We consider the drawing of a hollow Newtonian fibre with temperature-dependent viscosity. The drawing is affected by surface tension, inertia, hole pressurisation and externally applied cooling. We apply long-wavelength techniques to determine the steady states and examine their stability. In the presence of surface tension but with no cooling or internal hole pressure, we show the counter-intuitive result that the hole radius at the outlet of the device is a non-monotonic function of the hole radius at the inlet. We also show that if the internal hole is pressurised and the hole size at the inlet is sufficiently large, then the exit temperature of the fibre is a non-monotonic function of the applied cooling rate. We have found a number of surprising mechanisms related to how the various physical effects influence the stability of drawing. For the isothermal case, we show that increasing the internal hole pressure has a destabilising effect for non-zero surface tension while the stability is completely independent of the internal hole pressure for zero surface tension. We further show that there is a complicated interplay between internal hole pressure, external cooling and surface tension in determining the stability and that it is possible that increasing the hole size at the inlet can act to destabilise, then stabilise and finally destabilise the flow. We discuss the mechanisms that determine the counter-intuitive steady-state behaviour and stability.

This study seeks a low-rank representation of turbulent flow data obtained from multiple sources. To uncover such a representation, we consider finding a finite-dimensional manifold that captures underlying turbulent flow structures and characteristics. While nonlinear machine-learning techniques can be considered to seek a low-order manifold from flow field data, there exists an infinite number of transformations between data-driven low-order representations, causing difficulty in understanding turbulent flows on a manifold. Finding a manifold that captures turbulence characteristics becomes further challenging when considering multi-source data together due to the presence of inherent noise or uncertainties and the difference in the spatiotemporal length scale resolved in flow snapshots, which depends on approaches in collecting data. With an example of numerical and experimental data sets of transitional turbulent boundary layers, this study considers an observable-augmented nonlinear autoencoder-based compression, enabling data-driven feature extraction with prior knowledge of turbulence. We show that it is possible to find a low-rank subspace that not only captures structural features of flows across the Reynolds number but also distinguishes the data source. Along with machine-learning-based super-resolution, we further argue that the present manifold can be used to validate the outcome of modern data-driven techniques when training and evaluating across data sets collected through different techniques. The current approach could serve as a foundation for a range of analyses including reduced-complexity modelling and state estimation with multi-source turbulent flow data.

Flow dynamics around a stationary flat plate near a free surface is investigated using time-resolved two-dimensional particle image velocimetry. The study examines variations in angle of attack ($\theta =0^\circ {-}35^\circ {}$), Reynolds number ($Re$ $\approx$ $10^3$$-$3 $\times$ $10^4$) and plate proximity to the free surface ($H^*$). Under symmetric boundary conditions ($H^*\geqslant {15}$), increasing $\theta$ intensifies fluid–plate interaction, resulting in the shedding of leading-edge and trailing-edge vortices (LEV and TEV), each characterised by distinct strengths and sizes. In both symmetric ($H^*\geqslant {15}$) and asymmetric ($H^*=5$) boundary conditions at $\theta \lt 5^\circ {}$, fluid flow follows the contour of the plate, unaffected by Reynolds number. However, at $H^*=5$, three flow regimes emerge: the first Coanda effect (CI), regular shedding (RS) and the second Coanda effect (CII), each influenced by $\theta$ and $Re$. The CI regime dominates at lower angles ($5^\circ {}\leqslant \theta \leqslant 25^\circ {}$) and $Re \leqslant 12\,500$, featuring a Coanda-induced jet-like flow pattern. As the Reynolds number increases, the flow transitions into the RS regime, leading to detachment from the upper surface of the plate. This detachment results in the formation of LEV and TEV in the wake, along with surface deformation, secondary vortices and wavy shear layers beneath the free surface. At $22\,360\lt Re \leqslant 32\,200$ and $5^\circ {} \leqslant \theta \leqslant 25^\circ {}$, in the CII regime, significant surface deformation causes the Coanda effect to reattach the flow to the plate, forming a unique jet-like flow.

The present study investigates the gravity-driven settling dynamics of non-Brownian suspensions consisting of spherical and cubic particles within a triply periodic domain. We numerically examine the impact of solid volume fraction on the evolving microstructure of the suspension using the rigid multiblob method under Stokes flow conditions. Our simulations match macroscopic trends observed in experiments, and align well with established semi-empirical correlations across a broad range of volume fractions. At low to moderate solid volume fractions, the settling mechanism is governed primarily by hydrodynamic interactions between the particles and the surrounding fluid. However, frequent collisions between particles in a highly packed space tend to suppress velocity fluctuations at denser regimes. For dilute suspensions, transport properties are shaped predominantly by an anisotropic microstructure, though this anisotropy diminishes as many-body interactions intensify at higher volume fractions. Notably, cubic particles exhibit lower anisotropy in velocity fluctuations compared to spherical particles, owing to more efficient momentum and energy transfer from the gravity-driven direction to transverse directions. Finally, bidisperse suspensions with mixed particle shapes show enhanced velocity fluctuations, driven by shape-induced variations in drag and increased hydrodynamic disturbances. These fluctuations in turn affect the local sedimentation velocity field, leading to the segregation of particles in the mixture.

The lift aerodynamic admittances of an airfoil at different angles of attack (AoAs) in turbulent flow are investigated using a combination of theoretical and experimental approaches. Two theoretical one-wavenumber aerodynamic admittances, namely the Sears and Atassi functions, are reviewed and uniformly normalized for comparison with experimental results. In theory, generalized aerodynamic admittances are generated by introducing the spanwise influence into one-wavenumber aerodynamic admittances. The influence of AoA on generalized aerodynamic admittance includes its effect on both the spanwise influence term and one-wavenumber aerodynamic admittances. The experiment indicates that prior to the prestall region, the increase in the spanwise influence factor correlates with the increase in AoA, with the growth rate of the spanwise influence factor likewise accelerating. The Atassi functions demonstrate that the influence of AoA on one-wavenumber aerodynamic admittances is based on the assumption of full correlation in the spanwise direction. Experimental results suggest that one-wavenumber aerodynamic admittances are inapplicable to actual turbulence; however, the Atassi function accurately represents experimental values at the corresponding AoA when taking into account the spanwise effects.

This study obtains expressions for the force and moment coefficients for a finite-span circular cylinder rolling on a plane wall. It is assumed that a small, but finite, gap exists between the cylinder and the wall, as a result of, for example, surface roughness. Using the method of matched asymptotic expansions, the flow is decomposed into an inner solution, valid in the narrow interstice between the cylinder and the wall, and an outer solution, valid far from the interstice. Then, the force and moment coefficients are expressed as the sum of a gap-dependent term, which is computed from the inner solution, and a gap-independent term, which is computed from the outer solution. Solutions to the inner flow are obtained by solving numerically the two-dimensional Reynolds equation for the lubrication flow in the interstice. The inner solution depends only on a single parameter, the cylinder aspect ratio divided by the gap-diameter ratio, and the effects of this parameter on the gap-dependent force and moment coefficients are deduced. Solutions to the outer flow are obtained using thee-dimensional numerical simulations for a range of Reynolds numbers, cylinder aspect ratios and cylinder rotation rates. Then, the variation of the force and moment coefficients against each of these terms is obtained.

Planar entropy waves are commonly assumed for predicting indirect combustion noise. However, the non-planar and turbulent nature of flows found in most practical combustors challenges this assumption. In the present paper, we examine the indirect noise generated by non-planar and turbulent entropy fields through subsonic nozzles. Firstly, we introduce a new transfer function framework that accounts for the contribution of non-planar Fourier modes of the entropy field to the indirect noise spectra. When applied to a turbulent flow field, this method demonstrates a significant improvement in spectral predictions compared with a conventional approach that only considers the planar mode. Secondly, simulations show that non-planar Fourier modes become significant above a threshold frequency $f_{thresh}$, found in the mid- to high-frequency range. This contribution of non-planar modes is explained by two-dimensional shear effects that distort the entropy waves. A scaling relation that uses residence times along streamlines is developed for $f_{thresh}$, showing good agreement with simulation results. Finally, we show that the indirect noise from non-planar entropy modes found in aviation combustors can be significant at frequencies below 1 kHz, which might be relevant in situations of thermo-acoustic instabilities coupled to indirect noise.

In aerodynamic and hydrodynamic devices and locomotive organisms, passive appendages have practical purposes such as drag reduction and flow control. Although these appendages also affect the dynamics of freely falling bodies, underlying principles of their functions remain elusive. We investigate experimentally the dynamics of a falling sphere with a filament appended on its rear side by varying the ratio of filament length to sphere diameter ($l/D=0{-}3.0$) and sphere-to-fluid density ratio ($\rho _s/\rho _f= 1.06{-}1.36$), and maintaining a similar dimensionless moment of inertia ($I^* \approx 0.96$). At the Reynolds number of $O(10^3)$, a sphere without any filament exhibits vertical descent. However, the falling of the sphere with a filament is accompanied by periodic horizontal displacements, and the degree of zigzag motion is maximised under specific filament length. The filament induces periodic rotation of the sphere by shifting the centre of mass of the entire model and through the hydrodynamic interaction of the filament with the surrounding fluid. The rotation of the sphere increases the drag force acting on the model, reducing tangential velocity along the trajectory by 14 % compared to a plain sphere. Furthermore, the sphere rotation enhances the lift force normal to the trajectory, extending trajectory length by 5 %. These combined effects improve falling time over a certain vertical distance by 20 % compared to the plain sphere. With increasing sphere density, the effects of the filament on the falling dynamics weaken, because the offset distance between the centre of mass of the model and the geometric centre of the sphere becomes smaller.

Spanwise wall forcing in the form of streamwise-travelling waves is applied to the suction side of a transonic airfoil with a shock wave to reduce aerodynamic drag. The study, conducted using direct numerical simulations, extends earlier findings by Quadrio et al. (J. Fluid Mech. vol. 942(R2), 2022, pp. 1–10) and confirms that the wall manipulation shifts the shock wave on the suction side towards the trailing edge of the profile, thereby enhancing its aerodynamic efficiency. A parametric study over the parameters of wall forcing is carried out for the Mach number set at 0.7 and the Reynolds number at 300 000. Similarities and differences with the incompressible plane case are discussed; for the first time, we describe how the interaction between the shock wave and the boundary layer is influenced by flow control via spanwise forcing. With suitable combinations of control parameters, the shock is delayed, which results in a separated region whose length correlates well with friction reduction. The analysis of the transient process following the sudden application of control is used to link flow separation with the intensification of the shock wave.

Opposition control (OC) is a reactive flow-control approach that mitigates the near-wall fluctuations by imposing blowing and suction at the wall, being opposite to the off-wall observations. We carried out high-resolution large-eddy simulations to investigate the effects of OC on turbulent boundary layers (TBLs) over a wing at a chord-based Reynolds number (${Re}_c$) of $200 \ 000$. Two cases were considered: flow over the suction sides of the NACA0012 wing section at an angle of attack of $0^{\circ }$, and the NACA4412 wing section at an angle of attack of $5^{\circ }$. These cases represent TBLs subjected to mild and strong non-uniform adverse pressure gradients (APGs), respectively. First, we assessed the control effects on the streamwise development of TBLs and the achieved drag reduction. Our findings indicate that the performance of OC in terms of friction-drag reduction significantly diminishes as the APG intensifies. Analysis of turbulence statistics subsequently reveals that this is directly linked to the intensified wall-normal convection caused by the strong APG: it energizes the control intensity to overload the limitation that guarantees drag reduction. The formation of the so-called virtual wall that reflects the mitigation of wall-normal momentum transport is also implicitly affected by the pressure gradient. Control and pressure-gradient effects are clearly apparent in the anisotropy invariant maps, which also highlight the relevance of the virtual wall. Finally, spectral analyses indicate that the wall-normal transport of small-scale structures to the outer region due to the APG has a detrimental impact on the performance of OC. Uniform blowing and body-force damping were also examined to understand the differences between the various control schemes. Despite the distinct performance of friction-drag reduction, the effects of uniform blowing are akin to those induced by a stronger APG, while the effects of body-force damping exhibit similarities to those of OC in terms of the streamwise development of the TBL although there are differences in the turbulent statistics. To authors’ best knowledge, the present study stands as the first in-depth analysis of the effects of OC applied to TBL subjected to non-uniform APGs with complex geometries.

Scalar dissipation rate (SDR) evolution in a stopping turbulent jet was analysed using direct numerical simulations and a theoretical approach. After the jet is stopped, a deceleration wave for the SDR propagates downstream with a speed similar to that for axial velocity. Upstream of the deceleration wave, mean centreline SDR becomes proportional to axial distance, and inversely proportional to the square of time. After passing of the deceleration wave, normalised radial profiles of SDR and its axial, radial and azimuthal components reach self-similar states, denoted decelerating self-similar profiles, which are different from their steady-state counterparts. Production and destruction terms in the mean SDR transport equation remain dominant in the decelerating self-similar state. The theoretical approach provides an explicit prediction for the radial profile of a turbulent fluctuation term of the mean SDR transport equation. Three turbulent SDR models are validated, and modifications suitable for the decelerating jet are proposed, based on a self-similarity analysis.

An isolated Leidenfrost droplet levitating over its own vapour above a superheated flat substrate is considered theoretically, the superheating for water being up to several hundred degrees above the boiling temperature. The focus is on the limit of small, practically spherical droplets of several tens of micrometres or less. This may occur when the liquid is sprayed over a hot substrate, or just be a late life stage of an initially large Leidenfrost droplet. A rigorous numerically assisted analysis is carried out within verifiable assumptions such as quasi-stationarities and small Reynolds/Péclet numbers. It is considered that the droplet is surrounded by its pure vapour. Simple formulae approximating our numerical data for the forces and evaporation rates are preliminarily obtained, all respecting the asymptotic behaviours (also investigated) in the limits of small and large levitation heights. They are subsequently used within a system of ordinary differential equations to study the droplet dynamics and take-off (drastic height increase as the droplet vapourises). A previously known quasi-stationary inverse-square-root law for the droplet height as a function of its radius (at the root of the take-off) is recovered, although we point out different prefactors in the two limits. Deviations of a dynamic nature therefrom are uncovered as the droplet radius further decreases due to evaporation, improving the agreement with experiment. Furthermore, we reveal that, if initially large enough, the droplets vanish at a universal finite height (just dependent on the superheat and fluid properties). Scalings in various distinguished cases are obtained along the way.

An exact solution is developed for bubble-induced acoustic microstreaming in the case of a gas bubble undergoing asymmetric oscillations. The modelling is based on the decomposition of the solenoidal, first- and second-order, vorticity fields into poloidal and toroidal components. The result is valid for small-amplitude bubble oscillations without restriction on the size of the viscous boundary layer $(2\nu /\omega )^{1/2}$ in comparison to the bubble radius. The non-spherical distortions of the bubble interface are decomposed over the set of orthonormal spherical harmonics $Y_{n}^{m}(\theta , \phi )$ of degree $n$ and order $m$. The present theory describes the steady flow produced by the non-spherical oscillations $(n,\pm m)$ that occur at a frequency different from that of the spherical oscillation, as in the case of a parametrically excited surface oscillation. The three-dimensional aspect of the streaming pattern is revealed as well as the particular flow signatures associated with different asymmetric oscillations.

Oscillatory flows induced by a monochromatic forcing frequency $\omega$ close to a planar surface are present in many applications involving fluid–matter interaction such as ultrasound, vibrational spectra by microscopic pulsating cantilevers, nanoparticle oscillatory magnetometry, quartz crystal microbalance and more. Numerical solution of these flows using standard time-stepping solvers in finite domains present important drawbacks. First, hydrodynamic finite-size effects scale as $1/L_{\parallel }^2$ close to the surface and extend several times the penetration length $\delta \sim \omega ^{-1/2}$ in the normal $z$ direction and second, they demand rather long transient times $O(L_z^2)$ to allow vorticity to diffuse over the computational domain. We present a new frequency-based scheme for doubly periodic (DP) domains in free or confined spaces which uses spectral-accurate solvers based on fast Fourier transform in the periodic $(xy)$ plane and Chebyshev polynomials in the aperiodic $z$ direction. Following the ideas developed for the steady Stokes solver (Hashemi et al. J. Chem. Phys. vol. 158, 2023, p. 154101), the computational system is decomposed into an ‘inner’ domain (where forces are imposed) and an outer domain (where the flow is solved analytically using plane-wave expansions). Matching conditions leads to a solvable boundary value problem. Solving the equations in the frequency domain using complex phasor fields avoids time-stepping and permits a strong reduction in computational time. The spectral scheme is validated against analytical results for mutual and self-mobility tensors, including the in-plane Fourier transform of the Green function. Hydrodynamic couplings are investigated as a function of the periodic lattice length. Applications are finally discussed.

A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible particle representation model of Kassinos & Reynolds (1994), and preserves the exact nature of compressible rapid distortion theory (RDT). The adoption of a stochastic – rather than Fourier – perspective simplifies the transformation of statistics to physical space and serves as a starting point for the development of practical turbulence models. We assume small density fluctuations and isentropic flow to obtain a transport equation for the pressure fluctuation. This results in four fewer transport equations compared with the compressible RDT model of Yu & Girimaji (Phys. Fluids, vol. 19, 2007, 041702). The final formulation is closed in spectral space and only requires numerical approximation for the transformation integrals. The use of Monte Carlo for unit wavevector integration motivates the representation of the moments as stochastic variables. Consistency between the Fourier and stochastic representation is demonstrated by showing equivalency between the evolution equations for the velocity spectrum tensor in both representations. Sample clustering with respect to orientation allows for different techniques to be used for the wavevector magnitude integration. The performance of the stochastic model is evaluated for axially compressed turbulence, serving as a simplified model for shock–turbulence interaction, and is compared with linear interaction approximations and direct numerical simulation (DNS). Pure and compressed sheared turbulence at different distortion Mach numbers are also computed and compared with RDT/DNS data. Finally, two additional deformations are applied and compared with solenoidal and pressure-released limits to demonstrate the modelling capability for generic rapid deformations.

Travelling wave charges lying on the insulating walls of an electrolyte-filled capillary give rise to oscillatory modes which vanish when averaged over the period of oscillation. They also give rise to a zero mode (a unidirectional, time-independent velocity component) which does not vanish. The latter is a nonlinear effect caused by continuous symmetry breaking due to the quadratic nonlinearity associated with the electric body force in the time-dependent Stokes equations. In this paper, we provide a unified view of the effects arising in boundary-driven electrokinetic flows (travelling wave electroosmosis) and establish the universal behaviour exhibited by the observables. We show that the incipient velocity profiles are self-similar implying that those obtained with a single experimental configuration can be employed again to attain further insights without the need of repeating the experiment. Certain results from the literature are recovered as special cases of our formulation and we resolve certain paradoxes having appeared in the past. We present simple theoretical expressions, depending on a single-fit parameter, that reproduce these profiles, which could thus provide a rapid test of consistency between our theory and future experiment. The effect becomes more pronounced when reducing the transverse dimension of the system, relative to the velocity direction, and increasing the excitation wavelength, and can therefore be employed for unidirectional transport of electrolytes in thin and long capillaries. General relations, expressing the zero mode velocity in terms of the electric potential and the geometry of the system only, can thus be easily adapted to alternative experimental settings.

Large-eddy simulation (LES) is performed to study the tip vortex flow in a ducted propulsor geometry replicating the experiments of Chesnakas & Jessup (2003, pp. 257–267), Oweis et al. (2006a J. Fluids Engng 128, 751–764) and Oweis et al. (2006b J. Fluids Engng 128, 751–764). Inception of cavitation in these marine propulsion systems is closely tied to the unsteady interactions between multiple vortices in the tip region. Here LES is used to shed insight into the structure of the tip vortex flow. Simulation results are able to predict experimental propeller loads and show agreement with laser Doppler velocimetry measurements in the blade wake at design advance ratio, $J=0.98$. Results show the pressure differential across the blade produces a leakage vortex which separates off the suction side blade tip upstream of the trailing edge. The separation sheet aft of the primary vortex separation point is shown to take the form of a skewed shear layer which produces a complex arrangement of unsteady vortices corotating and counter-rotating with the primary vortex. Blade tip boundary layer vortices are reoriented to align with the leakage flow and produce instantaneous low-pressure regions wrapping helically around the primary vortex core. Such low-pressure regions are seen both upstream and downstream of the propeller blade trailing edge. The trailing edge wake is found to only rarely have a low-pressure vortex core. Statistics of instantaneous low pressures below the minimum mean pressure are found to be concentrated downstream of the blade’s trailing edge wake crossing over the primary vortex core and continue in excess of 40 % chord length behind the trailing edge. The rollup of the leakage flow duct boundary layer behind the trailing edge is also seen to produce counter-rotating vortices which interact with the primary leakage vortex and contribute to strong stretching events.

In this study, the propagation behaviour of detonation waves in a channel filled with stratified media is analysed using a detailed chemical reaction model. Two symmetrical layers of non-reactive gas are introduced near the upper and lower walls to encapsulate a stoichiometric premixed H2–air mixture. The effects of gas temperature and molecular weight of the non-reactive layers on the detonation wave’s propagation mode and velocity are examined thoroughly. The results reveal that as the non-reactive gas temperature increases, the detonation wave front transitions from a ‘convex’ to a ‘concave’ shape, accompanied by an increase in wave velocity. Notably, the concave wave front comprises detached shocks, oblique shocks and detonation waves, with the overall wave system propagating at a velocity exceeding the theoretical Chapman–Jouguet speed, indicating the emergence of a strong detonation wave. Furthermore, when the molecular weight of non-reactive layers varies, the results qualitatively align with those obtained from temperature variations. To elucidate the formation mechanism of different detonation wave front shapes, a dimensionless parameter $\eta$ (defined as a function of the specific heat ratio and sound speed) is proposed. This parameter unifies the effects of temperature and molecular weight, confirming that the specific heat ratio and sound speed of non-reactive layers are the primary factors governing the detonation wave propagation mode. Additionally, considering the effect of mixture inhomogeneity on the detonation reaction zone, the stream tube contraction theory is proposed, successfully explaining why strong detonation waves form in stratified mixtures. Numerical results show good agreement with theoretical predictions, validating the proposed model.