A low-density jet is known to exhibit global self-excited axisymmetric oscillations at a discrete natural frequency. This global mode manifests as large-scale periodic vortex ring structures in the near field. We experimentally investigate the effectiveness of axial and transverse forcing in controlling such global vortical structures. We apply acoustic forcing at a frequency ($f_{\!f}$) around the natural global frequency of the jet ($f_n$) leading up to and beyond lock-in. Using time-resolved stereoscopic particle image velocimetry, we find that the jet synchronises to $f_{\!f}$ when forced sufficiently strongly. When forced purely axially, the jet exhibits in-phase roll-up of the shear layers, producing axisymmetric vortex ring structures. When forced purely transversely, the jet exhibits anti-phase roll-up of the shear layers, producing tilted vortex ring structures. We find that the former produces relatively strong oscillations, while the latter produces oscillations that are even weaker than those of the unforced case due to asynchronous quenching. We show that the transverse forcing breaks the jet axisymmetry by altering the topology of the coherent structures in the near field, leading to global instability suppression. We also find that the wavelength of the applied forcing has a notable influence on the evolution of vortical structures, thereby modifying the forced response of the jet. The efficacy of transverse forcing and the influence of the forcing wavelength in suppressing the global mode of a self-excited low-density jet present new possibilities for the open-loop control of a variety of globally unstable flows.

In this paper, we perform a Floquet-based linear stability analysis of the centrifugal parametric resonance phenomenon in a Taylor–Couette system subjected to a time-quasiperiodic forcing where both the inner and outer cylinders are oscillating with the same amplitude and different angular velocities given respectively by $\varOmega _0 \cos (\omega _1t)$ and $\varOmega _0 \cos (\omega _2t)$. In this context, the frequencies $\omega _1$ and $\omega _2$ are incommensurate, where the ratio $\omega _2/\omega _1$ is irrational. Taking into account non-axisymmetric disturbances, a new set of partial differential equations is derived and solved using the spectral method along with the Runge–Kutta numerical scheme. The obtained results in this framework show that this forcing triggers new and numerous reversing and non-reversing Taylor vortex flows arising via either synchronous or period-doubling bifurcations. A rich and complex dynamics is found owing to strong mode competition between these modes that alters significantly the topology of the marginal stability curves. The latter exhibit a multitude of small and condensed parabolas, giving rise to several codimension-two bifurcation points, discontinuities and cusp points in the stability diagrams. Furthermore, a proper tuning of the frequency ratio leads to a significant control of both the instability threshold and the axisymmetric nature of the primary bifurcation. Moreover, using a local quasi-steady analysis when the cylinders are slowly oscillating, intermittent instabilities are detected, characterised by spike-like behaviour in the stability diagrams with several successive growths, dampings and periods of quietness. In this limit case, the inner cylinder drive becomes the responsible forcing of the Taylor vortices’ formation where the calculated critical instability parameters correspond to those of the inner oscillating cylinder case with fixed outer cylinder. The potentially unstable regions between the cylinders are determined on the basis of the Rayleigh discriminant, where an excellent agreement with the linear stability analysis results is pointed out.

Smooth surface features were recently found to stabilise stationary cross-flow instability (CFI) of swept-wing boundary layers, thus holding potential for passive laminar flow control. Notably, the effect of surface features on the transition location exhibited a significant dependence on the CFI amplitude. In this work, numerical solutions of the harmonic Navier–Stokes (HNS) equations are used to explore the impact of a smooth surface hump on the linear and nonlinear development of stationary CFI under various perturbation amplitudes. Linear simulations identify regions of successive inhibited and enhanced perturbation growth. Despite the recovery of the base flow and perturbation kinetic energy to the reference (i.e. no-hump) state, significantly reduced perturbation growth is observed. The distorted perturbation profile due to the interaction with the hump is postulated to be responsible for this. Increasing the perturbation amplitude results in a response of the flow that is qualitatively similar to the linear case, albeit with increasing local destabilisation of new fundamental (i.e. primary wavelength) structures and higher-order harmonics near the wall. An energy budget analysis reveals that the growth of the fundamental incoming CFI is inhibited through the reduced effectiveness of the lift-up mechanism downstream of the hump. This is preceded by a spatial perturbation shape deformation, governed by (spanwise) transport terms. The results suggest that stabilisation of incoming stationary CFI via smooth surface humps is most effective at low incoming perturbation amplitudes. At higher perturbation amplitudes, newly formed near-wall structures, pre-conditioned by the incoming CFI, overtake the incoming CFI and could anticipate the transition process.

The modal and non-modal stability of laminar flow in a rectangular microchannel is investigated by incorporating the effects of Coriolis forces due to rotation, cross-sectional aspect ratio and superhydrophobic wall slip. The full Navier–Stokes equations are linearised into modified Orr–Sommerfeld and Squire equations, which are then formulated as an eigenvalue problem using small disturbances of the Tollmien–Schlichting type. These equations are subsequently solved by the spectral collocation method. The transition to instability in rotating microchannel flows, influenced by aspect ratio and slip conditions, is analysed through eigenvalue spectra and neutral stability curves. For non-modal analysis, we express the solution in matrix exponential form and then, using the singular value decomposition method, calculate the maximum energy growth. The study reveals that the flow becomes unstable in the presence of rotation at a critical Reynolds number of $ Re_c \approx 40$ for a low aspect ratio and $ Re_c \approx 50.4$ for a high aspect ratio. We find that instability is more pronounced in spanwise-rotating flows at higher aspect ratios compared with those at lower aspect ratios. Rotation induces disturbances from both walls along the spanwise direction, forming secondary flow structures near the centreline. Furthermore, we examine the influence of anisotropic slip by separately considering streamwise and spanwise slip as limiting cases. The numerical results demonstrate that while streamwise slip has a stabilising effect on rotating flows at small scales, a sufficiently large spanwise slip length can trigger instability at Reynolds numbers lower than those observed in the no-slip case. Rotation has the potential to enhance non-modal transient energy growth, while streamwise slip can effectively suppress this instability. These findings suggest that the onset of instability and transient energy growth can be effectively regulated by adjusting the aspect ratio and spanwise slip of the channel walls.

This study presents an active flow control framework for fluid–structure interaction (FSI) systems involving a flexible plate in the wake of a cylinder, by integrating Koopman-based reduced-order models (ROMs) with model predictive control (MPC). Specifically, a novel switched-system control strategy is developed, wherein kernel dynamic mode decomposition (DMD) and residual DMD are jointly employed to construct accurate ROMs capable of capturing strongly nonlinear FSI dynamics. This approach ensures accurate low-order representations across multiple control inputs, while suppressing spurious modes. The resulting Koopman ROMs provide fast state predictions over a receding horizon, enabling an MPC optimiser to determine real-time actuation. To improve control performance, resolvent analysis is utilised to optimise the actuator–probe placement. Remarkably, only three strategically placed structural probes are sufficient to capture dominant Koopman modes and enable effective closed-loop control. The proposed framework is then applied to regulate synthetic jets on the cylinder to suppress the plate’s flapping. It successfully stabilises large-amplitude (LAF), small-deflection (SDF) and small-amplitude (SAF) flapping regimes within a unified control strategy. By combining Koopman modal decomposition with an analysis of system energy evolution, we elucidate distinct control mechanisms across these regimes. For LAF and SAF cases, control is achieved primarily through local modulation of existing saturated modes, which requires relatively low actuation energy. In contrast, stabilisation of the SDF case involves the emergence of entirely new Koopman modes that disrupt the original symmetry-breaking dynamics, resulting in increased control input. The framework matches the control performance of reinforcement learning while markedly reducing computational cost.

We investigate the effectiveness of linear optimal perturbation (LOP) for the flow past a finite span wing in reducing the lifespan of its trailing vortex system. Two approaches, referred to as local and model analysis, are introduced and used for our investigation. Both analyses assume that the baseflow is parallel. Local analysis is suited for intermediate distance from the wing where both tip vortices (TVs) and trailing edge wake (TEW) are present. Its results suggest that the unperturbed baseflow is stable. The separation between TVs and TEW increases downstream and their dynamics appear to be uncoupled at large distance from the wing. When perturbation corresponding to LOP is added to the baseflow, the vortices are displaced forming a helical twist. With time, the maximum displacement initially increases and then saturates. The perturbation retains its compact wavepacket-like structure, and perturbation energy within the tip vortex remains nearly constant. In the model analysis, the far wake is modelled as a pair of counter-rotating $q$-vortices. For low Reynolds number, the flow is stable. However, for higher Reynolds number, the trailing vortices develop Crow instability. Its growth rate is found to be in good agreement with earlier studies. Instability leads to contact of vortices, resulting in the formation of vortex rings. The time for vortex contact decreases with increase in the strength of the initial perturbation. The results suggest that LOP is effective in reducing the lifespan of trailing vortices.

The Richtmyer–Meshkov instability (RMI) develops when a planar shock front hits a rippled contact surface separating two different fluids. After the incident shock refraction, a transmitted shock is always formed and another shock or a rarefaction is reflected back. The pressure/entropy/vorticity fields generated by the rippled wavefronts are responsible of the generation of hydrodynamic perturbations in both fluids. In linear theory, the contact surface ripple reaches an asymptotic normal velocity which is dependent on the incident shock Mach number, fluid density ratio and compressibilities. In this work we only deal with the situations in which a shock is reflected. Our main goal is to show an explicit, closed form expression of the asymptotic linear velocity of the corrugation at the contact surface, valid for arbitrary Mach number, fluid compressibilities and pre-shock density ratio. An explicit analytical formula (closed form expression) is presented that works quite well in both limits: weak and strong incident shocks. The new formula is obtained by approximating the contact surface by a rigid piston. This work is a natural continuation of J. G. Wouchuk (2001 Phys. Rev. E vol. 63, p. 056303) and J. G. Wouchuk (2025 Phys. Rev. E vol. 111, p. 035102). It is shown here that a rigid piston approximation (RPA) works quite well in the general case, giving reasonable agreement with existing simulations, previous analytical models and experiments. An estimate of the relative error incurred because of the RPA is shown as a function of the incident shock Mach number $M_i$ and ratio of $\gamma $ values at the contact surface. The limits of validity of this approximation are also discussed. The calculations shown here have been done with the scientific software Mathematica. The files used to do these calculations can be retrieved as Supplemental Files to this article.

Dispersion is a common phenomenon in miscible displacement flows. In the primary cementing process displacement takes place in a narrow eccentric annulus. Both turbulent Taylor dispersion and laminar advective dispersion occur, depending on flow regime. Since dispersion can cause mixing and contamination close to the displacement front, it is essential to understand and quantify. The usual modelling approach is a form of Hele-Shaw model in which quantities are averaged across the narrow annular gap: a so-called two-dimensional narrow gap (2DGA) model. Zhang & Frigaard (J. Fluid Mech., vol. 947, 2022, A732), introduced a dispersive two-dimensional gap-averaged (D2DGA) model for displacement of two Newtonian fluids, by modifying the earlier 2DGA model. This brings a significant improvement in revealing physical phenomena observed experimentally and in three-dimensional computations, but is limited to Newtonian fluids. In this study we adapt the D2DGA model approach for two Herschel–Bulkley fluids. We first obtain weak velocity solutions using the augmented Lagrangian method, while keeping the same two-layer flow assumption as the Newtonian D2DGA model. These solutions are then used to define closure relationships that are needed to compute the dispersive two-dimensional flows. Results reveal that the modified version of the D2DGA model can now predict expected frontal behaviours for two Herschel–Bulkley fluids, revealing dispersion, frontal shock, spike and static wall layer solutions. We then explore the displacement behaviour in more detail by investigating the impact of rheological properties and buoyancy on the mobility of fluids in a planar frontal displacement flow and their vulnerability to fingering-type instabilities. As the underlying flows are dispersive, our analysis reveals three distinct behaviours: (i) stable, (ii) partial penetration of the dispersing front, and (iii) unstable regimes. We explore these regimes and how they are affected by the two fluid rheologies.

Compliant walls made from homogeneous viscoelastic materials may attenuate the amplification of Tollmien–Schlichting waves (TSWs) in a two-dimensional boundary-layer flow, but they also amplify travelling-wave flutter (TWF) instabilities at the interface between the fluid and the solid, which may lead to a premature laminar-to-turbulent transition. To mitigate the detrimental amplification of TWF, we propose to design compliant surfaces using phononic structures that aim at avoiding the propagation of elastic waves in the solid in the frequency range corresponding to the TWF. Thus, stiff inserts are periodically incorporated into the viscoelastic wall in order to create a band gap in the frequency spectrum of the purely solid modes. Fluid–structural resolvent analysis shows that a significant reduction in the amplification peak related to TWF is achieved while only marginal deterioration in the control of TSWs is observed. This observation suggests that the control of TSWs is still achieved by the overall compliance of the wall, while the periodic inserts inhibit the amplification of TWF. Bloch analysis is employed to discuss the propagation of elastic waves in the phononic surface to deduce design principles, accounting for the interaction with the flow.

In this paper we propose a novel control strategy for modulating nonlinear flapping and symmetry-breaking (S-B) bifurcations of a piezoelectric metamaterial beam behind a circular cylinder subjected to viscous flow. The beam incorporates distributed piezoelectric meta-cells connected via unidirectional circuits to enable self-sensing and adaptive control. A strongly coupled nonlinear fluid-structure-electro-control model within an arbitrary Lagrangian–Eulerian framework is developed for predicting the flapping dynamics of the large deformable piezoelectric metamaterial beam. The system exhibits multiple flow-induced modes, including limit-cycle oscillations, subharmonic responses and S-B deflections. These dynamic regimes arise from nonlinear bifurcations of the system, namely the period-doubling and spontaneous S-B bifurcations. Flapping control and wake topology transition of the system is achieved by suppressing the periodic-doubling bifurcation based on the vibration rebound effect through a self-sensing and adaptive-actuation mechanism of the beam. Floquet stability analysis confirms the effectiveness of control in delaying instability onset and suppressing chaotic transitions. Symmetry modulation of the beam is achieved via the localised perturbations induced from the piezoelectric meta-cells, which reshape the stability of the system. The transition from S-B mode to symmetry-recovery mode reflects a shift from a flow-separation-dominated to vibration-dominated vortex shedding pattern. This symmetry transition reorganises the energy exchange pathways between the flow and the beam. Quantitative analyses of the wake recovery and the energy harvesting efficiency confirm enhanced flow energy conversion under control. These results establish a framework for bifurcation control of slender structures in viscous flow, providing potential applications for underwater energy harvesting and flexible propulsion in unsteady environments.

When a low Mach flow is imposed through an orifice at the end of a cavity, intense whistling can occur. It results from the constructive feedback loop between the acoustic field of the cavity and coherent vortex shedding at the edges of the orifice with bias flow. Whistling is often a source of unwanted noise, demanding passive control strategies. In this study, it is shown that whistling can be suppressed by utilising the slow-sound effect. This periodic arrangement of small cavities detunes the cavity from the frequency range where the orifice flow exhibits a potential for acoustic energy amplification, by reducing the effective speed of sound inside the cavity. Acoustic and optical measurement techniques are employed, including scattering matrix and impedance measurements, and particle image velocimetry to reconstruct the velocity field downstream of the orifice. The production and dissipation of acoustic energy is investigated using Howe’s energy corollary. The spatio-temporal patterns of the vortex sound downstream of the orifice are revealed. They are deduced from phase-averaged acoustic and Lamb vector fields and give qualitative insight into the physical mechanisms of the whistling phenomenon.

We study the stationary, intermittent and nonlinear dynamics of nominally ideally expanded, natural and forced supersonic twin-rectangular turbulent jets using spectral modal decomposition. We decompose large-eddy simulation data into four reflectional symmetry components about the major and minor axes. In the natural jet, spectral proper orthogonal decomposition (SPOD) uncovers two resonant instabilities antisymmetric about the major axis. Known as screech tones, the more energetic of the two is a steady flapping instability, while the other is an intermittent double-flapping instability. We test the hypothesis that symmetry breaking can be leveraged for control design. Time-periodic forcing symmetric about the major and minor axes is implemented using a plasma actuation model, and succeeds in removing screech from a different symmetry component. We investigate the spectral peaks of the forced jet using an extension of bispectral mode decomposition (BMD), where the bispectrum is bounded by unity and which conditionally recovers the SPOD. We explain the appearance of harmonic peaks as three sets of triadic interactions between reflectional symmetries, forming an interconnected triad network. BMD modes of active triads distil coherent structures comprising multiple coupled instabilities, including Kelvin–Helmholtz, core and guided-jet modes (G-JM). Downstream-propagating core modes can be symmetric or antisymmetric about the major axis, whereas upstream-propagating G-JM responsible for screech closure (Edgington-Mitchell et al. J. Fluid Mech.945, 2022, p. A8) are antisymmetric only. The dependence of G-JM on symmetry hence translates from the azimuthal symmetry of the round jet to the dihedral group symmetry of the twin-rectangular jet, and explains why the twin jet exhibits antisymmetric but not symmetric screech modes.

The impact of two-dimensional (2-D) periodic forcing on transition dynamics in laminar separation bubbles (LSBs) generated on a flat plate is investigated experimentally. Laminar separation is caused by the favourable-to-adverse pressure gradient under an inverted modified NACA $64_3\text{-}618$ and periodic disturbances are generated by an alternating current dielectric barrier discharge plasma actuator located near the onset of the adverse pressure gradient. Surface pressure and time-resolved particle image velocimetry measurements along the centreline and several wall-parallel planes show significant reductions in bubble size with active flow control. Periodic excitation leads to amplification of the Kelvin–Helmholtz (K–H) instability resulting in strong 2-D coherent roller structures. Spanwise modulation of these structures is observed and varies with the forcing amplitude. Intermediate forcing amplitudes result in periodic spanwise deformation of the mean flow at large wavelength ($\lambda _z/L_{b,5kVpp} \approx 0.76$). For high-amplitude forcing, the spanwise modulation of the mean flow agrees with the much smaller wavelength of the difference interaction of two oblique subharmonic modes ($\lambda _z/L_{b,5kVpp} \approx 0.24$). Modal decomposition shows nonlinear interaction of the forced 2-D mode leading to growth of subharmonic and harmonic content, and the observation of several half-harmonics ($[n+1/2]f_{\textit{AFC}}$) at intermediate forcing amplitudes. Strongest amplitudes of the 2-D mode and delay of transition downstream of the time-averaged reattachment are observed for the intermediate forcing amplitudes, previously only observed in numerical simulations. Consistent with numerical results, further increase of the forcing amplitude leads to rapid breakdown to turbulence in the LSB. This suggests that the most effective exploitation of the K–H instability for transition delay is connected to an optimal (moderate) forcing amplitude.

The interaction between the dynamics of a flame front and the acoustic field within a combustion chamber represents an aerothermochemical problem with the potential to generate hazardous instabilities, which limit burner performance by constraining design and operational parameters. The experimental configuration described here involves a laminar premixed flame burning in an open–closed slender tube, which can also be studied through simplified modelling. The constructive coupling of the chamber acoustic modes with the flame front can be affected via strategic placement of porous plugs, which serve to dissipate thermoacoustic instabilities. These plugs are lattice-based, 3-D-printed using low-force stereolithography, allowing for complex geometries and optimal material properties. A series of porous plugs was tested, with variations in their porous density and location, in order to assess the effects of these variables on viscous dissipation and acoustic eigenmode variation. Pressure transducers and high-speed cameras are used to measure oscillations of a stoichiometric methane–air flame ignited at the tube’s open end. The findings indicate that the porous medium is effective in dissipating both pressure amplitude and flame-front oscillations, contingent on the position of the plug. Specifically, the theoretical fluid mechanics model is developed to calculate frequency shifts and energy dissipation as a function of plug properties and positioning. The theoretical predictions show a high degree of agreement with the experimental results, thereby indicating the potential of the model for the design of dissipators of this nature and highlighting the first-order interactions of acoustics, viscous flow in porous media and heat transfer processes.

This paper presents a method to stabilise oscillations occurring in a mixed convective flow in a nearly hemispherical cavity, using actuation based on the receptivity map of the unstable mode. This configuration models the continuous casting of metallic alloys, where hot liquid metal is poured at the top of a hot sump with cold walls pulled in a solid phase at the bottom. The model focuses on the underlying fundamental thermohydrodynamic processes without dealing with the complexity inherent to the real configuration. This flow exhibits three branches of instability. The solution of the adjoint eigenvalue problem for the convective flow equations reveals that the regions of highest receptivity for unstable modes of each branch concentrate near the inflow upper surface. Simulations of the linearised governing equations show that a thermomechanical actuation modelled on the adjoint eigenmode asymptotically suppresses the unstable mode. If the actuation’s amplitude is kept constant in time, which is easier to implement in an industrial environment, the suppression is still effective but only over a finite time, after which it becomes destabilising. Based on this phenomenology, we apply the same actuation during the stabilising phase only in the nonlinear evolution of the unstable mode. It turns out stabilisation persists, even when the unstable mode is left to evolve freely after the actuation period. These results not only demonstrate the effectiveness of receptivity-informed actuation in stabilising convective oscillations but also suggest a simple strategy for their long-term control.

Flow over bluff bodies encounters instability at supercritical Reynolds numbers, exhibiting the periodic vortex shedding that leads to structural vibrations and acoustic noise. In this paper, a new aerodynamic shape optimisation strategy based on resolvent analysis is proposed to passively control the vortex shedding over two-dimensional cylinders. Firstly, we show that when the flow satisfies the rank-1 approximation, minimizing the maximal resolvent gain enhances flow stability. Secondly, we formulate the geometry-constrained resolvent-based optimisation problem that can be solved by the nonlinear conjugate gradient algorithm. Compared with conventional stability-based optimisation, the proposed approach is more effective as it avoids the cumbersome eigendecomposition of the high-dimensional Jacobian matrix. The efficacy of the proposed resolvent-based optimisation is validated through improving the stability of the one-dimensional Ginzburg–Landau equation. Thirdly, this approach is applied to suppress the vortex shedding of bluff bodies, initialised by a circular cylinder. Although the optimisation is performed at a subcritical state $Re = 40$, reduced vortex shedding and drag forces can be achieved at supercritical Reynolds numbers, while the critical Reynolds number is extended from $47$ to $60$. Dynamic mode decomposition is then performed to reveal that the optimised system becomes more stable and satisfies the rank-1 approximation. Finally, we demonstrate that the combined effects of the flattened surface and the Coanda effect delay flow separation, keeping the separation point nearly unchanged at supercritical Reynolds numbers (e.g. between 80 and 140) for the optimised geometry. This results in a substantial reduction in the strength of vortex shedding, which in turn leads to decreased drag forces. The optimised shape still achieves drag reduction in turbulent flows at a relatively high Reynolds number.

A reactive control strategy is implemented to attenuate the streaks formed on a wing boundary layer due to free-stream turbulence (FST). Numerical simulations are performed on a section of a NACA0008 profile, considering its leading edge, while forced by FST with turbulence intensities of 0.5 % and 2.5 %. The controller is composed of localised sensors and actuators, with the control law consisting of a linear quadratic Gaussian regulator designed on a reduced-order model based only on the impulse responses of the system. Three configurations are evaluated by considering three different numbers of sensors/actuators along the spanwise direction. It is found that all configurations are effective in damping the streaks inside the boundary layer, whose effect is sustained downstream of the objective function location. However, distinct behaviours are observed when comparing the capability of the controllers with delay transition, where the best performance is attained for the case with larger number of sensors/actuators. This is attributed to the effectiveness of the controller in damping the streaks that will later break down, which in this case are associated with relatively short spanwise wavelength. This observation is confirmed by analysing the stability of the flow before the appearance of turbulent spots. Our results suggest that for an effective transition delay, efforts should not only be put into control of streaks with average spanwise wavelength, but also in the short spanwise wavelength associated with breakdown.

It is known that the complex eigenfrequencies of one-dimensional systems of large but finite extent are concentrated near the asymptotic curve determined by the dispersion relation of an infinite system. The global instability caused by uppermost pieces of this curve was studied in various problems, including hydrodynamic stability and fluid–structure interaction problems. In this study, we generalise the equation for the asymptotic curve to arbitrary frequencies. We analyse stable local topology of the curve and prove that it can be a regular point, branching point or dead-end point of the curve. We give a classification of unstable local tolopogies, and show how they break up due to small changes of the problem parameters. The results are demonstrated on three examples: supersonic panel flutter, flutter of soft fluid-conveying pipe, and the instability of rotating flow in a pipe. We show how the elongation of the system yields the attraction of the eigenfrequencies to the asymptotic curve, and how each locally stable curve topology is reflected on the interaction of eigenfrequencies.

The reduction of the hydrodynamic forces exerted on a bluff body in an incoming flow has been an issue of interest in fluid mechanics for many years. However, the Magnus effect indicates possible drag reduction but with the lift being increased significantly. This study is aimed at the simultaneous lift and drag reduction for which we consider a constant incoming flow past a circular cylinder or a sphere in the $x$-direction. Force element analysis (FEA) indicates the possibility of reducing the drag exerted on a circular cylinder or a sphere by rotating (say, clockwise about the $z$-axis) only the front half of the circular cylinder or the sphere. More precisely, we rotate the object but with the rear half covered by a closely spaced hood. Numerical simulations show that by increasing the dimensionless rotational speed $\alpha$: (i) the flow can be quickly stabilised to a steady state; (ii) the mean drag steadily decreases to zero and then becomes negative as $\alpha$ is further increased across the critical $\alpha _I = 4.11$ for the circular cylinder at $Re$ = 200, $\alpha _I = 4.81$ for the sphere at $Re$ = 200 and $\alpha _I = 4.92$ for the sphere at $Re$ = 300; (iii) the mean value of the lift decreases from zero to negative and then increases beyond zero, and in addition, the amplitude of the lift gradually decreases for the circular cylinder; the mean value of the lift decreases from zero to negative for the sphere; (iv) the side force is almost zero – the flow over the sphere is plane-symmetric about the $x{-}y$ plane. These features are compared with the flow past a rotating circular cylinder or a rotating sphere (Magnus effect). Notably, there is a range of flows that can be of practical use for: (a) the circular cylinder where the drag is greatly reduced while the lift is small in magnitude and (b) the sphere where the drag is greatly reduced while the lift is negative in magnitude and the side force is close to 0.

We demonstrate the first successful non-invasive stabilisation of nonlinear travelling waves in a straight cylindrical pipe using time-delayed feedback control working in various symmetric subspaces. By using an approximate linear stability analysis and by analysing the frequency-domain effect of the control using transfer functions, we find that solutions with well-separated unstable eigenfrequencies can have narrow windows of stabilising time delays. To mitigate this issue we employ a ‘multiple time-delayed feedback’ approach, where several control terms are included to attenuate a broad range of unstable eigenfrequencies. We implement a gradient descent method to dynamically adjust the gain functions in order to reduce the need for tuning a high-dimensional parameter space. This results in a novel control method where the properties of the target state are not needed in advance, and speculative guesses can result in robust stabilisation. This enables travelling waves to be stabilised from generic turbulent states and unknown travelling waves to be obtained in highly symmetric subspaces.