Polymer chains in turbulent flows are generally modelled as dumbbells, i.e. two beads joined by a nonlinear spring. The dumbbell only maps a single spatial configuration, described by the polymer end-to-end vector, thus a multi-bead FENE (finitely extensible nonlinear elastic) chain seems a natural improvement for a more accurate characterisation of the polymer spatial conformation. At a large Weissenberg number, a comparison with the more accurate Kuhn chain reveals that the multi-bead FENE chain drastically overestimates the probability of folded configurations. Surprisingly, the dumbbell turns out to be the only meaningful bead-spring model to coarse-grain a polymer macromolecule in turbulent pipe flows.

An additional distant wall is known to highly alter the jetting scenarios of wall-proximal bubbles. Here, we combine high-speed photography and axisymmetric volume of fluid (VoF) simulations to quantitatively describe its role in enhancing the micro-jet dynamics within the directed jet regime (Zeng et al., J. Fluid Mech., vol. 896, 2020, A28). Upon a favourable agreement on the bubble and micro-jet dynamics, both experimental and simulation results indicate that the micro-jet velocity increases dramatically as $\eta$ decreases, where $\eta =H/R_{max}$ is the distance between two walls $H$ normalized by the maximum bubble radius $R_{max}$. The mechanism is related to the collapsing flow, which is constrained by the distant wall into a reverse stagnation-point flow that builds up pressure near the bubble's top surface and accelerates it into micro-jets. We further derive an equation expressing the micro-jet velocity $U_{jet}=87.94\gamma ^{0.5}(1+(1/3)(\eta -\lambda ^{1.2})^{-2})$, where ${\gamma =d/R_{max}}$ is the stand-off distance to the proximal wall with $d$ the distance between the initial bubble centre and the wall, $\lambda =R_{y,m}/R_{max}$ with $R_{y,m}$ the distance between the top surface and the proximal wall at the bubble's maximum expansion. Viscosity has a minimal impact on the jet velocity for small $\gamma$, where the pressure buildup is predominantly influenced by geometry.

This paper reports on the efficacy of the Görtler number in scaling the laminar-turbulent boundary-layer transition on rotating cones facing axial inflow. Depending on the half-cone angle $\psi$ and axial flow strength, the competing centrifugal and cross-flow instabilities dominate the transition. Traditionally, the flow is evaluated by using two parameters: the local meridional Reynolds number $Re_l$ comparing the inertial versus viscous effects and the local rotational speed ratio $S$ accounting for the boundary-layer skew. We focus on the centrifugal effects, and evaluate the flow fields and reported transition points using Görtler number based on the azimuthal momentum thickness of the similarity solution and local cone radius. The results show that Görtler number alone dominates the late stages of transition (maximum amplification and turbulence onset phases) for a wide range of investigated $S$ and half-cone angle ($15^{\circ } \leq \psi \leq 50^{\circ }$), although the early stage (critical phase) seems to be not determined by the Görtler number alone on the broader cones ($\psi =30^{\circ }$ and $50^{\circ }$) where the primary cross-flow instability dominates the flow. Overall, this indicates that the centrifugal effects play an important role in the boundary-layer transition on rotating cones in axial inflow.

We develop a mean-field model to examine the stability of a ‘quasi-2-D suspension’ of elongated particles embedded within a viscous membrane. This geometry represents several biological and synthetic settings, and we reveal mechanisms by which the anisotropic mobility of particles interacts with long-ranged viscous membrane hydrodynamics. We first show that a system of slender rod-like particles driven by a constant force is unstable to perturbations in concentration – much like sedimentation in analogous 3-D suspensions – so long as membrane viscous stresses dominate. However, increasing the contribution of viscous stresses from the surrounding 3-D fluid(s) suppresses such an instability. We then tie this result to the hydrodynamic disturbances generated by each particle in the plane of the membrane and show that enhancing subphase viscous contributions generates extensional fields that orient neighbouring particles in a manner that draws them apart. The balance of flux of particles aggregating versus separating then leads to a wave number selection in the mean-field model.

Richtmyer–Meshkov (RM) instability at a single-mode interface impacted by a cylindrical divergent shock with low to moderate Mach numbers is investigated experimentally. The motion of an unperturbed interface is first examined to obtain the background flow. The shocked interface moves uniformly at the early stage, but later decelerates. The stronger the incident shock, the larger the interface deceleration, which is reasonably predicted by a one-dimensional model considering the effect of postshock non-uniformity. Such a deceleration greatly inhibits the growths of harmonics of an initially perturbed interface and, consequently, the divergent RM instability presents very weak nonlinearity from early to late stages. Particularly, higher-Mach-number cases present weaker nonlinearity due to larger deceleration there. This abnormal linear growth regime is reported for the first time. Benefiting from this, the incompressible linear model holds validity at all stages of divergent RM instability. It is also found that compressibility inhibits the initial growth rate, but produces a weak influence on the subsequent instability growth.

Three-dimensional effects of sidewalls on the low-frequency unsteadiness of the shock-wave/boundary-layer interaction (SBLI) are of academic and practical importance but not yet well understood. Considerable attention has been paid to the viscous effect of sidewalls, whereas the potential inviscid confinement effect of sidewalls has received little attention. The present work provides experimental evidence of multiscale spanwise travelling waves crossing the separation front under the confinement of sidewalls. Global pressure measurements were made for a sidewall-confined 24$^\circ$ compression ramp interaction in Mach-2.83 flow using fast-responding pressure-sensitive paint. The unsteady pressure in a statistically two-dimensional intermittent region suggests that in addition to the canonical streamwise oscillation, the separation front exhibits significant low-frequency, multiscale spanwise distortion. Modal analysis further reveals that multiscale spanwise unsteadiness has higher intensity and frequency than the streamwise oscillation. Such strong spanwise unsteadiness calls attention to the low-frequency unsteadiness in previous sidewall-confined SBLI experiments and encourages further study on the mechanism of the confinement effect.

We use video footage of a water-tunnel experiment to construct a 2-D reduced-order model of the flapping dynamics of an inverted flag in uniform flow. The model is obtained as the reduced dynamics on a 2-D attracting spectral submanifold (SSM) that emanates from the two slowest modes of the unstable fixed point of the flag. Beyond an unstable fixed point and a limit cycle expected from observations, our SSM-reduced model also confirms the existence of two unstable fixed points for the flag, which were found by previous studies. Importantly, the model correctly reconstructs the dynamics from a small number of general trajectories and no further information on the system. In the chaotic flapping regime, we construct a 4-D SSM-reduced model that captures the system's chaotic attractor.

Two sets of measurements utilizing hot-wire anemometry and oil-film interferometry for flat-plate turbulent boundary layers, exposed to various controlled adverse and favourable pressure gradients, are used to evaluate history effects of the imposed and varying free-stream gradients. The results are from the NDF wind tunnel at Illinois Tech (IIT) and the MTL wind tunnel at KTH, over the range $800 < Re_\tau < 22\,000$ (where $Re_{\tau }$ is the friction Reynolds number). The streamwise pressure-gradient parameter $\beta \equiv (-\ell /\tau _{w}) \cdot (\partial P_{e}/\partial x)$ varied between $-2 < \beta < 7$, where $\ell$ is an outer length scale for boundary layers equivalent to the half-height of channel flow and the radius of pipe flow, and is estimated for each boundary-layer profile; note that $\tau_w$ is the wall-shear stress and $P_e$ is the free-stream static pressure. Extracting from each profile the three parameters of the overlap region, following the recent work of Monkewitz & Nagib (J. Fluid Mech., vol. 967, 2023, p. A15) that led to an overlap region of combined logarithmic and linear parts, we find minimum history effects in the overlap region. Thus, the overlap region in this range of pressure-gradient boundary layers appears to be in ‘quasiequilibrium’.

Two simulations of turbulent Couette flows were performed at friction Reynolds numbers of 1000 and 2000 in a large box of dimensions $L_x=16{\rm \pi} h$, $L_y=2h$ and $L_z=6{\rm \pi} h$, where h is the semi-height of the channel. The study focuses on the differences in the intensity and scaling of turbulence at these two Reynolds numbers. The 2000 case showed a lack of a clear log layer with a higher value of the Von Kármán constant $\kappa$ than Poiseuille channels. The intensities were well-scaled in the buffer layer and below, with a second maximum of the streamwise intensity at approximately 350 wall units. Contrary to Poiseuille channels, the dissipation scales close to the wall in wall units. This fact can be attributed to the constant value of the derivative of the streamwise intensity in wall units. The intensities of the 2000 case showed remarkable differences compared with those at Reynolds number 1000 at the channel centre, likely due to the organization of large scales of the streamwise fluctuactions, $u$. These large scales were thought to be considered ‘infinite’. However, for the 2000 case, while all the structures have a width of $\ell _z \approx 6/8{\rm \pi} h$, their length varies from $\ell _x \approx 6{\rm \pi} h$ to $\ell _x \approx 16{\rm \pi} h$, which clearly contradicts the trends obtained in the past. This is a new effect that has not been reported for turbulent Couette flow and points to the uncertainty and sensitivity that is observed for certain statistical quantities.

We consider the process of convective dissolution in a homogeneous and isotropic porous medium. The flow is unstable due to the presence of a solute that induces a density difference responsible for driving the flow. The mixing dynamics is thus driven by a Rayleigh–Taylor instability at the pore scale. We investigate the flow at the scale of the pores using Hele-Shaw type experiment with bead packs, two-dimensional direct numerical simulations and physical models. Experiments and simulations have been specifically designed to mimic the same flow conditions, namely matching porosities, high Schmidt numbers and linear dependency of fluid density with solute concentration. In addition, the solid obstacles of the medium are impermeable to fluid and solute. We characterise the evolution of the flow via the mixing length, which quantifies the extension of the mixing region and grows linearly in time. The flow structure, analysed via the centreline mean wavelength, is observed to grow in agreement with theoretical predictions. Finally, we analyse the dissolution dynamics of the system, quantified through the mean scalar dissipation, and three mixing regimes are observed. Initially, the evolution is controlled by diffusion, which produces solute mixing across the initial horizontal interface. Then, when the interfacial diffusive layer is sufficiently thick, it becomes unstable, forming finger-like structures and driving the system into a convection-dominated phase. Finally, when the fingers have grown sufficiently to touch the horizontal boundaries of the domain, the mixing reduces dramatically due to the absence of fresh unmixed fluid. With the aid of simple physical models, we explain the physics of the results obtained numerically and experimentally. The solute evolution presents a self-similar behaviour, and it is controlled by different length scales in each stage of the mixing process, namely the length scale of diffusion, the pore size and the domain height.

The two-dimensional, steady, homogeneous flow field proposed by Astarita (J. Rheol., vol. 35, 1991, pp. 687–689) is studied for a range of viscoelastic constitutive equations of differential form including the models due to Oldroyd (the upper and lower convected Maxwell; UCM/LCM), Phan-Thien and Tanner (simplified, linear form; sPTT) and Giesekus. As the flow is steady and homogeneous, the sPTT model results also give the FENE-P model solutions via a simple transformation of parameters. The flow field has the interesting feature that a scalar parameter may be used to vary the flow ‘type’ continuously from solid-body rotation to simple shearing to planar extension whilst the rate of deformation tensor $\boldsymbol{\mathsf{D}}$ remains constant (i.e. independent of flow type). The response of the models is probed in order to determine how a scalar ‘viscosity’ function may be rigorously constructed which includes flow-type dependence. We show that for most of these models – the Giesekus being the exception – the first and second invariants of the resulting extra stress tensor are linearly related, and for models based on the upper convected derivative, this link is simply via a material property, i.e. half the modulus. By defining a frame-invariant coordinate system with respect to the eigenvectors of $\boldsymbol{\mathsf{D}}$, we associate a ‘viscosity’ for each of the flows to a deviatoric stress component and show how this quantity varies with the flow-type parameter. For elliptical motions, rate thinning is always observed and all models give essentially the UCM response. For strong flows, i.e. flow types containing at least some extension, thickening occurs and only a small element of extension is required to remove any shear thinning inherent in the model (e.g. as occurs in steady simple shearing for the sPTT/Giesekus models). Finally, a functional form of a viscosity equation which could incorporate flow type, but be otherwise inelastic, the so-called GNFFTy (generalised Newtonian fluid model incorporating flow type, pronounced ‘nifty’), is proposed. In the frame-invariant coordinate system proposed, this model is also capable of capturing normal-stress differences.

Understanding and controlling fluid entrapment during forced imbibition in porous media is crucial for many natural and industrial applications. However, the microscale physics and macroscopic consequences of fluid entrapment in these geometric-confined porous media remain poorly understood. Here, we introduce a novel multidepth microfluidic chip, which can mitigate the depth confinement of traditional two-dimensional (2-D) microfluidic chips and mimic the wide pore size distribution as natural-occurring three-dimensional (3-D) porous media. Based on microfluidic experiments and direct numerical simulations, we observe the fluid-entrapment scenarios and elucidate the underlying complex interaction between geometric confinement, capillary number and wettability. Increasing depth variation can promote fluid entrapment, whereas increasing capillary number and contact angle yield the opposite effect, which seemingly contradicts conventional expectations in traditional 2-D microfluidic chips. The fluid-entrapment scenario in depth-variable microfluidic chips stems from microscopic interfacial phenomena, classified as snap-off and bypass events. We provide theoretical analyses of these pore-scale events and validate corresponding phase diagrams numerically. It is shown that increasing depth variation triggers snap-off and bypass events. Conversely, a higher capillary number suppresses snap-off events under strong imbibition, and an increased contact angle inhibits bypass events under imbibition. These macroscopic imbibition patterns in microfluidic porous media can be linked with these pore-scale events by improved dynamic pore-network models. Our findings bridge the understanding of forced imbibition between 2-D and 3-D porous media and provide design principles for newly engineered porous media with respect to their desired imbibition behaviours.

Direct numerical simulations of channel flow and temporal boundary layer at a Reynolds number $Re_{\tau } = 1500$ are used to assess the scale-by-scale mechanisms of wall turbulence. From the peak of turbulence production embedded at the small scales of the near-wall region, spatially ascending reverse cascades are generated that move through self-similar eddies growing in size with the wall distance. These fluxes are followed by spatially ascending forward cascades through detached eddies thus reaching sufficiently small scales where eventually scale energy is dissipated. This phenomenology is shared by both boundary layer and channel flow and is recognized as a robust physical feature characterizing wall turbulence in general. Specific features related to the flow configuration are indeed identified in the outer region. In particular, the central region of channels is characterized by a generalized Richardson energy cascade where large scales are in equilibrium with small scales at different wall distances through a combined forward cascade and spatial flux. On the contrary, the interface region of boundary layers is characterized by an almost two-dimensional physics where spatially ascending reverse cascades sustain long and wide interface structures with a forward cascade that survives only in the wall-normal scales. The overall scenario consists in a variety of scale motions that while protruding from the turbulent core towards the external region, squeeze at the interface thus sustaining vertical shear in a thin layer. The observed multidimensional physics sheds light on the complex interactions between outer entrainment and near-wall self-sustaining mechanisms with possible repercussions for theories.

The twin-jet configuration allows two different scenarios to close the screech feedback. For each jet, there is one loop involving disturbances which originate in that jet and arrive at its own receptivity point in phase (self-excitation). The other loop is associated with free-stream acoustic waves that radiate from the other jet, reinforcing the self-excited screech (cross-excitation). In this work, the role of the free-stream acoustic mode and the guided-jet mode as a closure mechanism for twin rectangular jet screech is explored by identifying eligible points of return for each path, where upstream waves propagating from such a point arrive at the receptivity location with an appropriate phase relation. Screech tones generated by these jets are found to be intermittent with an out-of-phase coupling as a dominant coupling mode. The instantaneous phase difference between the twin jets computed by the Hilbert transform suggests that a competition between out-of-phase and in-phase coupling is responsible for the intermittency. To model wave components of the screech feedback while ensuring perfect phase locking, an ensemble average of leading spectral proper orthogonal decomposition modes is obtained from several segments of large-eddy simulation data that correspond to periods of invariant phase difference between the two jets. Each mode is then extracted by retaining relevant wavenumber components produced via a streamwise Fourier transform. Spatial cross-correlation analysis of the resulting modes shows that most of the identified points of return for the cross-excitation are synchronised with the guided jet mode self-excitation, supporting that it is preferred in closing rectangular twin-jet screech coupling.

There exists much research examining the role of surface-attached air bubbles in drag reduction. Most of this literature considers isothermal flows and so ignores temperature differences, e.g. with the solid boundary. Here, we relax this assumption and ask whether surface-attached air bubbles may prove useful as thermal insulators, e.g. when the solid temperature differs from that of the cargo liquid (water). Theoretical and numerical solutions, e.g. for the variation of the Nusselt number with bubble thickness, are presented for cases characterized by a uniform surface heat flux (USF). We examine channel and pipe flow geometries, and consider instances where the net mass flow rate within the (continuous) air bubble is zero or non-zero. When the thermal boundary condition is changed to uniform surface temperature (UST), our analysis limits attention to numerical solutions. We identify and discuss a remarkable connection between the drag reduction problem and the USF thermal insulation problem: the proportional change of water temperature with bubble thickness is identical to the proportional change of drag. Also, and although our analysis is conducted in the ‘perfect plastron limit’, we can, e.g. by evaluating hydrodynamic and thermal slip lengths, contrast our work against related studies where heat transfer occurs through the ridges or pillars that affix the air layer in place. This comparison indicates that the oft-applied adiabatic interface assumption may prove restrictive in some regions of the parameter space. We conclude by examining the implications of our work in the context of UST micro-channels, which are relevant to various lab-on-a-chip technologies.

In this work, we employ well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity (TV) relation, to systematically improve the algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient air boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semilocal scalings. Three targeted modifications are made. First, we employ a total-stress-based transformation (Griffin et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 34, 2021, e2111144118) to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, we utilize the van Driest transformation in the outer layer based on the compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, we design a two-layer strategy and use the TV relation to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4 % in the logarithmic wall-normal coordinate and 3.4 % in the outer coordinate, around one-third of those in the baseline model.

Studies of Kelvin–Helmholtz (KH) instability have typically modelled the initial mean flow as an isolated stratified shear layer. However, geophysical flows frequently exhibit multiple layers. As a step towards understanding these flows, we examine the case of two adjacent stratified shear layers using both linear stability analysis and direct numerical simulations. With sufficiently large layer separation, the characteristics of instability and mixing converge towards the familiar KH turbulence, and similarly when the separation is near zero and the layers add to make a single layer, albeit with a reduced Richardson number. Here, our focus is on intermediate separations, which produce new and complex phenomena. As the separation distance $D$ increases from zero to a critical value $D_c$, approximately half the thickness of the shear layer, the growth rate and wavenumber both decrease monotonically. The minimum Richardson number is relatively low, potentially inducing pairing, and shear-aligned convective instability (SCI) is the primary mechanism for transition. Consequently, mixing is relatively strong and efficient. When $D\sim D_c$, billow length is increased but growth is slowed. Despite the modest growth rate, mixing is strong and efficient, engendered primarily by secondary shear instability manifested on the braids, and by SCI occurring on the eyelids. Shear-aligned vortices are driven in part by buoyancy production; however, shear production and vortex stretching are equally important mechanisms. When $D>D_c$, neighbouring billow interactions suppress the growth of both KH instability and SCI. Strength and efficiency of mixing decrease abruptly as $D_c$ is exceeded. As turbulence decays, layers of marginal instability may arise.

This paper examines turbulent Rayleigh–Bénard convection in a two-dimensional square cavity with partially isothermal conducting plates on the horizontal walls. The study reveals that controlling the relative locations of the partially isothermal plates can accelerate or completely suppress the reversals of large-scale circulation. The heat transfer efficiency, which is characterised by the time-averaged Nusselt number, is generally higher than that of the traditional Rayleigh–Bénard convection, and can be further enhanced when the reversal is fully suppressed. The reversal in our cases is mainly caused by the competition between the two alternately growing ‘corner’ vortices, fed by the detaching plumes from the hot/cold plates. This differs from those reported in traditional Rayleigh–Bénard convection. Fourier mode decomposition of the kinetic energy, reflecting the diverse contributors, in the reversing cases further emphasises the distinction between the current system and traditional Rayleigh–Bénard convection. In addition, multiple states were observed where the conducting plates were positioned at specific relative locations and had different initial conditions. It has been observed that the difference in Nusselt numbers between the anticlockwise and clockwise states increases linearly with the distance between the upper cold and lower hot plates. Moreover, the analysis of the buoyancy moment and the stability of the primary roll structure suggests that the higher heat transfer efficiency between the two states is strongly linked to a more stable primary roll structure. This study presents a new approach for controlling flow reversal and improving heat transfer efficiency by modifying the non-global conducting boundary and initial conditions.

The shock wave accelerating a heavy fluid layer can induce reverberating waves that continuously interact with the first and second interfaces. In order to manipulate the perturbation growths at fluid-layer interfaces, we present a theoretical framework to eliminate the reverberating waves. A model is established to predict the individual freeze-out (i.e. stagnation of perturbation growth) for the first and second interfaces under specific flow conditions determined based on the shock dynamics theory. The theoretical model quantifies the controllable parameters required for freeze-out, including the initial amplitudes of the first and second interfaces, the interface coupling strength and the maximum initial layer thickness preventing the second interface's phase reversal. The effectiveness of the model in predicting individual freeze-out for the first and second interfaces is validated numerically over a wide range of initial conditions. The upper and lower limits of initial amplitudes for the freeze-out of the whole fluid-layer width growth are further predicted. Within this amplitude range, a slightly higher initial amplitude for the second interface is specified, effectively arresting the growth of the entire fluid-layer width before the phase reversal of the second interface.

The starting vortex generated at the trailing edge of a flat plate, that is impulsively translated at fixed angle of attack, is a widely studied canonical problem. Recent work that examined the effect of plate rotation on this starting vortex found that two new and distinct vortex sheet types can arise. We generalise this work to study the starting vortex generated at any sharp and straight edge of an arbitrary body under a general time-dependent two-dimensional motion. The dimensionless velocity field of the attached flow near any sharp edge is assumed to take the form, $\hat {z}^{-1/2} f(T) + g(T) + o (1)$, where $\hat {z}$ is the dimensionless position referenced to the edge, $f(T)$ and $g(T)$ are functions of dimensionless time, $T$, associated with the local flow perpendicular and parallel to the edge, respectively. This enables starting vortices to be generally calculated and their types related by simply inspecting the forms of $f(T)$ and $g(T)$. We elucidate the physics underlying all three vortex types and show that these vortices are generated by pure translation of the sharp edge. Several case studies are explored, including the leading/trailing edge vortices of a flat plate which can simultaneously be of different type (relevant to low-speed aircraft), the vortex formed by translation of a semi-infinite flat plate and the trailing-edge vortex of Joukowski aerofoils. With the ability to calculate the vortices at all edges, the theory is used to develop a general formula for the lift force of a flat plate which can find application in practice.