We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data of stratified flows. A fully connected deep neural network is trained using time-resolved experimental data in a salt-stratified inclined duct experiment, consisting of three-component velocity fields and density fields measured simultaneously in three dimensions at Reynolds number $= O(10^3)$ and at Prandtl or Schmidt number $=700$. The PINN enforces incompressibility, the governing equations for momentum and buoyancy, and the boundary conditions at the duct walls. These physics-constrained, augmented data are output at an increased spatio-temporal resolution and demonstrate five key results: (i) the elimination of measurement noise; (ii) the correction of distortion caused by the scanning measurement technique; (iii) the identification of weak but dynamically important three-dimensional vortices of Holmboe waves; (iv) the revision of turbulent energy budgets and mixing efficiency; and (v) the prediction of the latent pressure field and its role in the observed asymmetric Holmboe wave dynamics. These results mark a significant step forward in furthering the reach of experiments, especially in the context of stratified turbulence, where accurately computing three-dimensional gradients and resolving small scales remain enduring challenges.

Using thermal convection in liquid metal, we show that strong spatial confinement not only delays the onset Rayleigh number $Ra_c$ of Rayleigh–Bénard instability but also postpones the various flow-state transitions. The $Ra_c$ and the transition to fully developed turbulence Rayleigh number $Ra_f$ depend on the aspect ratio $\varGamma$ with $Ra_c\sim \varGamma ^{-4.05}$ and $Ra_f\sim \varGamma ^{-3.01}$, implying that the stabilization effects caused by the strong spatial confinement are weaker on the transition to fully developed turbulence when compared with that on the onset. When the flow state is characterized by the supercritical Rayleigh number $Ra/Ra_{c}$ ($Ra$ is the Rayleigh number), our study shows that the transition to fully developed turbulence in strongly confined geometries is advanced. For example, while the flow becomes fully developed turbulence at $Ra\approx 200Ra_c$ in a $\varGamma =1$ cell, the same transition in a $\varGamma =1/20$ cell only requires $Ra\approx 3Ra_c$. Direct numerical simulation and linear stability analysis show that in the strongly confined regime, multiple vertically stacked roll structures appear just above the onset of convection. With an increase of the driving strength, the flow switches between different-roll states stochastically, resulting in no well-defined large-scale coherent flow. Owing to this new mechanism that only exists in systems with $\varGamma <1$, the flow becomes turbulent in a much earlier stage. These findings shed new light on how turbulence is generated in strongly confined geometries.

Industrial applications of flow through fractures such as geothermal energy or hydraulic stimulation involve forcing large flow rates through small fractures, thereby inducing inertial fluid behaviours and turbulence. The most common fracture flow model, Poiseuille flow (the cubic law), is incapable of capturing these phenomena and thus the impact of inertial and turbulent forces in fracture flow has remained relatively unexplored. The GG22 flow model is a newly derived fracture flow model that is capable of capturing inertial, transient and turbulent forces. In this article, we apply the GG22 flow model to hydraulic stimulation of radial fractures for the first time to determine how these phenomena manifest. We show that inertia and turbulence only manifest near the wellbore (within 30 radii) and lead to changes in fracture shape and injection pressure but have little impact on tip behaviour. Turbulence increases wellbore pressure and aperture while inertia decreases wellbore pressure and aperture. The majority of the pressure loss along the fracture occurs near the wellbore and is captured by turbulence where entrance correction factors would otherwise be needed. Using water, turbulence is the dominant mechanism that causes departures from Poiseuille flow at high $Re$. The solution departs immediately upon the manifestation of turbulence ($Re\geq 2\times 10^3$), while inertial effects manifest at higher flow rates ($Re\geq 2\times 10^4$). Using slickwater, the opposite trend is observed: inertial effects manifest first ($Re\geq 5\times 10^3$), while turbulent effects are delayed ($Re\geq 10^4$). In both cases, the threshold for departures from the Poiseuille flow solution are low and the differences are large.

Beneitez et al. (Phys. Rev. Fluids, vol. 8, 2023, L101901) have recently discovered a new linear ‘polymer diffusive instability’ (PDI) in inertialess rectilinear viscoelastic shear flow using the finitely extensible nonlinear elastic constitutive model of Peterlin (FENE-P) when polymer stress diffusion is present. Here, we examine the impact of inertia on the PDI for both plane Couette and plane Poiseuille flows under varying Weissenberg number ${W}$, polymer stress diffusivity $\varepsilon$, solvent-to-total viscosity ratio $\beta$ and Reynolds number ${Re}$, considering the FENE-P and simpler Oldroyd-B constitutive relations. Both the prevalence of the instability in parameter space and the associated growth rates are found to significantly increase with ${Re}$. For instance, as $Re$ increases with $\beta$ fixed, the instability emerges at progressively lower values of $W$ and $\varepsilon$ than in the inertialess limit, and the associated growth rates increase linearly with $Re$ when all other parameters are fixed. For finite $Re$, it is also demonstrated that the Schmidt number $Sc=1/(\varepsilon Re)$ collapses curves of neutral stability obtained across various $Re$ and $\varepsilon$. The observed strengthening of PDI with inertia and the fact that stress diffusion is always present in time-stepping algorithms, either implicitly as part of the scheme or explicitly as a stabilizer, implies that the instability is likely operative in computational work using the popular Oldroyd-B and FENE-P constitutive models. The fundamental question now is whether PDI is physical and observable in experiments, or is instead an artifact of the constitutive models that must be suppressed.

Direct numerical simulations of turbulent flows over highly permeable porous walls were performed at various Reynolds numbers to examine the effects of the Reynolds number on permeable wall turbulence. The porous medium consisted of Kelvin cell arrays with porosity $0.95$, and the permeability Reynolds number $Re_K$ ranged from approximately 7 to 50. Simulations with thin and thick porous walls were performed to investigate the effects of spanwise roller vortices associated with the Kelvin–Helmholtz instability. The results show that the effect of the Kelvin–Helmholtz instability becomes more significant with increasing the permeability Reynolds number, and spanwise rollers, for which length scale is an order of channel height, dominate turbulence when $Re_K \gtrsim 30$. Spanwise rollers reinforce the negative correlation between the wall-normal and streamwise velocity fluctuations close to the porous/fluid interface, and intensify the turbulent velocity fluctuations away from the porous walls, leading to increased frictional resistance. An investigation of the Reynolds number dependence of the modified logarithmic law indicates that the zero-plane displacement and equivalent roughness height are proportional to the square root of permeability, whereas the von Kármán constant increases with the permeability Reynolds number because of the increased mixing length resulting from the relatively large-scale velocity fluctuations induced by spanwise rollers. We developed a model for the modified log law for permeable wall turbulence based on permeability, and confirmed that the skin friction coefficient obtained from the model reasonably predicts the skin friction coefficient for several types of high-porosity porous media. Hence, permeability is a key parameter that characterizes the logarithmic mean velocity profiles over a variety of porous media with high porosity.

Splashing of impacting drops produces a myriad of secondary spray droplets, which generate aerosols during rain on the ocean and can cause health hazards during the spraying of pesticides or enhance the droplet transmission of disease. Determining the size and number of the finest splashed droplets is therefore of practical interest. Herein, we use a novel experimental facility with a 26 m tall vacuum tube, to study well-controlled drop impacts at velocities as high as 22 m s$^{-1}$, where we reach parameter regimes not studied before using freely falling drops. Using extreme video frame rates, we pinpoint the primary source of the finest spray, coming from the catastrophic bending and rupture of the sub-micron-thick ejecta sheet, which emerges at a high speed from the neck connecting the drop and pool. The axisymmetric bending and convoluted ejecta shapes are driven primarily by resistance from the surrounding air, but also depend on the viscosity difference between drop and pool, which influences the initial ejection angle of the sheet. These extreme impact conditions provide new insights into general spray formation, through a sequence of bucklings of the rising ejecta, which dances next to the drop surface and can also form an enclosed air torus.

The tangential strain rate in premixed flames impacts significantly the flame surface area generation and thus the combustion process. Studies on incompressible isotropic turbulence have revealed that the mean tangential strain rate at material and iso-scalar surfaces is positive and exhibits a universal value when normalized by the Kolmogorov time. This is associated with the preferential alignment of the surface normal with the most compressive principal strain rate. The present study investigates such effects in premixed hydrogen and iso-octane flame kernels using direct numerical simulations. It is shown that the normalized mean tangential strain rate of the investigated flames has a very similar value compared with the incompressible flows. However, in the reaction zone, the flame surface normal aligns preferentially with the most extensive principal strain rate. Furthermore, this alignment depends on the reaction progress variable and the Lewis number, while the tangential strain rate remains independent of these parameters. Such counter-intuitive behaviour is systematically investigated by decomposing the effects of dilatation and residual solenoidal turbulence. It is found that the solenoidal turbulence influences significantly the tangential strain rate. A general effect of turbulence on the tangential strain rate is identified, which is consistent with incompressible flows and independent of the Lewis number and the reaction progress variable. This is a remarkable finding indicating that models of the tangential strain rate developed based on incompressible flows apply also to premixed flames with different Lewis numbers, and, for the modelling, only the solenoidal turbulence should be considered.

Direct numerical simulations of temporally developing mixing layers have been performed to investigate the effects of compressibility on statistics and structures near the interfaces of high- and low-speed large-scale structures (LSSs), covering a range of convective Mach numbers from $M_c=0.2$ to $1.8$ and Taylor Reynolds numbers up to 290. The interfaces of LSSs are directly defined by the isosurface of zero fluctuating streamwise velocity. The characteristic velocity jump at the interfaces grows rapidly in the transition stage and then decreases until reaching a gradual self-similar stage. The evolution of velocity jump is evidently delayed as the convective Mach number increases. The interface layer is formed by the shearing motion of neighbouring LSSs. A small vortical motion characterized by the Kolmogorov scale is induced in the interface layer by shear-dominated outer regions. The strengths of outer shearing motion and central vortical motion are greater at the leading edge, but smaller at the trailing edge, which is also reflected in a larger velocity jump at the leading edge. As the convective Mach number increases, the small-scale vortical structure is obviously suppressed by compressibility. At high convective Mach number $M_c=1.8$, the compressive shear-dominated outer regions are linked with a sheet-like structure passing through the centre of the expansion region corresponding to a small-scale vortical structure. The compressibility and shearing strength near the interface are highly dependent on the interface orientation.

Rotational effects are commonly neglected when considering the dynamics of freely rising or settling isotropic particles. Here, we demonstrate that particle rotations play an important role for rising as well as for settling cylinders in situations when mass eccentricity, and thereby a new pendulum time scale, is introduced to the system. We employ two-dimensional simulations to study the motion of a single cylinder in a quiescent unbounded incompressible Newtonian fluid. This allows us to vary the Galileo number, density ratio, relative moment of inertia (MOI) and centre-of-mass (COM) offset systematically and beyond what is feasible experimentally. For certain buoyant density ratios, the particle dynamics exhibits a resonance mode, during which the coupling via the Magnus lift force causes a positive feedback between translational and rotational motions. This mode results in vastly different trajectories with significantly larger rotational and translational amplitudes and an increase of the drag coefficient easily exceeding a factor two. We propose a simple model that captures how the occurrence of the COM offset induced resonance regime varies, depending on the other input parameters, specifically the density ratio, the Galileo number and the relative MOI. Remarkably, depending on the input parameters, resonance can be observed for COM offsets as small as a few per cent of the particle diameter, showing that the particle dynamics can be highly sensitive to this parameter.

We study a thin, laterally confined heated liquid layer subjected to mechanical parametric forcing without gravity. In the absence of parametric forcing, the liquid layer exhibits the Marangoni instability, provided the temperature difference across the layer exceeds a threshold. This threshold varies with the perturbation wavenumber, according to a curve with two minima, which correspond to long- and short-wave instability modes. The most unstable mode depends on the lateral confinement of the liquid layer. In wide containers, the long-wave mode is typically observed, and this can lead to the formation of dry spots. We focus on this mode, as the short-wave mode is found to be unaffected by parametric forcing. We use linear stability analysis and nonlinear computations based on a reduced-order model to investigate how parametric forcing can prevent the formation of dry spots. At low forcing frequencies, the liquid film can be rendered linearly stable within a finite range of forcing amplitudes, which decreases with increasing frequency and ultimately disappears at a cutoff frequency. Outside this range, the flow becomes unstable to either the Marangoni instability (for small amplitudes) or the Faraday instability (for large amplitudes). At high frequencies, beyond the cutoff frequency, linear stabilization through parametric forcing is not possible. However, a nonlinear saturation mechanism, occurring at forcing amplitudes below the Faraday instability threshold, can greatly reduce the film surface deformation and therefore prevent dry spots. Although dry spots can also be avoided at larger forcing amplitudes, this comes at the expense of generating large-amplitude Faraday waves.

A new wall function method for hypersonic laminar boundary layers (HLBLs) is proposed to reduce the near-wall grid dependence of skin friction $c_f$ and wall heat flux $q_w$ in numerical simulations, aiming for fast and accurate predictions. First, an analytic laminar velocity law of the wall is derived, which achieves a universal scaling of the near-wall velocity of HLBLs. Then an accurate temperature–velocity relation is deduced by introducing the general recovery factor to address the invalidation of the Walz relation under the cold wall effect. Based on the laminar laws of the wall, a new wall function method for HLBLs is proposed. To avoid introducing the boundary layer edge quantities, the laminar laws of the wall are reformed by modifying the outer boundary conditions of the differential equation in deriving the temperature–velocity relation. Unlike the wall function method in turbulence, the new wall function obtains directly the accurate $c_f$ and $q_w$ by post-processing without being involved in the simulation iteration. The numerical experiments of a Mach 8 HLBL over the flat plate show that effectively, the new wall function can enlarge the distance of the first grid point off the wall $\Delta y_1$ from $10^{-6}$ m to $10^{-3}$ m, which brings a 50 times enhancement of the simulation efficiency. Meanwhile, the simulation errors of $c_f$ and $q_w$ of the mesh with $\Delta y_1=10^{-3}$ m are reduced significantly from 24.2 % and 18.5 % to 0.5 % and 0.1 %, respectively. Due to the new wall function removing the boundary layer edge quantities, success is also achieved under the curved walls.

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al., J. Fluid Mech., vol. 917, 2021, A6). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O($10^8$). As a function of the Prandtl number, $Pr$, and the height-to-width aspect ratio of the domain, $A$, the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly, the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$. For $Pr \lessapprox 0.4$ and $A>1$, the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$, the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm 0.15$ and $A <2$.

Flow generation by colloidal motors activated by external stimuli is an important issue for active matter physics and several nanotechnological or biomedical applications. For instance, flow recirculation generated by rotating magnetic self-assemblies allows effective ‘pumping’ of a thrombolytic drug towards a blood clot along a blocked vessel. However, the physics of the flow generation in this case remains still poorly explored. This study is focused on the generation of a recirculation flow of a magnetic colloid (aqueous suspension of iron oxide nanoparticles with partially screened electrostatic repulsion) within a closed microfluidic channel via application of an external rotating magnetic field. The colloid undergoes reversible phase separation manifested through the appearance of micron-sized elongated aggregates. They synchronously rotate with the magnetic field and can generate macroscopic flows only in the presence of gradients of the aggregate concentration across the channel induced by superposition of a weak magnetic field gradient to the homogeneous rotating field. We achieve recirculation flows with a characteristic speed ${\sim} 5{-}8\;{\rm \mu}\textrm{m}\;{\textrm{s}^{ - \textrm{1}}}$ at low magnetic field amplitude and frequency (${H_0} \approx 3{-}10\;\textrm{kA}\;{\textrm{m}^{ - 1}}$, ${f = 5{-}15\ \textrm{Hz}}$) at low nanoparticle volume fraction ${\varphi _p} = (1.6{-}3.2) \times {10^{ - 3}}$. The concentration and velocity profiles have been assessed experimentally through particle tracking and particle image velocimetry, and have also been computed using the hydrodynamic diffusion approach coupled with the momentum balance equation with a magnetic torque term. The model correctly reproduces the shape of the experimental concentration and velocity fields and explains complex behaviours of the average recirculation speed as a function of governing parameters (${H_0}$, f, ${\varphi _p}$, channel size).

In this paper, we investigate periodic travelling waves in a three-layer system with the rigid-lid assumption. Solutions are recovered numerically using a boundary integral method. We consider the case where the density difference between the layers is small (i.e. a weakly stratified fluid). We consider the system both with and without the Boussinesq assumption to explore the effect the assumption has on the solution space. Periodic solutions of both mode-1 and mode-2 are found, and their bifurcation structure and limiting configurations are described in detail. Similarities are found with the two-layer case, where large-amplitude solutions are found to overhang with an internal angle of $120^{\circ }$. However, the addition of a second interface results in a richer bifurcation space, in part due to the existence of mode-2 waves and their resonance with mode-1 waves. New limiting profiles are found.

This study reports the first time-resolved particle image velocimetry characterization of a planar two-phase mixing layer flow, whose velocity field is measured simultaneously in gas and liquid streams. Two parallel air and water flows meet downstream of a splitter plate, giving rise to an initially spanwise invariant configuration. The aim is to elucidate further the mechanisms leading to the flow breakup in gas-assisted atomization. The complete experimental characterization of the velocity field represents a database that could be used in data-driven reduced-order models to investigate the global behaviour of the flow system. After the analysis of a selected reference case, a parametric study of the flow behaviour is performed by varying the liquid ($Re_l$) and gas ($Re_g$) Reynolds numbers, and as a consequence also the gas-to-liquid dynamic pressure ratio ($M$), shedding light on both time-averaged (mean) and unsteady velocity fields. In the reference case, it is shown that the mean flow exhibits a wake region just downstream of the splitter plate, followed by the development of a mixing layer. By increasing both $Re_l$ and $Re_g$, the streamwise extent of the wake decreases and eventually vanishes, the flow resulting in a pure mixing layer regime. The spectral analysis of the normal-to-flow velocity fluctuations outlines different flow regimes by variation of the governing parameters, giving more insights into the global characteristics of the flow field. As a major result, it is found that at high $Re_g$ and $M$ values, the velocity fluctuations are characterized by low-frequency temporal oscillations synchronized in several locations within the flow field, which suggest the presence of a global mode of instability. The proper orthogonal decomposition of velocity fluctuations, performed in both gas and liquid phases, reveals finally that the synchronized oscillations are associated with a low-frequency dominant flapping mode of the gas–liquid interface. Higher-order modes correspond to interfacial wave structures travelling with the so-called Dimotakis velocity. For lower gas Reynolds numbers, the leading modes describe higher frequency fingers shedding at the interface.

In the context of large off-shore wind farms, power production is influenced greatly by the turbine array's interaction with the atmospheric boundary layer. One of the most influencing manifestations of such complex interaction is the increased level of shear stress observed within the farm. This leads to higher momentum fluxes that affect the wind speed at the turbine locations and in the cluster wake. At the wind farm entrance, an internal boundary layer (IBL) grows due to the change in effective roughness imposed by the wind turbines, and for large enough clusters, this can reach the unperturbed boundary layer height in what is referred to as the fully developed regime. Downwind, a second IBL starts growing, while the shear stress profile decays exponentially to its unperturbed state. In the present study, we propose a simple analytical model for the vertical profile of the horizontal shear stress components in the three regions identified above. The model builds upon the top-down model of Meneveau (J. Turbul., vol. 13, 2012, N7), and assumes that the flow develops in a conventionally neutral boundary layer. The proposed parametrization is verified successfully against large-eddy simulations, demonstrating its ability to capture the vertical profile of horizontal shear stress, and its evolution both inside and downwind of the wind farm. Our findings suggest that the developed model can prove extremely useful to enhance the physical grounds on which new classes of coupled wind farm engineering models are based, leading to a better estimation of meso-scale phenomena affecting the power production of large turbine arrays.

Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range $Re_\tau \approx 550\unicode{x2013}5200$. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of $\lambda _x/y \approx 14$ (and $\lambda _x/y \approx 8$ for the wall-normal velocity). When extending the analysis to both homogeneous directions in $x$ and $y$, the peak coherence is centred at $\lambda _x/\lambda _z \approx 2$ and $\lambda _x/\lambda _z \approx 1$ for $p_w$ and $u$, and $p_w$ and $v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of $Re_\tau \approx 2$k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of $\approx$0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.

We report an experimental study about the effect of an obstructed centre on heat transport and flow reversal by inserting an adiabatic cylinder at the centre of a quasi-two-dimensional Rayleigh–Bénard convection cell. The experiments are carried out in a Rayleigh number ($Ra$) range of $2\times 10^7 \leq Ra \leq 2\times 10^9$ and at a Prandtl number ($Pr$) of $5.7$. It is found that for low $Ra$, the obstructed centre leads to a heat transfer enhancement of up to 21 $\%$, while as $Ra$ increases, the magnitude of the heat transfer enhancement decreases and the heat transfer efficiency ($Nu$) eventually converges to that of the unobstructed normal cell. Particle image velocimetry measurements show that the heat transfer enhancement originates from the change in flow topology due to the presence of the cylindrical obstruction. In the low-$Ra$ regime the presence of the obstruction promotes the transition of the flow topology from the four-roll state to the abnormal single-roll state then to the normal single-roll state with increasing obstruction size. While in the high-$Ra$ regime, the flow is always in the single-roll state regardless of the obstruction size, although the flow becomes more coherent with the size of the obstruction. We also found that in the presence of the cylindrical obstruction, the stability of the corner vortices is significantly reduced, leading to a large reduction in the frequency of flow reversals.

Active flow control for drag reduction with reinforcement learning (RL) is performed in the wake of a two-dimensional square bluff body at laminar regimes with vortex shedding. Controllers parametrised by neural networks are trained to drive two blowing and suction jets that manipulate the unsteady flow. The RL with full observability (sensors in the wake) discovers successfully a control policy that reduces the drag by suppressing the vortex shedding in the wake. However, a non-negligible performance degradation ($\sim$50 % less drag reduction) is observed when the controller is trained with partial measurements (sensors on the body). To mitigate this effect, we propose an energy-efficient, dynamic, maximum entropy RL control scheme. First, an energy-efficiency-based reward function is proposed to optimise the energy consumption of the controller while maximising drag reduction. Second, the controller is trained with an augmented state consisting of both current and past measurements and actions, which can be formulated as a nonlinear autoregressive exogenous model, to alleviate the partial observability problem. Third, maximum entropy RL algorithms (soft actor critic and truncated quantile critics) that promote exploration and exploitation in a sample-efficient way are used, and discover near-optimal policies in the challenging case of partial measurements. Stabilisation of the vortex shedding is achieved in the near wake using only surface pressure measurements on the rear of the body, resulting in drag reduction similar to that in the case with wake sensors. The proposed approach opens new avenues for dynamic flow control using partial measurements for realistic configurations.

Experiments were performed to document the complex flow field around and over a $70^{\circ }$ swept fin mounted on a $7^{\circ }$ half-angle right-circular cone in a Mach 6 free-stream. Of particular interest is the turbulent transition of the boundary layer over the swept fin, which is expected to be dominated by a cross-flow instability. Stationary features in the surface temperature distribution over the fin are documented using infrared thermal imaging. These were processed further to determine average spatial Stanton number distributions over the fin. Wavelet analysis of the Stanton number distributions revealed stationary patterns with wavelengths near the fin leading edge that were consistent with linear theory predictions of stationary cross-flow modes. Further from the leading edge, the wavelength of the stationary patterns was observed to increase prior to turbulence onset. Based on these observations, specially designed arrays of discrete roughness elements (DREs) were investigated as a means of delaying turbulence transition with the objective of reducing surface heat flux on the swept fin. The DRE designs followed our previous approach used for cross-flow transition control (Corke et al., J. Fluid Mech., vol. 856, issue 10, 2018, pp. 822–849; Arndt et al., J. Fluid Mech., vol. 887, 2020, A30). These focused on either the shorter wavelengths near the leading edge, or the longer wavelengths that developed near turbulence onset. With regard to delaying transition and reducing the surface heat flux, the DREs that focused on the larger wavelengths of stationary modes were most effective. The fin included an array of pressure sensors that were used to document travelling disturbances that could include those associated with travelling cross-flow modes. Phase analysis of the pressure fluctuation time series was used to determine the wavelength, wave angle and phase speed that were consistent with the travelling cross-flow modes. Cross-bicoherence analysis between the stationary and travelling disturbances indicates a nonlinear phase locking that can account for the development of the longer-wavelength stationary features in the surface heat flux, presumed to be due to stationary cross-flow modes, prior to turbulence onset.