We perform direct numerical simulations of laminar separated flows over finite-aspect-ratio swept wings at a chord-based Reynolds number of $Re = 400$ to reveal a variety of wake structures generated for a range of aspect ratios (semi aspect ratio $sAR=0.5\text {--}4$), angles of attack ($\alpha =16^{\circ }\text {--}30^{\circ }$) and sweep angles ($\varLambda =0^{\circ }\text {--}45^{\circ }$). Flows behind swept wings exhibit increased complexity in their dynamical features compared to unswept-wing wakes. For unswept wings, the wake dynamics are predominantly influenced by the tip effects. Steady wakes are mainly limited to low-aspect-ratio wings. Unsteady vortex shedding takes place near the midspan of higher-$AR$ wings due to weakened downwash induced by the tip vortices. With increasing sweep angle, the source of three-dimensionality transitions from the tip to the midspan. The three-dimensional midspan effects are responsible for the formation of the stationary vortical structures at the inboard part of the span, which expands the steady wake region to higher aspect ratios. At higher aspect ratios, the midspan effects of swept wings diminish at the outboard region, allowing unsteady vortex shedding to develop near the tip. In the wakes of highly swept wings, streamwise finger-like structures form repetitively along the wing span, providing a stabilizing effect. The insights revealed from this study can aid the design of high-lift devices and serve as a stepping stone for understanding the complex wake dynamics at higher Reynolds numbers and those generated by unsteady wing manoeuvres.

Entropy perturbations generate sound when accelerated/decelerated by a non-uniform flow. Current analytical models provide a good prediction of this entropy noise when the flow cross-sectional area changes are gradual, as is the case for nozzle flows. However, they typically rely on quasi-1-D and isentropic assumptions, and their predictions differ significantly from experimental measurements when sudden area increases are involved. This work uses a theoretical approach to quantitatively identify the main mechanisms responsible for the mismatch. A new form of the acoustic analogy is derived in which the entropy-related source terms are systematically identified for the first time. The theory includes three-dimensional and non-isentropic effects. The approach is applied to the flow through a sudden area expansion, for which the large-scale flow separation creates a recirculation zone. The derived acoustic analogy is simplified for low Mach numbers and frequencies, and solved using a Green's function method. The results provide the first quantitative evidence that the presence and spatial extent of the recirculation zone, rather than the flow non-isentropicity, is the dominant factor causing deviation from predictions from quasi-1-D, isentropic theory.

The production of broadband frequency spectra from narrowband wave forcing in geophysical flows remains an open problem. Here we consider a related theoretical problem that points to the role of time-dependent vortical flow in producing this effect. Specifically, we apply multi-scale analysis to the transport equation of wave action density in a homogeneous stationary random background flow under the Wentzel–Kramers–Brillouin approximation. We find that, when some time dependence in the mean flow is retained, wave action density diffuses both along and across surfaces of constant frequency in wavenumber–frequency space; this stands in contrast to previous results showing that diffusion occurs only along constant-frequency surfaces when the mean flow is steady. A self-similar random background velocity field is used to show that the magnitude of this frequency diffusion depends non-monotonically on the time scale of variation of the velocity field. Numerical solutions of the ray-tracing equations for rotating shallow water illustrate and confirm our theoretical predictions. Notably, the mean intrinsic wave frequency increases in time, which by wave action conservation implies a concomitant increase of wave energy at the expense of the energy of the background flow.

Steady two-dimensional Rayleigh–Bénard convection between stress-free isothermal boundaries is studied via numerical computations. We explore properties of steady convective rolls with aspect ratios ${\rm \pi} /5\leqslant \varGamma \leqslant 4{\rm \pi}$, where $\varGamma$ is the width-to-height ratio for a pair of counter-rotating rolls, over eight orders of magnitude in the Rayleigh number, $10^3\leqslant Ra\leqslant 10^{11}$, and four orders of magnitude in the Prandtl number, $10^{-2}\leqslant Pr\leqslant 10^2$. At large $Ra$ where steady rolls are dynamically unstable, the computed rolls display $Ra \rightarrow \infty$ asymptotic scaling. In this regime, the Nusselt number $Nu$ that measures heat transport scales as $Ra^{1/3}$ uniformly in $Pr$. The prefactor of this scaling depends on $\varGamma$ and is largest at $\varGamma \approx 1.9$. The Reynolds number $Re$ for large-$Ra$ rolls scales as $Pr^{-1} Ra^{2/3}$ with a prefactor that is largest at $\varGamma \approx 4.5$. All of these large-$Ra$ features agree quantitatively with the semi-analytical asymptotic solutions constructed by Chini & Cox (Phys. Fluids, vol. 21, 2009, 083603). Convergence of $Nu$ and $Re$ to their asymptotic scalings occurs more slowly when $Pr$ is larger and when $\varGamma$ is smaller.

We investigate experimentally the behaviour of an elongated flexible cylinder settling at moderate Reynolds number under the effect of buoyancy in a fluid otherwise at rest. The experiments uncover the development of large-amplitude periodic deformations of the cylinder (of the order of its diameter) in specific parameter ranges. Bending oscillations are observed to occur for two base flow situations, involving either a steady or an unsteady wake. In both cases, the sequence of oscillatory deformations emerging when the cylinder length is increased involves the bending modes of an unsupported cylinder with free ends. Comparison of the deformation frequency measured for the falling cylinder with the vortex shedding frequency expected for a non-deformable cylinder at the same Reynolds number indicates that the deformation is coupled to the wake unsteadiness. It also suggests that the cylinder degrees of freedom in deformability allow wake instability to be triggered at Reynolds numbers that would be subcritical for fixed rigid cylinders.

A new formulation of the model used in the near-wall region for the turbulent heat flux is developed, in order to extend the elliptic blending differential flux model of Dehoux et al. (Intl J. Heat Fluid Flow, vol. 63, 2017, pp. 190–204) to various boundary conditions for the temperature: imposed wall temperature, imposed heat flux or conjugate heat transfer. The new model is developed on a theoretical basis in order to satisfy the near-wall budget of the turbulent heat flux and, consequently, its asymptotic behaviour in the vicinity of the wall, which is crucial for the correct prediction of heat transfer between the fluid and the wall. The models of the different terms are derived using Taylor series expansions and comparisons with recent direct numerical simulation data of channel flows with various boundary conditions. A priori tests show that this methodology makes it possible to drastically improve the physical representation of the wall–turbulence interaction. This new differential flux model relies on the thermal-to-mechanical time scale ratio which depends on the thermal boundary condition at the wall. The key element entering this ratio is $\varepsilon _\theta$, the dissipation rate of the temperature variance $\overline {{\theta '}^2}$. Thus, a new near-wall model for this dissipation rate is proposed, in the framework of the second-moment closure based on the elliptic blending strategy. The computations carried out in order to validate the new differential flux model demonstrate the very satisfactory prediction of heat transfer in the forced convection regime for all kinds of thermal boundary condition.

The aim of this paper is to provide a complete description of the bifurcation scenario of a uniform flow past a rotating circular cylinder up to $Re = 200$. Linear stability theory is used to depict the neutral curves and analyse the arising unstable global modes. Three codimension-two bifurcation points are identified, namely a Takens–Bogdanov, a cusp and generalised Hopf, which are closely related to qualitative changes in orbit dynamics. The occurrence of the cusp and Takens–Bogdanov bifurcations for very close parameters (corresponding to an imperfect codimension-three bifurcation) is shown to be responsible for the existence of multiple steady states, as already observed in previous studies. Two bistability regions are identified, the first with two stable fixed points and the second with a fixed point and a cycle. The presence of homoclinic and heteroclinic orbits, which are classical in the presence of Takens–Bogdanov bifurcations, is confirmed by direct numerical simulations. Finally, a weakly nonlinear analysis is performed in the neighbourhood of the generalised Hopf, showing that above this point the Hopf bifurcation is subcritical, leading to a third range of bistability characterised by both a stable fixed point and a stable cycle.

Near-interface colloidal monolayers are often used as model systems for research on hydrodynamics in biophysics systems and in the chemical industry. Using microrheological methods, the correlated diffusion of particles is experimentally measured in colloidal monolayers near a water–air interface. The results show that the scaling lengths $({\chi _{||}},{\chi _ \bot })$ of such colloidal monolayers are anisotropic in two orthogonal directions within the monolayer, which are parallel and perpendicular to the line connecting the centres of a particle pair. The former $({\chi _{||}})$ is the Saffman length of the monolayer, while the latter $({\chi _ \bot })$ is a function of both the Saffman length and the radius of the colloids. The size of the colloids is involved in ${\chi _ \bot }$ but not ${\chi _{||}}$, which reflects the discrete nature of the monolayer in the transverse direction and the continuous nature of the monolayer in the longitudinal direction. From the scaling lengths, the viscosities of the colloidal monolayers are obtained, which agree with those obtained from the single-particle diffusion coefficients. The influence of the boundary condition imposed by the nearby interface on the hydrodynamic interactions is in a power-law behaviour of the distance z.

The dissipation element analysis is applied to the mixture fraction fields of a series of datasets from direct numerical simulations of non-premixed temporally evolving jet flames with jet Reynolds numbers ranging from 4500 to 10 000 and varying stoichiometric mixture fractions. Dissipation elements are space-filling regions where a scalar field behaves monotonically and allow for the analysis of scalar fields in homogeneous isotopic turbulence as well as in complex, highly inhomogeneous and anisotropic flows such as turbulent flames. Statistics of the dissipation element parameters of non-premixed flames are compared to those obtained from non-reacting jets. It is found that the universality of the normalized length distribution of the dissipation elements observed in non-reacting cases also holds true for the reacting flows. The characteristic scaling with the Kolmogorov micro-scale $\eta$ is obtained as well. The effects of combustion on the scalar difference in the dissipation elements are shown and are found to diminish as the Reynolds number and the fuel dilution is increased. The dissipation elements provide the means for a local comparison of the turbulent and characteristic flame scales. A new regime diagram for non-premixed combustion is introduced using coherent structures in the scalar fields, the dissipation element parameters for a local classification of the turbulent flame surface into flamelet-like zones and fine-scale mixing zones in addition to the burning and non-burning zones. The soundness of the regime diagram and the potential consequences for combustion modelling in the individual regimes is demonstrated by the investigation of the correlation between the chemical field and the dissipation element parameters in the individual regimes.

We report the first shock-tube experiments on dual-mode Richtmyer–Meshkov instability (RMI). An extended soap-film technique is adopted to generate a dual-mode gaseous interface such that its initial wavenumber ($k_0$) and phase of the fundamental waves are well controlled. By extracting interfacial contours from the distinct schlieren images, a Fourier analysis is performed from linear to weakly nonlinear stages and the growth of each basic wave is obtained. A noticeable difference between the growth of each basic mode and the corresponding single-mode RMI is observed, which suggests evident mode coupling effects in the dual-mode RMI. For dual-mode interfaces with in-phase $k_0$ and $k_0/2$ waves, the mode coupling suppresses (promotes) the growth of the $k_0$ ($k_0/2$) mode, while for interfaces with anti-phase $k_0$ and $k_0/2$ modes, the growth of the $k_0$ ($k_0/2$) mode is weakly influenced (evidently inhibited). However, for the combination of $k_0$ and $k_0/3$ waves, the mode coupling has a negligible influence on the growth of each basic wave. The modal theory of Haan (Phys. Fluids B, vol. 3, 1991, pp. 2349–2355), originally for multi-mode Rayleigh–Taylor instability, is reformulated for the dual-mode RMI, and it is found that this model overestimates the present experimental results for ignoring the nonlinear saturation. This model is then modified by accounting for both the mode coupling and nonlinear saturation, which well predicts the experimental results not only for the growth of the basic waves but also for the growth of second harmonics.

Townsend's attached-eddy hypothesis (AEH) provides a theoretical description of turbulence statistics in the logarithmic region in terms of coherent motions that are self-similar with the wall-normal distance ($y$). This hypothesis was further extended by Perry and coworkers who proposed attached-eddy models that predict the coexistence of the logarithmic law in the mean velocity and streamwise turbulence intensity as well as spectral scaling for the streamwise energy spectra. The AEH can be used to predict the statistical behaviours of wall turbulence, yet revealing such behaviours has remained an elusive task because the proposed description is established within the limits of asymptotically high Reynolds numbers. Here, we show the self-similar behaviour of turbulence motions contained within wall-attached structures of streamwise velocity fluctuations using the direct numerical simulation dataset of turbulent boundary layer, channel, and pipe flows ($Re_{\tau } \approx 1000$). The physical sizes of the identified structures are geometrically self-similar in terms of height, and the associated turbulence intensity follows the logarithmic variation in all three flows. Moreover, the corresponding two-dimensional energy spectra are aligned along a linear relationship between the streamwise and spanwise wavelengths ($\lambda _x$ and $\lambda _z$, respectively) in the large-scale range ($12y < \lambda _x <3\text{--}4\delta$), which is reminiscent of self-similarity. Consequently, one-dimensional spectra obtained by integrating the two-dimensional spectra over the self-similar range show some evidence for self-similar scaling $\lambda _x \sim \lambda _z$ and the possible existence of $k_x^{-1}$ and $k_z^{-1}$ scaling regions in a similar subrange. The present results reveal that the asymptotic behaviours can be obtained by identifying the self-similar coherent structures in canonical wall turbulence, albeit in low-Reynolds-number flows.

We present results of $\approx$300 miscible Newtonian displacement flow experiments carried out in a dimensionally scaled laboratory set-up. Annulus eccentricity, density difference and viscosity of the fluids are varied, over a wide range of laminar Reynolds numbers. Comparisons with predictions from the two-dimensional gap-averaged (2DGA) model of Carrasco-Teja et al. (J. Fluid Mech., vol. 605, 2008, pp. 293–327) show excellent agreement in predicting the underlying competition between buoyancy and eccentricity, which results in either top side or slumping flows. Other features of the experiments are not predicted as well. The main discrepancy results from a variety of dispersive effects that are not present in the 2DGA model, e.g. dispersion within the annular gap and due to azimuthal secondary flows. We find that dispersive effects dominate to the extent that the slumping flows are best described by bulk diffusive spreading of the height-averaged concentrations, relative to the mean flow. A variety of flow structures and wave-like instabilities are discussed. The study is relevant to the oilfield process of primary cementing of horizontal wells.

Cellular membranes are elastic lipid bilayers that contain a variety of proteins, including ion channels, receptors and scaffolding proteins. These proteins are known to diffuse in the plane of the membrane and to influence the bending of the membrane. Experiments have shown that lipid flow in the plane of the membrane is closely coupled with the diffusion of proteins. Thus, there is a need for a comprehensive framework that accounts for the interplay between these processes. Here, we present a theory for the coupled in-plane viscous flow of lipids, diffusion of transmembrane proteins and elastic deformation of lipid bilayers. The proteins in the membrane are modelled such that they influence membrane bending by inducing a spontaneous curvature. We formulate the free energy of the membrane with a Helfrich-like curvature elastic energy density function modified to account for the chemical potential energy of proteins. We derive the conservation laws and equations of motion for this system. Finally, we present results from dimensional analysis and numerical simulations and demonstrate the effect of coupled transport processes in governing the dynamics of membrane bending and protein diffusion.

We investigate the self-propulsion of an inertial swimmer in a linearly density stratified fluid using the archetypal squirmer model which self-propels by generating tangential surface waves. We quantify swimming speeds for pushers (propelled from the rear) and pullers (propelled from the front) by direct numerical solution of the Navier–Stokes equations using the finite volume method for solving the fluid flow and the distributed Lagrange multiplier method for modelling the swimmer. The simulations are performed for Reynolds numbers ($Re$) between 5 and 100 and Froude numbers ($Fr$) between 1 and 10. We find that increasing the fluid stratification strength reduces the swimming speeds of both pushers and pullers relative to their speeds in a homogeneous fluid. The increase in the buoyancy force experienced by these squirmers due to the trapping of lighter fluid in their respective recirculatory regions as they move in the heavier fluid is one of the reasons for this reduction. With increasing the stratification, the isopycnals tend to deform less, which offers resistance to the flow generated by the squirmers around them to propel themselves. This resistance increases with stratification, thus, reducing the squirmer swimming velocity. Stratification also stabilizes the flow around a puller keeping it axisymmetric even at high $Re$, thus, leading to stability which is otherwise absent in a homogeneous fluid for $Re$ greater than $O(10)$. On the contrary, a strong stratification leads to instability in the motion of pushers by making the flow around them unsteady and three-dimensional, which is otherwise steady and axisymmetric in a homogeneous fluid. A pusher is a more efficient swimmer than a puller owing to efficient convection of vorticity along its surface and downstream. Data for the mixing efficiency generated by individual squirmers explain the trends observed in the mixing produced by a swarm of squirmers.

Detecting the turbulent/non-turbulent interface is a challenging topic in turbulence research. In the present study, machine learning methods are used to train detectors for identifying turbulent regions in the flow past a circular cylinder. To ensure that the turbulent/non-turbulent interface is independent of the reference frame of coordinates and is physics-informed, we propose to use invariants of tensors appearing in the transport equations of velocity fluctuations, strain-rate tensor and vortical tensor as the input features to identify the flow state. The training samples are chosen from numerical simulation data at two Reynolds numbers, $Re=100$ and 3900. Extreme gradient boosting (XGBoost) is utilized to train the detector, and after training, the detector is applied to identify the flow state at each point of the flow field. The trained detector is found robust in various tests, including the applications to the entire fields at successive snapshots and at a higher Reynolds number $Re=5000$. The objectivity of the detector is verified by changing the input features and the flow region for choosing the turbulent training samples. Compared with the conventional methods, the proposed method based on machine learning shows its novelty in two aspects. First, no threshold value needs to be specified explicitly by the users. Second, machine learning can treat multiple input variables, which reflect different properties of turbulent flows, including the unsteadiness, vortex stretching and three-dimensionality. Owing to these advantages, XGBoost generates a detector that is more robust than those obtained from conventional methods.

Taylor–Couette (TC) flow is the shear-driven flow between two coaxial independently rotating cylinders. In recent years, high-fidelity simulations and experiments revealed the shape of the streamwise and angular velocity profiles up to very high Reynolds numbers. However, due to curvature effects, so far no theory has been able to correctly describe the turbulent streamwise velocity profile for a given radius ratio, as the classical Prandtl–von Kármán logarithmic law for turbulent boundary layers over a flat surface at most fits in a limited spatial region. Here, we address this deficiency by applying the idea of a Monin–Obukhov curvature length to turbulent TC flow. This length separates the flow regions where the production of turbulent kinetic energy is governed by pure shear from that where it acts in combination with the curvature of the streamlines. We demonstrate that for all Reynolds numbers and radius ratios, the mean streamwise and angular velocity profiles collapse according to this separation. We then develop the functional form of the velocity profile. Finally, using the newly developed angular velocity profiles, we show that these lead to an alternative constant in the model proposed by Cheng et al. (J. Fluid Mech., vol. 890, 2020, A17) for the dependence of the torque on the Reynolds number, or, in other words, of the generalized Nusselt number (i.e. the dimensionless angular velocity transport) on the Taylor number.

This paper is concerned with the interaction of vertically sheared currents with two-dimensional flexural–gravity waves in finite depth. A third-order Stokes expansion is carried out and fully nonlinear computations are performed for symmetric, steadily travelling waves on a linear shear current. For upstream periodic waves, two global bifurcation mechanisms are discovered. Both branches bifurcate from infinitesimal periodic waves, with one stopping at another infinitesimal wave of different phase speed, and the other terminating at a stationary configuration. Generalised solitary waves are found for downstream waves. More surprisingly, the central pulse of the generalised solitary wave can become wide and flat as the computational domain is enlarged. This provides strong evidence for the existence of wave fronts in single-layer free-surface waves. Particle trajectories and streamline structures are studied numerically for the fully nonlinear equations. Two patterns, closed orbits and pure horizontal transport, are observed for both periodic and solitary waves in moving frames. The most striking phenomenon is the existence of net vertical transport of particles beneath some solitary waves due to wave–current interactions. The streamline patterns alternate between net vertical transport and a closed orbit, resulting in the formation of a series of nested cat's-eye structures.

We study the axisymmetric interaction of two chemically active Janus particles. By relying on the linearity of the field equations and symmetry arguments, we derive a generic solution for the relative velocity of the particles. We show that, regardless of the chemical properties of the system, the relative velocity can be written as a linear summation of geometrical functions which only depend on the gap size between the particles. We evaluate these functions via an exact approach which accounts for the full chemical and hydrodynamic interactions. Using the obtained solution, we expose the role of each compartment in the relative motion, and also discuss the contribution of different interactions. We then show that the dynamical system describing the relative motion of two Janus particles can have up to three fixed points. These fixed points can be stable or unstable, indicating that a system of two Janus particles can exhibit a variety of non-trivial behaviours depending on their initial gap size, and their chemical properties. We also look at the specific case of Janus particles in which one compartment is inert, and present regime diagrams for their relative behaviour in the activity–mobility parameter space.

Inertial particle data from three-dimensional direct numerical simulations of particle-laden homogeneous isotropic turbulence at high Reynolds number are analysed using Voronoi tessellation of the particle positions and considering different Stokes numbers. A finite-time measure to quantify the divergence of the particle velocity by determining the volume change rate of the Voronoi cells is proposed. For inertial particles, the probability distribution function of the divergence deviates from that for fluid particles. Joint probability distribution functions of the divergence and the Voronoi volume illustrate that the divergence is most prominent in cluster regions and less pronounced in void regions. For larger volumes, the results show negative divergence values which represent cluster formation (i.e. particle convergence) and, for small volumes, the results show positive divergence values which represents cluster destruction/void formation (i.e. particle divergence). Moreover, when the Stokes number increases the divergence takes larger values, which gives some evidence why fine clusters are less observed for large Stokes numbers.

In this paper, sparsity-promoting regression techniques are employed to automatically identify from data relevant triadic interactions between modal structures in large Galerkin-based models of two-dimensional unsteady flows. The approach produces interpretable, sparsely connected models that reproduce the original dynamical behaviour at a much lower computational cost, as fewer triadic interactions need to be evaluated. The key feature of the approach is that dominant interactions are selected systematically from the solution of a convex optimisation problem, with a unique solution, and no a priori assumptions on the structure of scale interactions are required. We demonstrate this approach on models of two-dimensional lid-driven cavity flow at Reynolds number $Re = 2 \times 10^{4}$, where fluid motion is chaotic. To understand the role of the subspace utilised for the Galerkin projection in the sparsity characteristics, we consider two families of models obtained from two different modal decomposition techniques. The first uses energy-optimal proper orthogonal decomposition modes, while the second uses modes oscillating at a single frequency obtained from discrete Fourier transform of the flow snapshots. We show that, in both cases, and despite no a priori physical knowledge being incorporated into the approach, relevant interactions across the hierarchy of modes are identified in agreement with the expected picture of scale interactions in two-dimensional turbulence. Yet, substantial structural changes in the interaction pattern and a quantitatively different sparsity are observed. Finally, although not directly enforced in the procedure, the sparsified models have excellent long-term stability properties and correctly reproduce the spatio-temporal evolution of dominant flow structures in the cavity.