the magnitudes of which depend on the tip speed ratio ($\lambda$). Contrastingly, the modes associated with the sheddings from the nacelle or tower and wake meandering are found to be primarily energised by the mean flow. We show that the tip vortex system exchanges energy with the mean flow primarily through the turbine's rotational frequency. In fact, the system transfers energy back to the mean flow through the turbine's rotational frequency at some distance downstream marking the onset location of wake recovery ($x_{wr}$). Here $x_{wr}$ is shown to reduce with $\lambda$ due to stronger interaction and earlier merging of the tip vortices at a higher $\lambda$.

Direct numerical simulation of the three-dimensional (3-D) wake transition of a heated square cylinder subjected to horizontal cross-flow is performed in the presence of buoyancy. In order to capture the effects of large-scale heating, a non-Oberbeck–Boussinesq model is utilized, which includes the governing equations for compressible gas flow. All computations are performed at low free stream Mach number $M=0.1$ using air (free stream Prandtl number, $Pr=0.71$) as the working fluid. The 3-D instability modes A and B, which correspond to free stream Reynolds numbers of 180 and 250, are observed with longer and shorter spanwise wavelengths, respectively, and the onset of three-dimensionality is triggered at a Reynolds number of 173. In the presence of buoyancy, baroclinic vorticity production in the near-wake plays an important role for streamwise vorticity generation. The chaotic wake of the Mode-A instability bifurcates into periodic and quasiperiodic wakes at various heating levels, expressed by the overheat ratio, $\varepsilon =(T_w-T_\infty )/T_\infty$, where $T_w$ and $T_\infty$ are the temperature of the cylinder surface and the ambient air, respectively. At low heating ($\varepsilon =0.2$), the 3-D Mode-A instability is suppressed leading to a two-dimensional wake flow. Further increase in heating, again brings back the three-dimensionality in the wake through Mode-E instability. The variation of thermophysical properties and the effective Reynolds number with increase in heating level around the cylinder is examined. It is shown that the effect of thermophysical properties competes with the baroclinic streamwise vorticity generation at higher levels of heating ($\varepsilon \geqslant 0.4$) to control the 3-D modes and wake dynamics.

We perform direct numerical simulations of actively controlled laminar separated wakes around low-aspect-ratio wings with two primary goals: (i) reducing the size of the separation bubble and (ii) attenuating the wing tip vortex. Instead of preventing separation, we modify the three-dimensional (3-D) dynamics to exploit wake vortices for aerodynamic enhancements. A direct wake modification is considered using optimal harmonic forcing modes from triglobal resolvent analysis. For this study, we consider wings at angles of attack of $14^\circ$ and $22^\circ$, taper ratios $0.27$ and $1$, and leading edge sweep angles of $0^\circ$ and $30^\circ$, at a mean-chord-based Reynolds number of $600$. The wakes behind these wings exhibit 3-D reversed-flow bubble and large-scale vortical structures. For tapered swept wings, the diversity of wake vortices increases substantially, posing a challenge for flow control. To achieve the first control objective for an untapered unswept wing, root-based actuation at the shedding frequency is introduced to reduce the reversed-flow bubble size by taking advantage of the wake vortices to significantly enhance the aerodynamic performance of the wing. For both untapered and tapered swept wings, root-based actuation modifies the stalled flow, reduces the reversed-flow region and enhances aerodynamic performance by increasing the root contribution to lift. For the goal of controlling the tip vortex, we demonstrate the effectiveness of actuation with high-frequency perturbations near the tip. This study shows how insights from resolvent analysis for unsteady actuation can enable global modification of 3-D separated wakes and achieve improved aerodynamics of wings.

Modons, or dipolar vortices, are common and long-lived features of the upper ocean, consisting of a pair of counter-rotating monopolar vortices moving through self-advection. Such structures remain stable over long times and may be important for fluid transport over large distances. Here, we present a semi-analytical method for finding fully nonlinear modon solutions in a multi-layer quasi-geostrophic model with arbitrarily many layers. Our approach is to reduce the problem to a multi-parameter linear eigenvalue problem which can be solved using numerical techniques from linear algebra. The method is shown to replicate previous results for one- and two-layer models and is applied to a three-layer model to find a solution describing a mid-depth propagating, topographic vortex.

At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding and unsteady force production. Furthermore, low-aspect-ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading-edge flow separation and a strong, persistent tip vortex over a Reynolds number range of $600 \leq Re \leq 10{\,}000$. In performing this study, we aim to bridge the insight gained from existing low-Reynolds-number studies of separated flow on finite wings ($Re \approx 10^2$) and turbulent flows at higher Reynolds numbers ($Re \approx 10^4$). Our study suggests two primary effects of the Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from $Re = 600$ to $Re = 2500$. Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond $Re = 2500$, an observation attributed to the stabilising impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flow field may be adjusted for higher-Reynolds-number applications.

A two-dimensional body that moves suddenly in a viscous fluid can instantly generate vortices at its sharp edges. Recent work using inviscid flow theory, based on the Birkhoff–Rott equation and the Kutta condition, predicts that the ‘starting vortices’ generated by the sharp and straight edges of a body – i.e. the vortices formed immediately after motion begins – can be one of three distinct self-similar types. We explore the existence of these starting vortices for a flat plate and two symmetric Joukowski aerofoils immersed in a viscous fluid, using high-fidelity direct numerical simulations (DNS) of the Navier–Stokes equations. A lattice Green's function method is employed and simulations are performed for chord Reynolds numbers ranging from 5040 to 45 255. Vortices generated at the leading and trailing edges of the flat plate show agreement with the derived inviscid theory, for which a detailed assessment is reported. Agreement is also observed for the two symmetric Joukowski aerofoils, demonstrating the utility of the inviscid theory for arbitrary bodies. While this inviscid theory predicts an abrupt transition between the starting-vortex types, DNS shows a smooth transition. This behaviour occurs for all Reynolds numbers and is related to finite-time effects – there is a maximal time for which the (self-similar) starting vortices exist. We confirm the inviscid prediction that the leading-edge starting vortex of a flat plate can be suppressed dynamically. This has implications for the performance of low-speed aircraft such as model aeroplanes, micro air vehicles and unmanned air vehicles.

A high-resolution simulation of a thermal vortex ring is analysed from the point of view of the vortex dynamics. A power-spectrum analysis of vortex-ring sections suggests that the simulated flows are overall ‘two dimensional’ in the large-scale limit, being dominated by axisymmetric components, but with a substantial contribution from the non-axisymmetric component at small scales. Contribution of the non-axisymmetric components is negligible in budgets of volume integrals of the vorticity and potential vorticity as well as the impulse (moments of the vorticity weighted by $s^n$ with $n=-1$, 0, 1, where $s$ is the distance from the vertical axis of the vortex ring). A concise description of the dynamics is obtained as a function of geometrical factors together with these three integral variables. Analysis shows that the geometrical factors are fairly close to constant with time, and thus, a redundant closed description of the system is obtained in the similarity regime after spin up of the vortex ring. This redundancy leads to a constraint on the geometrical factors, which is reasonably satisfied by the simulation. A closed description is also obtained over the initial spin-up period of the vortex ring by adding a phenomenologically derived prognostic equation for the source for the volume integral of the potential vorticity (with $n=-1$). Analysis of the budget supports this description.

Motivated by contradicting or insufficient information regarding the large-scale flow dynamics around surface-mounted finite-height square prisms of small aspect ratio, the present study investigates the dominant vortex shedding and low-frequency dynamics around a surface-mounted cube. These flow modes were obtained from the spectral proper orthogonal decomposition of large-eddy simulation results, at a Reynolds number of $\textit {Re}=1\times 10^4$ and two different types of boundary layer: a thin and laminar boundary layer with thickness $\delta /D=0.2$ and a thick and turbulent boundary layer with $\delta /D=0.8$. The main antisymmetric mode pair revealed a new flow pattern with the alternate shedding of streamwise flow structures, indicating a transition from the half-loops of taller prisms to only streamwise strands (i.e. no vertical core) for smaller aspect ratio. The formation process of the streamwise structures is due to a reorientation of the vorticity of the arch vortex in the streamwise direction characteristic of the shed structures. The low-frequency drift mode affected the length of the recirculation region, the strength of vortex shedding, and the near-wall flow field and pressure distribution on the cube's faces, leading to low-frequency variations in the fluctuating drag and normal force coefficients. These large-scale flow dynamics were similar for both boundary layers, but minor differences were identified, related mostly to the occurrence of flow attachment and the formation of a headband vortex for the thicker boundary layer.

The nonlinear dynamics of a helical vortex disturbed by a long-wave-instability mode is studied by direct numerical simulation. Vortex reconnection or self-reconnection of the helical vortex is shown to play a crucial role depending on the pitch of the helical vortex. For the larger pitch, a vortex ring is created after the vortex reconnection; it detaches from the remaining helical vortex, whose pitch is doubled. A vortex ring is also created for the smaller pitch; however, it forms a linked system with the remaining vortex. The topological constraint due to this linkage forces strong interaction between the different parts of the helical vortex, leading to turbulent transition.

The initial flow past an impulsively started rotating and translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier–Stokes equation. In our previous study (J. Fluid Mech., vol. 929, 2021, A31), the asymptotic solution was obtained within the second approximation with respect to the small parameter, $\epsilon$, that is of the order of $1 / \lambda$. Here, $\lambda$ is the penalization parameter. In addition, the Reynolds number based on the cylinder radius and the translating velocity is assumed to be of the order of $\epsilon$. The previous study asymptotically analysed the initial flow past an impulsively started translating circular cylinder and investigated the influence of the penalization parameter $\lambda$ on the drag coefficient. It was concluded that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625–647) as $\lambda \to \infty$. Furthermore, the derivative of vorticity in the normal direction was found to be discontinuous on the cylinder surface, which is caused by the tangential gradient of the pressure on the cylinder surface. The present study hence aims to investigate the variance on the drag coefficient against the result of Bar-Lev & Yang (1975). First, we investigate the problem of an impulsively started rotating circular cylinder. In this situation, the moment coefficient is independent of the pressure on the cylinder surface so that we can elucidate the role of the pressure to the hydrodynamic coefficients. Then, the problem of an impulsively started rotating and translating circular cylinder is investigated. In this situation, the pressure force induced by the unsteady flow far from the cylinder is found to play a key role on the drag force for the agreement with the result of Bar-Lev & Yang (1975), whereas the variance still exists on the lift force. To resolve the variance, an alternative formula to calculate the hydrodynamic force is derived, assuming that there is the pressure jump between the outside and inside of the cylinder surface. The pressure jump is obtained in this analysis asymptotically. Of particular interest is the fact that this pressure jump can cause the variance on the lift force calculated by the integration of the penalization term.

A turbulent two-vortex system (T-2VS) is obtained by inserting analytical model wake vortices into very weak homogeneous isotropic turbulence (HIT) and by evolving them in time using large-eddy simulation until a turbulent state at statistical equilibrium is reached. The T-2VS is characterised as follows: circulation distribution of the vortices; energy of the mean and fluctuating fields; energy dissipation rate. It is also verified that essentially the same T-2VS is obtained when varying the initial model or initial HIT perturbation. A wall-resolved simulation of the T-2VS further interacting with a smooth ground is then performed at $Re_\varGamma = 2 \times 10^5$; this is $10 \times$ higher than in previous works, which allows us to better capture the high Reynolds number behaviour. The high release height of the T-2VS also ensures a physically correct approach to the ground. The results are compared with the literature and also to what is obtained for the case of non-turbulent vortices interacting with the same ground at the same Reynolds number. The flow topologies are discussed, and significant differences are highlighted regarding the separation of the boundary layer generated at the ground, and the way this secondary vorticity interacts with the primary vortices and makes them decay. The vortex trajectories are also measured, together with their circulation distribution and global circulation evolution, and the differences are discussed.