The existence of a turbulent/turbulent interface (TTI) has recently been verified in the far wake of a circular cylinder exposed to free-stream turbulence (Kankanwadi & Buxton, J. Fluid Mech., vol. 905, 2020, p. A35). This study aims to understand the physics within the TTI. The wake boundary, approximately 40 diameters downstream of a circular cylinder subjected to grid-generated turbulence, was investigated through simultaneous cinematographic, stereoscopic particle image velocimetry and planar laser induced fluorescence experiments. With no grid placed upstream of the cylinder, the behaviour of the resultant interface, our closest approximation to a turbulent/non-turbulent interface, exactly matched what is observed in existing literature. When background turbulence is present, viscous action is no longer the only method by which enstrophy is transported to the background fluid, unlike for turbulent/non-turbulent interfaces. The presence of rotational fluid on both sides of the TTI allows the vorticity stretching term of the enstrophy budget equation to be the dominant actor in this process. The role of viscosity within a TTI is greatly diminished as the vorticity stretching term takes over responsibilities for enstrophy production. The turbulent strain rate normal to the TTI was found to be enhanced in the interfacial region. Decomposing the vorticity stretching term into components aligned with the three principal strain-rate directions, it was found that the term most aligned with the interface-normal direction contributed to the largest share of enstrophy production. This indicates that better ‘organised’ vorticity on the wake side of the interface yields the enstrophy amplification leading to the previously discovered enstrophy jump across the TTI by Kankanwadi & Buxton (J. Fluid Mech., vol. 905, 2020, p. A35).

Modern biomedical applications such as targeted drug delivery require a delivery system capable of enhanced transport beyond that of passive Brownian diffusion. In this work, an osmotic mechanism for the propulsion of a vesicle immersed in a viscous fluid is proposed. By maintaining a steady-state solute gradient inside the vesicle, a seepage flow of the solvent (e.g. water) across the semipermeable membrane is generated, which in turn propels the vesicle. We develop a theoretical model for this vesicle–solute system in which the seepage flow is described by a Darcy flow. Using the reciprocal theorem for Stokes flow, it is shown that the seepage velocity at the exterior surface of the vesicle generates a thrust force that is balanced by the hydrodynamic drag such that there is no net force on the vesicle. We characterize the motility of the vesicle in relation to the concentration distribution of the solute confined inside the vesicle. Any osmotic solute is able to propel the vesicle so long as a concentration gradient is present. In the present work, we propose active Brownian particles (ABPs) as a solute. To maintain a symmetry-breaking concentration gradient, we consider ABPs with spatially varying swim speed, and ABPs with constant properties but under the influence of an orienting field. In particular, it is shown that at high activity, the vesicle velocity is $\boldsymbol {U}\sim [K_\perp /(\eta _e\ell _m) ]\int \varPi _0^{swim} \boldsymbol {n}\,{\rm d}\varOmega$, where $\varPi _0^{swim}$ is the swim pressure just outside the thin accumulation boundary layer on the vesicle interior surface, $\boldsymbol {n}$ is the unit normal vector of the vesicle boundary, $K_\perp$ is the membrane permeability, $\eta _e$ is the viscosity of the solvent, and $\ell _m$ is the membrane thickness.

The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions – both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the self-similar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical self-similarity in the size of ‘wrinkles’ along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of large-scale coherent velocity regions such as uniform momentum zones. The self-similarity of isosurfaces yields power-law trends in subsequent one-dimensional statistics. For instance, the theoretical 2/3 power-law exponent for the structure function can be recovered by considering the collective behaviour of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the self-similar wrinkles of isosurfaces.

In this paper, we investigate the phenomenon of particle rebound in a viscous incompressible fluid environment. We focus on the important case of no-slip boundary conditions, where it is now well established that collisions cannot occur in finite time under certain assumptions. In a simplified framework, we provide conditions which allow us to prove that rebound is possible even in the absence of a topological contact. Our results lead to the conjecture that a qualitative change in the shape of the solid is necessary to obtain a physically meaningful rebound in fluids. We support the conjecture by comparing numerical simulations performed for the reduced model with finite element solutions obtained for corresponding well-established partial differential equation systems describing elastic solids interacting with incompressible fluids.

Direct numerical simulations of turbulent flow in a channel with one rigid and one viscoelastic wall are performed. An Eulerian–Eulerian model is adopted with a level-set approach to identify the fluid–compliant material interface. Focus is placed on the propagation of Rayleigh waves in the compliant material, whose speed depends on the shear modulus of elasticity and whose dominant wavelength depends on the thickness of the viscoelastic layer. These parameters are selected to ensure coupling between the compliant surface and turbulence. When the phase speed of Rayleigh waves is commensurate with the advection velocity of near-wall pressure fluctuations, sheets of vorticity are lifted up and detached near the critical layer and lead to a local pressure minimum. These events are caused by the inflectional velocity profile near the troughs, and are controlled by the net vorticity flux at the elastic surface. This phenomenon is central to understanding the statistical characteristics of the flow, including the surface deformation–pressure correlation and enhanced stochastic Reynolds shear stresses. Finally, we discuss the influence of three-dimensionality of the surface topography on the generation of streamwise vorticity, secondary motions and lateral turbulent transport.

We numerically explore the propagation of reacting fronts in a shallow and horizontal layer of fluid. We focus on fronts that couple with the fluid due to density differences between the products and reactants and also due to heat release from the reaction. We explore fronts where this solutal and thermal coupling is cooperative or antagonistic. We quantify the fluid motion induced by the front and investigate the interactions of the front with the fluid as it propagates through quiescent, cellular and chaotic flow fields. The solutal coupling induces an extended convection roll that travels with the front, the thermal coupling due to heat release from the reaction generates a pair of convection rolls that travels with the front, and when both couplings are present there is a complex signature of these contributions. The details of the front dynamics depend significantly upon the interactions of the front-induced flow field with the fluid ahead of the front.

The heat transfer behaviour of convection-driven dynamos in a rotating plane layer between two parallel plates, heated from the bottom and cooled from the top, is investigated. At a fixed rotation rate (Ekman number, $E=10^{-6}$) and fluid properties (thermal and magnetic Prandtl numbers, $Pr=Pr_m=1$), both dynamo convection (DC) and non-magnetic rotating convection (RC) simulations are performed to demarcate the effect of magnetic field on heat transport at different thermal forcings (Rayleigh number, $Ra=3.83\times 10^{9}\unicode{x2013}3.83\times 10^{10}$). In this range, our turbulence resolving simulations demonstrate the existence of an optimum thermal forcing, at which heat transfer between the plates in DC exhibits maximum enhancement, as compared with the heat transport in the RC simulations. Unlike any global force balance reported in the literature, the present simulations reveal an increase in the Lorentz force in the thermal boundary layer, due to stretching of magnetic field lines by the vortices near the walls with a no-slip boundary condition. This increase in Lorentz force mitigates turbulence suppression due to the Coriolis force, resulting in enhanced turbulence and heat transfer.

A large-scale spanwise and wall-normal array of sonic anemometers in the atmospheric surface layer is used to acquire all three components of instantaneous fluctuating velocity as well as temperature in a range of stability conditions. These data permit investigation of the three-dimensional statistical structure of turbulence structures. Based on a similar dataset, Krug et al. (Boundary-Layer Meteorol., vol. 172, 2019, pp. 199–214) reported a self-similar range of wall-attached turbulence structures under both unstable and near-neutral stability conditions. They considered only a wall-normal array and thus assessed statistical structure in the wall-normal direction, in relation to the streamwise wavelength. The present work extends the view of a self-similar range of turbulence structures, by including the statistical structure in the spanwise direction. Moreover, by analysing the phase shift between synchronized measurements in the spectral domain, it is inferred how a scale-dependent inclination angle in the streamwise/wall-normal plane varies with stability. Results suggest that the self-similar wall-attached structures have similar aspect ratios between streamwise/wall-normal scales and streamwise/spanwise scales such that $\lambda _x/\Delta z : \lambda _x/\Delta y \approx 1$ for both near-neutral and unstable conditions. Under the most unstable conditions, coherent structures with $\lambda _x/\delta = 1$ are inclined at angles as high as $65^{\circ }$ relative to the solid boundary, while larger scales $\lambda _x/\delta = 6$ exhibit inclination angles of approximately $35^{\circ }$. For near-neutral stability conditions, the angle tends towards $12^{\circ }$ for all scales. It is noted that in the near-neutral condition, the structure inclination angle and the aspect ratio – and thus the statistical modelling of coherent structures in the atmospheric surface layer – are highly sensitive to the value of the stability parameter.

We report experimental measurements of kinematic and dynamic particle concentration kernels conditioned by the separation distances of solid inertialess particles in isotropic turbulence by three-dimensional particle tracking velocimetry with particle diameters smaller than the Kolmogorov length scale. Particle radial relative velocity statistics are measured from the dissipation to the integral length-scale range. The radial scaling of particle and fluid relative velocity variance $\langle w_r(r)^{2} \rangle \sim r^{2/3}$ in the inertial subrange, consistent with Kolmogorov's theory, is reported, while a new scaling is found for small distances due to finite-size effects between particles. The measured concentration kernels at small separation distances therefore deviate from those in the theory of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) at small inter-particle distances due to hydrodynamic interactions. A real kernel taking into account the history of the particle tracks and excluding multiple events is also calculated, while the normalised particle concentration kernels are found to be essentially insensitive to the flow Reynolds number.

The present study focuses on identifying dynamical transition boundaries and presents an order-to-chaos map for the unsteady flow field of a flapping foil in the low Reynolds number regime. The effect of an extensive parametric space, covering a large number of kinematic conditions, has been investigated. It is shown that the conventional non-dimensional parameters cannot effectively capture the changes in the flow field due to the variations in the relevant kinematic parameters and are unable to demarcate the dynamical transition boundaries. Two new non-dimensional measures – maximum effective angle of attack and a leading-edge amplitude-based Strouhal number – are proposed here, which can capture the physical effect of the parametric variations on the wake dynamics. The study proposes generalised transition boundaries and an order-to-chaos map through a transitional regime in terms of these two newly proposed parameters. Published data from the existing literature have also been tested to verify the proposed transition model. It is seen that despite the wide variety of the parametric combinations, the dynamical states from both the new and the published data corroborate well the proposed boundaries, giving credibility to the order-to-chaos map.

This study experimentally investigates reacting jets in cross-flow (RJICF), considering flame/shear layer offset, momentum flux ratio ($J$) and density ratio ($S$) effects. These results demonstrate that non-reacting JICF and RJICF can exhibit very similar or completely different dynamics and controlling physics, depending upon streamwise and radial flame location. Consistent with prior measurements of Getsinger et al. (Exp. Fluids, vol. 53 (3), 2012, pp. 783–801), spatial amplification rates of shear layer vortex (SLV) structures increased with decreasing $S$ for non-reacting cases. Similar $S$ dependencies exist for reacting cases in which the flame lay outside the jet shear layer, whose flow topology is also quite similar to non-reacting cases, albeit with reduced SLV growth rates. However, although the reacting cases have lower growth rates, these SLV structures ultimately reach approximately the same peak strength as in the non-reacting cases. Finally, the SLV decay rate in both non-reacting and reacting cases was found to similarly scale inversely with the initial SLV growth rate. As such, primarily inertial mechanisms govern SLV growth and decay for reacting cases where the flame lies outside the shear layer. In contrast, very different behaviour is exhibited by reacting cases where the flame lies inside the shear layer, where the locally increased viscosity exerts significant influences. In these reacting cases, SLV roll-up is completely suppressed and the entire jet column undulates over a long length scale relative to the jet diameter. As such, the relative roles of inertial and viscous mechanisms in controlling combustion influences on the SLV dynamics, changes markedly with shear layer–flame offset.

The outer layer dynamics of a high-Reynolds-number boundary layer recovering from non-equilibrium is studied utilising the multi-resolution approach of zonal detached eddy simulation mode 3. The non-equilibrium conditions are obtained from a boundary layer separation over a rounded step enhancing the turbulent production, and recovery happens during redevelopment after reattachment at high Reynolds numbers ($Re_{\theta,max}\approx 24{,}000$). Most of the outer layer turbulence is resolved by the simulation, which reproduces accurately the experimental boundary layer relaxation. The spectral analysis of streamwise velocity fluctuations and turbulent kinetic energy (TKE) production evidences the different turbulent content distribution at separation and within the redevelopment region, at which very large-scale motions are identified with streamwise wavelengths up to $\lambda _x = 9\delta$, where $\delta$ is the boundary layer thickness. The redevelopment of the boundary layer is analysed in terms of the persistence of a secondary peak in the TKE production and the evolution of the wall-shear stress statistics. The skewness and probability density function of the skin friction show a slower relaxation than the downstream flow fraction. This confirms the long-lasting impact of perturbations of the outer layer in high-Reynolds-number wall-bounded flows. This persistent non-equilibrium state is suggested to be the reason for the reported lack of accuracy of the considered Reynolds-averaged Navier–Stokes models in the relaxation region.

Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$. This damping rate is found to scale as $1/L$, leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$, a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

We perform direct numerical simulation of supersonic turbulent channel flow over cubical roughness elements, spanning bulk Mach numbers $M_b=0.3$–$4$, both in the transitional and fully rough regime. We propose a novel definition of roughness Reynolds number which is able to account for the viscosity variations at the roughness crest and should be used to compare rough-wall flows across different Mach numbers. As in the incompressible flow regime, the mean velocity profile shows a downward shift with respect to the baseline smooth wall cases, however, the magnitude of this velocity deficit is largely affected by the Mach number. Compressibility transformations are able to account for this effect, and data show a very good agreement with the incompressible fully rough asymptote, when the relevant roughness Reynolds number is used. Velocity statistics present outer layer similarity with the equivalent smooth wall cases, however, this does not hold for the thermal field, which is substantially affected by the roughness, even in the channel core. We show that this is a direct consequence of the quadratic temperature–velocity relation which is also valid for rough walls. Analysis of the heat transfer shows that the relative drag increase is always larger than the relative heat transfer enhancement, however, increasing the Mach number brings data closer to the Reynolds analogy line due to the rising relevance of the aerodynamic heating.

A set of boundary conditions called the transpiration-resistance model (TRM) is investigated in altering near-wall turbulence. The TRM was proposed by Lacis et al. (J. Fluid Mech., vol. 884, 2020, p. A21) as a means of representing the net effect of surface micro-textures on their overlying bulk flows. It encompasses conventional Navier-slip boundary conditions relating the streamwise and spanwise velocities to their respective shears through the slip lengths $\ell _x$ and $\ell _z$. In addition, it features a transpiration condition accounting for the changes induced in the wall-normal velocity by expressing it in terms of variations of the wall-parallel velocity shears through the transpiration lengths $m_x$ and $m_z$. Greater levels of drag increase occur when more transpiration takes place at the boundary plane, with turbulent transpiration being predominately coupled to the spanwise shear component for canonical near-wall turbulence. The TRM reproduces the effect of a homogeneous and structured roughness up to $k^{+}\approx 18$, encompassing the regime of smooth-wall-like turbulence described using virtual origins (Luchini, 1996 Reducing the turbulent skin friction. In Computational Methods in Applied Sciences’ 96 (Paris, 9–13 Sept. 1996), pp. 465–470. Wiley; Ibrahim et al., J. Fluid Mech., vol. 915, 2021, p. A56) and slightly beyond it. The transpiration factor is defined as the product of the slip and transpiration lengths, i.e. $(m\ell )_{x,z}$. This factor contains the compound effect of the wall-parallel velocity occurring at the boundary plane and increased permeability, both of which lead to the transport of momentum in the wall-normal direction. A linear relation between the transpiration factor and the roughness function is observed for regularly textured surfaces in the transitionally rough regime of turbulence. This shows that such effective flow quantities can be suitable measures for characterizing rough surfaces in this flow regime.

Magnetic buoyancy instability, which is of astrophysical importance, results from the influence of magnetic pressure variations on the density of a fluid in a gravitational field. It is inherently a compressible phenomenon and is, as such, fully described by the equations of compressible magnetohydrodynamics (MHD). For analytical and computational reasons, it is often convenient to study compressible MHD within simpler, asymptotically consistent reduced systems; the two most widely used result from the Boussinesq and anelastic approximations. Within the standard Boussinesq approximation of MHD, leading to the equations of Boussinesq magnetoconvection, magnetic buoyancy is excluded. It can, however, be included by a rescaling of the basic-state variables and by making further assumptions about the perturbation length scales. Within the anelastic approximation, no special measures are taken to incorporate magnetic buoyancy. It is, however, a priori unclear as to whether this neglect is justified, particularly in the light of the Boussinesq results. Our aims here are thus twofold. The first is to formulate the relationship between descriptions of magnetic buoyancy in the compressible, anelastic and Boussinesq systems. In so doing, we show that, under both the anelastic and Boussinesq approximations, magnetic buoyancy can be included either through a combination of a weak field and strong gradient, or, conversely, a strong field and weak gradient. Each has its own asymptotically consistent reduction, with dedicated governing equations. Our second aim is to address, through a linear stability analysis, under which conditions the standard anelastic system provides a faithful representation of magnetic buoyancy instability. For completeness, we also formulate the energy principle of ideal MHD within the anelastic framework, and demonstrate the relation with its fully compressible counterpart.

This work aims to investigate experimentally the effect of the Reynolds number Re, based on the nozzle diameter D, on jet mixing manipulation using an unsteady radial minijet. A novel artificial intelligence (AI) control system has been developed to manipulate the jet over Re = 5800–40 000. The system may optimize simultaneously the control law and a time-independent parameter, which dictate the actuation ON/OFF states and amplitude, respectively. The control parameters include the mass flow rate, excitation frequency and diameter ratios (Cm, fe/f0 and d/D) of the minijet to the main jet as well as the duty cycle (α) of minijet injection. Jet mixing is quantified using Ke and K0, where K is the decay rate of the jet centreline mean velocity, and subscripts e and 0 denote the manipulated and unforced jets, respectively. It has been found that the maximum Ke achievable does not vary with Re. Scaling analysis of the huge volume of experimental data obtained from the AI system reveals that the relationship Ke = g1 (Cm, fe/f0, α, d/D, Re, K0) may be reduced to Ke/K0 = g2 $(\zeta )$, where g1 and g2 are different functions and the scaling factor $\zeta = ({C_m}/\alpha ){(D/d)^{1 - n}}(1/Re){({f_e}/{f_{e,opt}})^m}$, m and 1 − n are the power indices, and subscript opt denotes the value at which Ke is maximum. The scaling law is discussed in detail, along with the physical meanings of the dimensionless parameters Ke/K0, ζ, $({C_m}/\alpha ){(D/d)^{1 - n}}(1/Re)$ and ${({f_e}/{f_{e,opt}})^m}$.

The flow from a supersonic nozzle when operated at off-design conditions exhibits a wide variety of complex flow structures. The prominent ones are the shock reflections inside the jet. The two main types of shock interactions are the regular reflection (RR) and Mach reflection (MR). The prominent characteristic change in the shock pattern when an RR transforms into an MR is the appearance of the Mach stem with a subsonic region downstream of it. The estimation of the Mach stem height gives the size of the subsonic domain and is a direct method to predict the transition from RR to MR or vice versa. The present study is carried out to estimate the size of the Mach stem in an inviscid jet in the overexpanded regime. The analytical methods employed here are the extension of the techniques developed to estimate the Mach stem size in the wedge flows by Li & Ben-Dor (J. Fluid Mech., vol. 341, 1997a, pp. 101–125), Mouton & Hornung (AIAA J., vol. 45, issue 8, 2007, pp. 1977–1987) and Bai & Wu (J. Fluid Mech., vol. 818, 2017, pp. 116–140). The results from the analytical formulation have been compared with the high resolution computational and experimental results. The analytical method reveals that the open jet has a unique, stable MR configuration and forms an upper limit for achievable Mach stem height for the wedge flows. Apart from the estimation of Mach stem height, the growth rates of Mach stem where the RR–MR transition takes place are also calculated and compared with the ones corresponding to wedge flows.

We investigate the submerged collapse of weakly polydisperse, loosely packed cohesive granular columns, as a function of aspect ratio and cohesive force strength, via grain-resolving direct numerical simulations. The cohesive forces act to prevent the detachment of individual particles from the main body of the collapsing column, reduce its front velocity, and yield a shorter and thicker final deposit. All of these effects can be captured accurately across a broad range of parameters by piecewise power-law relationships. The cohesive forces reduce significantly the amount of available potential energy released by the particles. For shallow columns, the particle and fluid kinetic energy decreases for stronger cohesion. For tall columns, on the other hand, moderate cohesive forces increase the maximum particle kinetic energy, since they accelerate the initial free-fall of the upper column section. Only for larger cohesive forces does the peak kinetic energy of the particles decrease. Computational particle tracking indicates that the cohesive forces reduce the mixing of particles within the collapsing column, and it identifies the regions of origin of those particles that travel the farthest. The simulations demonstrate that cohesion promotes aggregation and the formation of aggregates. Furthermore, they provide complete information on the temporally and spatially evolving network of cohesive and direct contact force bonds. While the normal contact forces are aligned primarily in the vertical direction, the cohesive bonds adjust their preferred spatial orientation throughout the collapse. They result in a net macroscopic stress that counteracts deformation and slows the spreading of the advancing particle front.

We rework some of the die-swell singularity analysis for Stokes flow, originally by Ramalingam (Ramalingam, 1994 Fiber spinning and rheology of liquid-crystalline polymers, PhD thesis, Massachusetts Institute of Technology) in appendix A of his PhD thesis, in an attempt to demonstrate that for capillary numbers in the range $(0,\infty )$ the curvature may enter into the normal stress balance on the free surface and lead to separation angles exceeding $180^{\circ }$ and infinite curvature at the separation point. The singular coefficients in the asymptotic solution and the free surface shape in a neighbourhood of the separation point cannot be determined by a local analysis of the Michael type (Michael, Mathematika, vol. 5, 1958, pp. 82–84) but must be found from matching with the solution valid away from the die edge. The numerical method that we use in the truncated die-swell domain is a boundary element method incorporating the singular solution near the separation point. Although there is some variation in the extrudate swell ratios at different capillary numbers reported in the numerical literature, our results for capillary numbers $Ca$ from $1$ to $1000$ are within the range of values published in earlier papers. The computed separation angles at different values of $Ca$ agree well with the range of separation angles to be found in experimental and numerical papers. The separation angle appears to converge to a value different from $180^{\circ }$ as $Ca$ increases, leading us to conclude that the case of zero surface tension ($Ca=\infty$, with corresponding separation angle of $180^{\circ }$), is a singular limit.