This article extends the previous investigation of the spatial evolution of energy-containing motions in wall-bounded turbulent flows (Kannadasan et al., J. Fluid Mech., vol. 955, 2023, R1) by examining their scale-interactions through spectral analysis based on the spanwise scale decomposition of turbulent kinetic energy and the Reynolds stress transport equation. The energy-containing motions located at the inflow of a turbulent channel flow are artificially removed and the interscale transport mechanisms involved in their spatial evolution are studied. This scale interaction analysis reveals the presence of a significant inverse transfer of streamwise Reynolds stress from the near-wall streaks to larger scales in the spatial evolution of energy-containing motions. This transfer is due to the spanwise variation of streamwise velocity fluctuations, represented by $\partial u'/\partial z$, which is the primary mechanism of streak instability. The analysis presented in this study also shows that the inverse cascade of spanwise energy may correspond to the regeneration of streamwise vortices in the process of reactivating the self-sustaining mechanism in the spatial evolution of energy-containing motions.

This study demonstrates an experimental realization of turbulence control strategies previously explored by Choi et al. (J. Fluid Mech., vol. 262, 1994, pp. 75–110) through numerical simulations. To conduct the experiments, a deformable surface with a streamwise array of 16 independently controlled actuators was developed. A real-time particle image velocimetry (RT-PIV) system was also created for flow measurements. The objective of the control strategy was to target the sweep and ejection motions of the vortex shedding from a spherical cap placed in a laminar boundary layer. Reactive control strategies consisted of wall-normal surface deformations that opposed or complied with the wall-normal (v) or streamwise (u) velocity fluctuations obtained from the RT-PIV. The results showed two primary outcomes of the control approach. Firstly, it effectively hindered the advancement of sweep motions towards the wall. Secondly, it disrupted the periodic shedding of vortices. The v-control with opposing wall motions and u-control with compliant wall motions exhibited strong inhibition of sweep motions, while the v-control with compliant and u-control with opposing wall motions showed weaker inhibition. All reactive control cases resulted in the disruption of vortex shedding. In some instances, this disruption was accompanied by increased turbulent kinetic energy due to the generation of additional flow motions. However, the v-control with opposing wall motions significantly reduced the vortex-shedding energy while maintaining total turbulent kinetic energy close to or below that of the unforced flow. Overall, the experiments show the effectiveness of reactive control strategies in mitigating sweep motions and disrupting vortical structures, offering insights for developing reactive control strategies.

We have performed numerical simulations to investigate the phenomenon of axial pattern formation exhibited by a non-neutrally buoyant concentrated suspension. Continuum modelling of the concentrated suspension is done using the suspension balance model to identify the underlying mechanism of the phenomenon. We demonstrate that axial concentration variations become amplified to axial bands owing to the influence of the second normal stress difference ($N_2$), and the first normal difference ($N_1$) accentuates the effect of $N_2$. We demonstrate that the end walls of the rotating cylinder are necessary to prevent the smearing out of axial bands but are not a direct cause of the phenomenon.

Using low-dimensional numerical simulations, we investigate the characteristics of complex and three-dimensional surface waves in a liquid film flowing over a rotating disk, focusing on large flow rates from a nozzle. Existing integral boundary layer (IBL) models, which are based on spatially averaged variables along the direction normal to the disk surface, have primarily focused on the formation of axisymmetric waves under relatively small flow rates. In this study, an extended IBL model that accounts for both laminar and turbulent regimes is developed by considering the non-uniformity of the local flow rate in the spreading film flow and incorporating closure models dependent on the local Reynolds number. Our numerical results successfully capture the generation of concentric waves by an impinging circular liquid jet and their transition into three-dimensional solitary waves. These findings are in good agreement with visualization images and time-series data of free-surface fluctuations from a displacement sensor. The backscattering of small-scale three-dimensional turbulence into large-scale horizontal turbulence inside the film plays a critical role in determining the transition of wave modes and the nonlinear dynamics of the waves in the turbulent regime. Furthermore, the behaviour of three-dimensional waves in the downstream region, including frequent wave coalescence in the transition region and the breakup of small-scale solitons, is distinct from that of gravity-driven falling film flows. The amplitude of the three-dimensional waves is inversely related to the generalized Reynolds number defined for rotating films.

We investigate systematically the free settling of a single Platonic polyhedron in an unbounded domain filled with an otherwise quiescent Newtonian fluid. We consider a particle–fluid density mimicking a rock in water. Five Platonic polyhedrons of increasing sphericity are studied for a range of Galileo numbers $10 \leqslant \mathcal {G}a \leqslant 300$. We construct a regime map in the parameter space of Galileo number and particle volume fraction ($\mathcal {G}a, \phi$), highlighting how the angularity of the Platonic polyhedron impacts its settling path and the onset of instabilities. We find that the initial angular position solely affects the transient settling process. All the Platonic polyhedrons maintain a stable settling angular position at low $\mathcal {G}a$. Higher angularity leads to path unsteadiness at lower $\mathcal {G}a$. Path instability progresses from steady vertical to unsteady vertical, followed by oblique settling observed for highly spherical particles, but helical settling (HS) for more angular particles. The particle autorotation is found to be the pivotal factor influencing path instability and the regime transition of angular particles. Beginning in the unsteady oblique and helical regimes, particle autorotation becomes more prevalent, escalating further in the chaotic regime as $\mathcal {G}a$ increases. The particle angular velocity vector is shown to be predominantly situated in the horizontal plane. A thorough force balance in the horizontal plane reveals that the Magnus force is the primary driving force of the HS regime. Additionally, we establish two new empirical correlations to predict the particle settling velocity and the disturbed wake length that solely require the physical properties of the system ($\mathcal {G}a$ and $\phi$). Our numerical results suggest that an increase of the density ratio from $2$ to $3$ exerts only a marginal impact on the path instability of the most angular particle, the settling tetrahedron.

The aeroacoustics of a boundary layer ingesting (BLI) ducted fan is investigated experimentally. The study examines a ducted fan immersed in an adverse streamwise pressure gradient turbulent boundary layer developed over a curved wall. Aeroacoustics measurements indicate that the noise from the BLI ducted fan results from a complex interaction among the fan, duct and the incoming boundary layer. The fundamental mechanisms of noise generation are explained using a general source separation strategy. A detailed noise comparison is made at varying fan rotational speeds and across a wide range of axial inflow velocities. In a low thrust regime, the noise is found to be driven by the fan loading, coupled with duct acoustics and the haystacking phenomenon. In a high thrust regime, the contribution from duct acoustics diminishes, and the noise is predominantly driven by the fan loading coupled with the haystacking phenomenon.

Dense suspensions of solid particles in viscous liquid are ubiquitous in both industry and nature, and there is a clear need for efficient numerical routines to simulate their rheology and microstructure. Particles of micron size present a particular challenge: at low shear rates, colloidal interactions control their dynamics while at high rates, granular-like contacts dominate. While there are established particle-based simulation schemes for large-scale non-Brownian suspensions using only pairwise lubrication and contact forces, common schemes for colloidal suspensions generally are more computationally costly and thus restricted to relatively small system sizes. Here, we present a minimal particle-based numerical model for dense colloidal suspensions that incorporates Brownian forces in pairwise form alongside contact and lubrication forces. We show that this scheme reproduces key features of dense suspension rheology near the colloidal-to-granular transition, including both shear thinning due to entropic forces at low rates and shear thickening at high rates due to contact formation. This scheme is implemented in LAMMPS, a widely used open source code for parallelised particle-based simulations, with a runtime that scales linearly with the number of particles, making it amenable for large-scale simulations.

We consider a thin horizontal layer of a non-magnetic electrolyte containing a bulk solution of salt and carrying an electric current. The layer is bounded by two deformable free surfaces loaded with an insoluble surfactant and is placed in a vertical magnetic field. The arising Lorentz force drives the electrolyte in the plane of the layer. We employ the long-wave approximation to derive general two-dimensional hydrodynamic equations describing symmetric pinching-type deformations of the free surfaces. These equations are used to study the azimuthal flow in an annular film spanning the gap between two coaxial cylindrical electrodes. In weakly deformed films, the base azimuthal flow and its linear stability with respect to azimuthally invariant perturbations are studied analytically. For relatively thick layers and weak magnetic fields, the leading mode with the smallest decay rate is found to correspond to a monotonic azimuthal velocity perturbation. The Marangoni effect leads to further stabilisation of the flow while perturbations of the solute concentration in the bulk of the fluid have no influence on the flow stability. In strongly deformed films in the diffusion-dominated regime, the azimuthal flow becomes linearly unstable with respect to an oscillatory mixed mode characterised by the combination of radial and azimuthal velocity perturbations when the voltage applied between electrodes exceeds the critical value.

In the present paper, the sloshing flow in a cuboid tank forced to oscillate horizontally is investigated with both experimental and numerical approaches. The filling depth chosen is $h/L=0.35$ (with h the water depth and L the tank height), which is close to the critical depth. According to Tadjbakhsh & Keller (J. Fluid Mech., vol. 8, issue 3, 1960, pp. 442–451), as the depth passes through this critical value the response of the resonant sloshing dynamics changes from ‘hard spring’ to ‘soft spring’. The experimental tank has a thickness of $0.1L$, reducing three-dimensional effects. High-resolution digital camera and capacitance wave probes are used for time recording of the surface elevation. By varying the oscillation period and the amplitude of the motion imposed on the tank, different scenarios are identified in terms of free-surface evolution. Periodic and quasi-periodic regimes are found in most of the frequencies analysed but, among these, sub-harmonic regimes are also identified. Chaotic energetic regimes are found with motions of greater amplitude. Typical tools of dynamical systems, such as Fourier spectra and phase maps, are used for the regime identification, while the Hilbert–Huang transform is used for further insight into doubling-frequency and tripling-period bifurcations. For the numerical investigation, an advanced and well-established smoothed particle hydrodynamics method is used to aid the understanding of the physical phenomena involved and to extend the range of frequencies investigated experimentally.

Detailed observations of the velocities of Jovian vortices exist at only one height in the atmosphere, so their vertical structures are poorly understood. This motivates this study that computes stable three-dimensional, long-lived planetary vortices that satisfy the equations of motion. We solve the anelastic equations with a high-resolution pseudo-spectral method using the observed Jovian atmospheric temperatures and zonal flow. We examine several families of vortices and find that constant-vorticity vortices, which have nearly uniform vorticity as a function of height, and horizontal areas that go to zero at their tops and bottoms, converge to stable vortices that look like the Great Red Spot (GRS) and other Jovian anticyclones. In contrast, the constant-area vortices proposed in previous studies, which have nearly uniform areas as a function of height, and vertical vorticities that go to zero at their tops and bottoms, are far from equilibrium, break apart, and converge to constant-vorticity vortices. Our late-time vortices show unexpected properties. Vortices that are initially non-hollow become hollow (i.e. have local minima of vertical vorticity at their centres), which is a feature of the GRS that cannot be explained with two-dimensional simulations. The central axes of the final vortices align with the planetary spin axis even if they align initially with the local direction of gravity. We present scaling laws for how vortex properties change with the Rossby number and other non-dimensional parameters. We prove analytically that the horizontal mid-plane of a stable vortex must lie at a height above the top of the convective zone.

This study explores the dynamics of finite-size fibres suspended freely in a viscoelastic turbulent flow. For a fibre suspended in Newtonian flows, two different flapping regimes were identified by Rosti et al. (Phys. Rev. Lett., vol. 121, issue 4, 2018, 044501): one dominated by time scales from the flow, and another dominated by time scales associated with its natural frequency. We explore in this work how the fibre dynamics is modified by the elasticity of the carrier fluid. For this, we perform direct numerical simulations of a two-way coupled fibre–fluid system in a parametric space spanning different Deborah numbers, fibre bending stiffness (flexible to rigid) and linear density difference between the fibre and the flow (neutrally buoyant to denser-than-fluid fibres). We examine how these parameters influence various fibre characteristics such as the frequency of flapping, curvature, and alignment with the fluid strain and polymer stretching directions. Results reveal that the neutrally buoyant fibres, depending on their flexibility, oscillate with large and small time scales transpiring from the flow, but the smaller time scales are suppressed as the polymer elasticity increases. Polymer stretching is uncommunicative to denser-than-fluid fibres, which flap with large time scales from the flow when flexible, and with their natural frequency when rigid. Thus the characteristic elastic time scale has a subdominant effect when the fibres are neutrally buoyant, while its effect is absent when the fibres become more inertial. In addition, we also explore the fibre's bending curvature and its preferential alignment with the flow to identify the other roles of viscoelasticity in modifying the coupled fluid–structure dynamics. Inertial fibres have larger curvatures and are less responsive to the polymer presence, whereas the neutrally buoyant fibres show quantitative changes. The perceptible passivity of the denser fibres is again reflected in the way they align preferentially with the polymeric stretching directions: the neutrally buoyant fibres show a higher alignment with the polymer stretching directions compared to the denser ones. In a nutshell, the polymers exert a larger influence on neutrally buoyant fibres, which are more reflective of the polymeric influence in the flow. The study addresses comprehensively the interplay between polymer elasticity and the fibre structural properties in determining its response behaviour in an elasto-inertial turbulent flow.

When two fluid drops touch, they coalesce due to surface tension. At early times, there is only a relatively small fluid bridge joining the drops. An asymptotic solution is presented for an inertial regime of early-time coalescence, in which inertial forces balance surface tension at leading order. It is demonstrated that viscosity nevertheless has a leading-order effect. Radial momentum is created at the tightly curved edge of the fluid bridge by the net force $2\gamma$ (per unit length) due to surface tension. This momentum is left behind the radially expanding bridge edge in a thin viscous wake. The divergent volume flux in the wake entrains fluid from above and below the bridge, and drives an inviscid irrotational flow in the drops on the scale of the bridge radius. This flow widens the gap between the drops ahead of the bridge, and the larger gap width results in a lower rate of coalescence. Including viscosity in this way improves the agreement between theory and the available experimental and numerical data.

The slamming wave force and pressure variabilities for monopile wave impacts are studied as functions of wave breaking shape and transverse perturbations on the breaking wave front. The impacting wave topology is characterized as slosh, flip-through, $\varOmega$, overturning and fully broken. Fifty test repetitions are conducted for each type of wave impact to assess the variability of force impulse, force and pressure. The results for the unperturbed cases show that the slamming force is highest among the nominal slosh, flip-through and $\varOmega$ tests, and that the slamming force variability is highest for the first two. We demonstrate that the slamming force and pressure variabilities decrease notably after selecting and regrouping the tests by similar crest heights and temporal slopes measured at an upstream wave gauge. The group representing $\varOmega$ wave impacts shows the largest mean slamming force and peak pressure, and their variability is the highest among all groups. Further, the effect of lateral perturbations on the pressure, force and impulse variabilities is investigated. Due to the perturbations, the slamming pressure variability for the wave impacts in which the wave front hits the monopile surface increases significantly. The variability of the slamming force is also increased for the perturbed impacts; however, it is smaller than the slamming pressure variability. The force impulse variability shows a low sensitivity to perturbations, and its magnitude is smaller than that of the force variability. Finally, the slamming pressure using fifteen pressure sensors for five selected events is studied. For these tests, oscillations at frequencies associated with structural or bubble oscillations are seen. Further, the air entertainment is documented through video recordings.

The accurate simulation of complex dynamics in fluid flows demands a substantial number of degrees of freedom, i.e. a high-dimensional state space. Nevertheless, the swift attenuation of small-scale perturbations due to viscous diffusion permits in principle the representation of these flows using a significantly reduced dimensionality. Over time, the dynamics of such flows evolves towards a finite-dimensional invariant manifold. Using only data from direct numerical simulations, in the present work we identify the manifold and determine evolution equations for the dynamics on it. We use an advanced autoencoder framework to automatically estimate the intrinsic dimension of the manifold and provide an orthogonal coordinate system. Then, we learn the dynamics by determining an equation on the manifold by using both a function-space approach (approximating the Koopman operator) and a state-space approach (approximating the vector field on the manifold). We apply this method to exact coherent states for Kolmogorov flow and minimal flow unit pipe flow. Fully resolved simulations for these cases require $O(10^3)$ and $O(10^5)$ degrees of freedom, respectively, and we build models with two or three degrees of freedom that faithfully capture the dynamics of these flows. For these examples, both the state-space and function-space time evaluations provide highly accurate predictions of the long-time dynamics in manifold coordinates.

Turbulent flows over porous lattices consisting of rectangular cuboid pores are investigated using scale-resolving direct numerical simulations. Beyond a certain threshold which is primarily determined by the wall-normal Darcy permeability, ${{\mathsf{K}}_y}$, near-wall turbulence transitions from its canonical regime, marked by the presence of streak-like structures, to another marked by the presence of Kelvin–Helmholtz-like (K–H-like) spanwise-coherent structures. The threshold agrees well with that previously established in studies where permeable-wall boundary conditions had been used as surrogates for a porous substrate (Gómez-de Segura & García-Mayoral, J. Fluid Mech., vol. 875, 2019, pp. 124–172). In the smooth-wall-like regime, none of the investigated substrates demonstrate any reduction in drag relative to a smooth-wall flow. At the permeable surface, a notable component of the flow is that which adheres to the pore geometry and undergoes modulation by the turbulent scales of motions due to the interaction mechanism described by Abderrahaman-Elena et al. (J. Fluid Mech., vol. 865, 2019, pp. 1042–1071). Its resulting effect can be quantified in terms of an amplitude modulation (AM) using the approach of Mathis et al. (J. Fluid Mech., vol. 628, 2009, pp. 311–337). This pore-coherent flow component persists throughout the porous substrate, highlighting the importance of a given substrate's microstructure in the presence of an overlying turbulent flow. This geometry-related aspect of the flow is not accounted for when continuum-based models for a porous medium or effective representations of them, such as wall boundary conditions, are used. The intensity of the AM effect is enhanced in the K–H-like regime and becomes strengthened with larger permeability. As a result, structured porous materials may be designed to exploit or mitigate these flow features depending upon the intended application.

The phenomenon of the ‘coil-stretch’ (C-S) transition, wherein a long-chain polymer initially in a coiled state undergoes a sudden configuration change to become fully stretched under steady elongational flows, has been widely recognized. This transition can display intricate hysteresis behaviours under specific critical conditions, giving rise to unique rheological characteristics in dilute polymer solutions. Historically, microscopic stochastic models and Brownian dynamics simulations have shed light on the underlying mechanisms of the transition by uncovering bistable configurations of polymer chains. Following the initial work by Cerf (J. Chem. Phys., vol. 20, 1952, pp. 395–402), we introduce a continuum model in this study to investigate the C-S transition in a constant uniaxial elongational flow. Our approach involves approximating the unfolding process of the polymer chain as an axisymmetric deformation of an elastic particle. We make the assumption that the particle possesses uniform material properties, which can be represented by a nonlinear, strain-hardening constitutive equation to replicate the finite extensibility of the polymer chain. Subsequently, we analytically solve for the steady-state deformation using a polarization method. By employing this reduced model, we effectively capture the C-S transition and establish its specific correlations with material and geometric properties. The hysteresis phenomena can be comprehended through a force-balance analysis, which involves comparing the externally applied viscous forces with the intrinsic elastic responsive forces. We demonstrate that our model, while simple, unveils rich elastohydrodynamics of the C-S transition.

Direct numerical simulations of hypersonic turbulent Couette flows are performed for top-wall Mach numbers of 6, 7 and 8, inspired by non-reactive high-enthalpy wind tunnel free-stream conditions, with the goal of analysing the physical processes driving the sub-filter-scale (SFS) stresses to inform development of large-eddy simulation techniques for hypersonic wall-bounded flows. Semi-local scaling laws collapse mean profiles and second-order turbulent statistics well, in spite of the strong wall-normal gradients of temperature and density. On the other hand, the SFS shear stresses exhibit an unexpected profile characterized by a region of pronounced shear stress deficit, which becomes more pronounced for higher Mach numbers. Instantaneous visualizations suggest that the SFS shear stress deficit is induced by the counter-gradient resolved momentum transport driven by residual velocity motions at the interface between high-density low-speed streaks being ejected away from the wall, and low-density high-speed ones replacing the displaced fluid, qualifying this as a compressibility effect. It is shown that the SFS shear stresses are primarily driven by second-order interactions between residual velocities, in spite of their triply nonlinear nature. This, in turn, motivated a statistical quadrant analysis revealing the presence of a SFS shear stress deficit, that is, SFS processes driving momentum transport of the resolved field towards the top wall. Additionally, higher-Reynolds-number simulations reveal that there is an upper limit of spatial filter widths to resolve large-scale structures, and such deficit is observable at any Reynolds number when a reasonable spatial filter is applied.

Soft intertwined channel systems are frequently found in fluid flow networks in nature. The passage geometry of these systems can deform due to fluid flow, which can cause the relationship between flow rate and pressure drop to deviate from the Hagen–Poiseuille linear law. Although fluid–structure interactions in single deformable channels have been extensively studied, such as in Starling's resistor and its variations, the flow transport capacity of an intertwined channel with multiple self-intersections (a ‘hydraulic knot’), is still an open question. We present experiments and theory on soft hydraulic knots formed by interlinked microfluidic devices comprising two intersecting channels separated by a thin elastomeric membrane. Our experiments show flow–pressure relationships similar to flow limitation, where the limiting flow rate depends on the knot configuration. To explain our observations, we develop a mathematical model based on lubrication theory coupled with tension-dominated membrane deflections that compares favourably with our experimental data. Finally, we present two potential hydraulic knot applications for microfluidic flow rectification and attenuation.

We present a systematic simulation campaign to investigate the pairwise interaction of two mobile, monodisperse particles submerged in a viscous fluid and subjected to monochromatic oscillating flows. To this end, we employ the immersed boundary method to geometrically resolve the flow around the two particles in a non-inertial reference frame. We neglect gravity to focus on fluid–particle interactions associated with particle inertia and consider particles of three different density ratios aligned along the axis of oscillation. We systematically vary the initial particle distance and the frequency based on which the particles show either attractive or repulsive behaviour by approaching or moving away from each other, respectively. This behaviour is consistently confirmed for the three density ratios investigated, although particle inertia dictates the overall magnitude of the particle dynamics. Based on this, threshold conditions for the transition from attraction to repulsion are introduced that obey the same power law for all density ratios investigated. We furthermore analyse the flow patterns by suitable averaging and decomposition of the flow fields and find competing effects of the vorticity induced by the fluid–particle interactions. Based on these flow patterns, we derive a circulation-based criterion that provides a quantitative measure to categorize the different cases. It is shown that such a criterion provides a consistent measure to distinguish the attractive and repulsive arrangements.

This work is a numerical and experimental study of a rectangular thin plate undergoing stall flutter at Mach 0.8. This constitutes one of the first studies of this kind where three-dimensionality is fully implemented in a numerical simulation including the test-section effects characterizing wind-tunnel experiments. In order to break down the fluid–structure interaction to its main driving phenomena, an aerodynamic model is proposed that is based on computationally inexpensive steady-state simulations. Two types of dynamic instability are observed in the numerical simulations; Flutter by mode coalescence is promoted at zero flow incidence, however, high bending precludes this from happening for higher values of angle of attack. Stall flutter is instead a nonlinear one-degree type of instability. Both of these instability mechanisms can be explained in terms of hysteretic behaviour of the pressure distribution, which becomes more pronounced at high angles of attack, when a large separation region is formed. Tests were conducted employing titanium alloy plates in order to survive the aerodynamic loads characterizing the wind-tunnel initial transient. However, due to wall interference, high bending was promoted so that the internal stress exceeded the yield values before flutter could be measured. Numerical simulations were in general agreement with the experiment in terms of both amplitude and oscillation frequency.