A complete understanding of jet dynamics is greatly enabled by the accurate separation of acoustically efficient wavepackets from their higher-energy convecting turbulent counterparts. Momentum potential theory (MPT) has proven highly effective in filtering the desired acoustic component irrespective of operating conditions or nozzle complexity. However, MPT is a data-intensive method predicated on the knowledge of fluctuation quantities in the entire flow field; as such, it has to date been applied only to numerically obtained data. This work develops an approach to extend its application to extract coherent wavepacket data from high-speed schlieren images. Pixel intensities from the schlieren image are mapped to a scaled surrogate for the line-of-sight integrated density gradient. The linear relation between the irrotational scalar MPT potential and time derivatives of density fluctuations is then exploited to perform the filtering. The effectiveness of the procedure is demonstrated using experimental as well as numerical schlieren images representing a wide range of imperfectly expanded free and impinging jet configurations. When combined with spectral proper orthogonal decomposition (SPOD), the method yields modes that accurately capture (i) the Mach wave radiation from a military-style jet, (ii) the mode shapes of the feedback tones in an impinging jet and (iii) the screech signature in twin rectangular jets, without recourse to user adjusted parameters. This technique can greatly enhance the use of high-speed diagnostics for real-time monitoring of the near-field acoustic content for potential feedback control. Additionally, the general nature of the approach allows a straightforward application to other flows, such as cavity and airfoil flow-acoustic interactions.

The non-dimensional energy of starting vortex rings typically converges to values around 0.33 when they are created by a piston-cylinder or a bluff body translating at a constant speed. To explore the limits of the universality of this value and to analyse the variations that occur outside of those limits, we present an alternative approach to the slug-flow model to predict the non-dimensional energy of a vortex ring. Our approach is based on the self-similar vortex sheet roll-up described by Pullin (J. Fluid Mech., vol. 88, 1978, pp. 401–430). We derive the vorticity distribution for the vortex core resulting from a spiralling shear layer roll-up and compute the associated non-dimensional energy. To demonstrate the validity of our model for vortex rings generated through circular nozzles and in the wake of disks, we consider different velocity profiles of the vortex generator that follow a power law with a variable time exponent $m$. Higher values of $m$ indicate a more uniform vorticity distribution. For a constant velocity ($m=0$), our model yields a non-dimensional energy of ${{E}^{{*}}}=0.33$. For a constant acceleration ($m=1$), we find ${{E}^{{*}}}=0.19$. The limiting value $m \rightarrow \infty$ corresponds to a uniform vorticity distribution and leads to ${{E}^{{*}}}=0.16$, which is close to values found in the literature for Hill's spherical vortex. The radial diffusion of the vorticity within the vortex core results in the decrease of the non-dimensional energy. For a constant velocity, we obtain realistic vorticity distributions by radially diffusing the vorticity distribution of the Pullin spiral and predict a decrease of the non-dimensional energy from 0.33 to 0.28, in accordance with experimental results. Our proposed model offers a practical alternative to the existing slug flow model to predict the minimum non-dimensional energy of a vortex ring. The model is applicable to piston-generated and wake vortex rings and only requires the kinematics of the vortex generator as input.

Enormous efforts have been devoted to the prediction and control of turbulent wall flows. A primary consideration here is the Reynolds number scaling problem in which non-dimensional representations are sought that render the normalized variables of interest unchanged for varying Reynolds number. Relative to this objective and in contrast to the mean velocity, there remains a considerable lack of clarity associated with the apparent failure of inner normalization (i.e. using the friction velocity and kinematic viscosity) when applied to the statistical profiles of fluctuating quantities in the near-wall region. In their present work Chen & Sreenivasan (J. Fluid Mech., vol. 933, 2022, A20) generalize their earlier effort, Chen & Sreenivasan (J. Fluid Mech., vol. 908, 2021, R3), and present a rational framework for characterizing and describing the evolution of turbulence quantities that either attain a near-wall peak or have non-zero wall values. Their analysis enjoys considerable empirical support. Physically, the asymptotic boundedness of the inner-normalized dissipation is used to reason that there is a limiting state of near-wall turbulence at asymptotically large Reynolds numbers. The law of bounded dissipation arguments put forth by Chen and Sreenivasan prescribe the recovery of inner scaling and suggest new possibilities regarding the physics of how wall turbulence matures to its asymptotic state.

Our understanding of turbulent boundary layer scaling and structure has advanced greatly in the past 20 to 30 years. On the computational side, direct numerical simulations and large-eddy simulations have made extraordinary contributions as numerical methods and computational resources have advanced, while on the experimental side major advances in instrumentation have made available new imaging and quantitative techniques that provide unprecedented accuracy and detail. Here, I illustrate how the development of such experimental methods have aided our progress by reference to some particular topics related to the structure of turbulent boundary layers: the power law scaling of the mean velocity and its relationship to the mesolayer; the scaling of the outer layer with regard to the log law in turbulence; the development of the outer peak; and the scaling of the turbulent stresses in the near-wall region, with an emphasis on the streamwise component.

The objective of this work is to provide physical insight into the mechanisms governing flame–turbulence interactions and explore the impact of the ubiquitous Darrieus–Landau instability on the propagation. It is based on the hydrodynamic theory of premixed flames that considers the flame thickness much smaller than all other fluidynamical length scales. In this asymptotic limit, the flame is thus confined to a surface whilst the diffusion and reaction processes occurring inside the flame zone are accounted for by two parameters: the unburned-to-burned density ratio and the Markstein length. The robust model, which is free of phenomenology and turbulence modelling assumptions, makes transparent the mutual interactions between the flame and the fluid flow, and permits examining trends in flame and flow characteristics while varying the turbulence intensity and mixture properties. It is used in this study to examine the morphological changes of the flame surface that result from the intertwined effects of the turbulence and instability, as demonstrated by the local displacement and curvature of the flame front, the extent of wrinkling and folding of the flame surface, and the overall flame brush thickness. It also provides a direct evaluation of the turbulent flame speed and its dependence on the mean flame curvature and on the hydrodynamic strain that it experiences. Also discussed are the effects of the flame on the flow by examining the various mechanisms of enstrophy and scalar gradient production/destruction, the degree of anisotropy created in the burned gas, and the restructuring of the vortical motion beyond the flame.

The binary scaling law is a classical similarity law used in analysing hypersonic flow fields. The objective of this study is to investigate the applicability of the binary scaling law in thermochemical non-equilibrium airflow. Dimensional analysis of vibrational and electron–electronic energy conservation equations was employed to explore the theoretical reasons for the failure of the binary scaling law. Numerical simulation based on a multi-temperature model (translational–rotational temperature T, electron–electronic excitation temperature ${T_e}$ and the vibrational temperatures of ${\textrm{O}_2}$ and ${\textrm{N}_2}$, $\; {T_{{v_{{\textrm{O}_2}}}}}$and ${T_{{v_{{\textrm{N}_2}}}}}$) with two chemical models (the Gupta model and the Park model) was adopted to study the accuracy of the binary scaling law for electron distribution at high altitude with extremely high Mach number. The results of theoretical analysis indicate that the three-body collision reactions and the translation–electron energy exchange from collisions between electrons and ions, ${Q_{t - e\_ions}}$, can cause the failure of the binary scaling law. The results of numerical simulation show that the electron-impact ionization reactions are the main reasons for the invalidation of the binary scaling law for electron distribution at high altitude with high Mach number. With an increase of free-stream Mach number, the negative effect on the binary scaling law caused by ${Q_{t - e\_ions}}$ cannot be ignored.

Dispersion and mixing of inertial point particles in the unsteady and three-dimensional wake of a circular cylinder at $Re=200$ are investigated via one-way coupled simulations. The presence of streamwise-oriented vortical braids originating from the mode A instability in the transition regime has a profound impact on the particle dynamics and preferential concentration in the near wake. Particles trapped between the Kármán rollers and the streamwise braids form an inner layer of densely concentrated particles, while discrete particle clumps on the otherwise thin ribbon-like clusters between two consecutive Kármán rollers are another manifestation of the streamwise braids. The effect of particle inertia on the size of clusters and voids ascribed to centrifugal ejection is examined by volume-averaged Voronoï analysis. A distinct dependence on Stokes number ($Sk$) is seen at the cluster scale, whereas the void scale exhibits self-similarity. New physics-based threshold values of clusters and voids are distinctly different from the probability-distribution-based threshold at cluster scale. Increasing inertia is found to suppress particle acceleration more than deceleration. The particle velocity is further suppressed by the presence of the streamwise vortical braids. The effects of particle inertia vary non-monotonically in $Sk$ with the strongest effect at $Sk=1$ when most particles tend to reside in high-strain/low-vorticity regions.

The dynamics of spherical laser-induced cavitation bubbles in water is investigated by plasma photography, time-resolved shadowgraphs and sensitive single-shot probe beam scattering that portrays the transition from initial nonlinear to late linear oscillations. The frequency of late oscillations yields the bubble's gas content. Numerical simulations with an extended Gilmore model using plasma size as input and oscillation times as fit parameter provide insights into experimentally not accessible bubble parameters and shock wave emission. Model extensions include a term covering the initial shock-driven acceleration of the bubble wall, an automated method determining shock front position and pressure decay and a complete energy balance for the partitioning of absorbed laser energy into vaporization, bubble and shock wave energy and dissipation through viscosity and condensation. These tools are used for analysing a scattering signal covering 102 oscillation cycles from a bubble with 36 μm maximum radius produced by a plasma with 1550 K average temperature. Predicted bubble wall velocities during expansion agree well with experimental data. Upon first collapse, most energy was stored in the compressed liquid around the bubble and radiated away acoustically. The collapsed bubble contained more vapour than gas and had a pressure of 13.5 GPa. The decay of the rebound shock wave pressure with radius r was initially $\mathrm{\ \propto }{r^{ - 1.8}}$, and energy dissipation at the shock front heated the liquid near the bubble wall to temperatures above the superheat limit. The shock-induced temperature rise reduces damping during late bubble oscillations. Damping in first collapse increases significantly for small bubbles with less than 10 μm radius.

This study addresses the question of whether a thin, relatively heavy solid body with a smooth under-surface can skim on a shallow layer of liquid (for example water), i.e. impact on the layer and rebound from it. The body impacts obliquely onto the liquid layer with the trailing edge of the underbody making the initial contact. The wetted region then spreads along the underbody and eventually either retracts, generating a rebound, or continues to the leading edge of the body and possibly leads to the body sinking. The present inviscid study involves numerical investigations for increased mass ($M$, in scaled terms) and moment of inertia ($I$, proportional to the mass) together with an asymptotic analysis of the influential parameters and dynamics at different stages of the skimming motion. Comparisons between the asymptotic analysis and numerical results show close agreement as the body mass becomes large. A major finding is that, for a given impact angle of the underbody relative to the liquid surface, only a narrow band of initial conditions is found to allow the heavy-body skim to take place. This band includes reduced impact velocities of the body vertically and rotationally, both decreasing like $M^{-2/3}$, while the associated total time of the skim from entry to exit is found to increase like $M^{1/3}$ typically. Increased mass thereby enhances the super-elastic behaviour of the skim.

Interactions between the boundary layer and two successive incident shock waves (ISWs) often occur in the supersonic mixed-compression inlets. However, the flow mechanism involved in such interactions has been studied rarely. In this study, we investigate experimentally and analytically the turbulent boundary layer separation flow induced by the single ISW and dual ISWs at the identical total deflection angles in a Mach 2.73 flow. Schlieren photography, wall pressure measurement and surface oil-flow visualisation are employed to diagnose the flow field. Experiments with the impingement points of the two ISWs intersecting on the bottom wall exhibit a separated flow with a triangle-like separation bubble, namely the first kind of dual-ISW/turbulent boundary layer interaction (ISWTBLI). Comparative studies show that various flow features of this kind of dual-ISWTBLI, including the extent of the separation region, pressure distribution and surface-flow topological structures, are nearly identical to those of the single-ISWTBLI with an identical total deflection angle. As the distance between the two ISWs increases, the shape of the separation region in the dual-ISWTBLI changes from triangle-like to quadrilateral-like, and the height of the separation region decreases accordingly, forming the second kind of dual-ISWTBLI. Furthermore, an inviscid model is developed for the dual-ISWTBLI to describe the complex shock wave system and elucidate the cause of a quadrilateral-like separation bubble in the second kind of dual-ISWTBLI. Moreover, based on a previous work by Souverein et al. (J. Fluid Mech., vol. 714, 2013, pp. 505–535) on the single-ISWTBLI, a modified scaling method is established for the first kind of dual-ISWTBLI.

When a fluid stream in a conduit splits in order to pass around an obstruction, it is possible that one branch will be critically controlled while the other remains not so. This is apparently the situation in Pacific Ocean abyssal circulation, where most of the northward flow of Antarctic bottom water passes through the Samoan Passage, where it is hydraulically controlled, while the remainder is diverted around the Manihiki Plateau and is not controlled. These observations raise a number of questions concerning the dynamics necessary to support such a regime in the steady state, the nature of upstream influence and the usefulness of rotating hydraulic theory to predict the partitioning of volume transport between the two paths, which assumes the controlled branch is inviscid. Through the use of a theory for constant potential vorticity flow and accompanying numerical model, we show that a steady-state regime similar to what is observed is dynamically possible provided that sufficient bottom friction is present in the uncontrolled branch. In this case, the upstream influence that typically exists for rotating channel flow is transformed into influence into how the flow is partitioned. As a result, the partitioning of volume flux can still be reasonably well predicted with an inviscid theory that exploits the lack of upstream influence.

In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. For instance, one may choose to consider a fluid with uniform dynamic viscosity, but, then, compressible effects will generate a density gradient and consequently the kinematic viscosity will not be uniform. In the present work, we consider a very peculiar equation of state, whereby entropy is solely dependent on density, so that a nearly isentropic fluid domain is nearly isochoric. Within this class of equations of state, there is a thermal adiabatic gradient and a key property of compressible convection is still present, namely its capacity to viscously dissipate a large fraction of the thermal energy involved, of the order of the well-named dissipation number. In the anelastic approximation, under the assumption of an infinite Prandtl number, the number of governing parameters can be brought down to two, the Rayleigh number and the dissipation number. This framework is proposed as a playground for compressible convection, an opportunity to extend the vast corpus of theoretical analyses on the Oberbeck–Boussinesq equations regarding stability, bifurcations or the determination of upper bounds for the turbulent heat transfer. Here, in a two-dimensional geometry, we concentrate on the structure of numerical solutions. For all Rayleigh numbers, a change in the vertical temperature profile is observed in the range of dissipation number between $0$ and less than $0.4$, associated with the weakening of ascending plumes. For larger dissipation numbers, the heat flux dependence on this number is found to be well predicted by Malkus's model of critical layers. For dissipation numbers of order unity, and large Rayleigh numbers, dissipation becomes related to the entropy heat flux at each depth, so that the vertical dissipation profile can be predicted, and so does the total ratio of dissipation to convective heat flux.

The motion of the three-phase contact line between two immiscible fluids and a solid surface arises in a variety of wetting phenomena and technological applications. One challenge in continuum theory is the effective representation of molecular motion close to the contact line. Here, we characterize the molecular processes of the moving contact line to assess the accuracy of two different continuum two-phase models. Specifically, molecular dynamics simulations of a two-dimensional droplet between two moving plates are used to create reference data for different capillary numbers and contact angles. We use a simple-point-charge/extended water model. This model provides a very small slip and a more realistic representation of the molecular physics than Lennard-Jones models. The Cahn–Hilliard phase-field model and the volume-of-fluid model are calibrated against the drop displacement from molecular dynamics reference data. It is shown that the calibrated continuum models can accurately capture droplet displacement and droplet break-up for different capillary numbers and contact angles. However, we also observe differences between continuum and atomistic simulations in describing the transient and unsteady droplet behaviour, in particular, close to dynamical wetting transitions. The molecular dynamics of the sheared droplet provide insight into the line friction experienced by the advancing and receding contact lines. The presented results will serve as a stepping stone towards developing accurate continuum models for nanoscale hydrodynamics.

The recently discovered centre-mode instability of rectilinear viscoelastic shear flow (Garg et al., Phys. Rev. Lett., vol. 121, 2018, 024502) has offered an explanation for the origin of elasto-inertial turbulence that occurs at lower Weissenberg numbers ($Wi$). In support of this, we show using weakly nonlinear analysis that the subcriticality found in Page et al. (Phys. Rev. Lett., vol. 125, 2020, 154501) is generic across the neutral curve with the instability becoming supercritical only at low Reynolds numbers ($Re$) and high $Wi$. We demonstrate that the instability can be viewed as purely elastic in origin, even for $Re=O(10^3)$, rather than ‘elasto-inertial’, as the underlying shear does not feed the kinetic energy of the instability. It is also found that the introduction of a realistic maximum polymer extension length, $L_{max}$, in the FENE-P model moves the neutral curve closer to the inertialess $Re=0$ limit at a fixed ratio of solvent-to-solution viscosities, $\beta$. At $Re=0$ and in the dilute limit ($\beta \rightarrow 1$) with $L_{max} =O(100)$, the linear instability can be brought down to more physically relevant $Wi\gtrsim 110$ at $\beta =0.98$, compared with the threshold $Wi=O(10^3)$ at $\beta =0.994$ reported recently by Khalid et al. (Phys. Rev. Lett., vol. 127, 2021, 134502) for an Oldroyd-B fluid. Again, the instability is subcritical, implying that inertialess rectilinear viscoelastic shear flow is nonlinearly unstable – i.e. unstable to finite-amplitude disturbances – for even lower $Wi$.

Breaking spatial symmetry is an essential requirement for phoretic active particles to swim at low Reynolds number. This fundamental prerequisite for swimming at the micro scale is fulfilled either by chemical patterning of the surface of active particles or alternatively by exploiting geometrical asymmetries to induce chemical gradients and achieve self-propulsion. In the present paper, a far-field analytical model is employed to quantify the leading-order contribution to the induced phoretic velocity of a chemically homogeneous isotropic active colloid near a finite-sized disk of circular shape resting on an interface separating two immiscible viscous incompressible Newtonian fluids. To this aim, the solution of the phoretic problem is formulated as a mixed-boundary-value problem that is subsequently transformed into a system of dual integral equations on the inner and outer domains. Depending on the ratio of different involved viscosities and solute solubilities, the sign of phoretic mobility and chemical activity, as well as the ratio of particle–interface distance to the radius of the disk, the isotropic active particle is found to be repelled from the interface, be attracted to it, or reach a stable hovering state and remain immobile near the interface. Our results may prove useful in controlling and guiding the motion of self-propelled phoretic active particles near aqueous interfaces.

Unsteadiness occurs in the motion of swimmers while they start from rest or escape from a predator, or attack prey. In this paper, we study the behaviour of an unsteady chiral swimmer, with a prescribed surface slip velocity, in the low-Reynolds-number regime, and its response to an external chemical gradient. In the first part, by solving the unsteady Stokes equation, we calculate the migration velocity ($\boldsymbol {U}$), rotation rate ($\boldsymbol {\varOmega }$) and flow field of the unsteady swimmer in a closed form. We compare these results with some previously known results in appropriate limits. In the second part, we investigate the response of the unsteady chiral swimmer to an external chemical gradient, which can influence the swimmer's surface slip velocity. Consequently, the swimmer either steers towards the source of the chemical gradient or moves away from it, depending on the strengths of $\boldsymbol {U}$ and $\boldsymbol {\varOmega }$, and the corresponding angle ($\chi$) between them. Interestingly, the swimmer swims in a closed orbit in the vicinity of the chemical target, depending on the strengths of $\boldsymbol {\varOmega }$ and $\chi$. We present a complete state diagram representing the successful, unsuccessful and orbital states for various strengths of $\boldsymbol {\varOmega }$ and $\chi$. This study is useful to understand the unsteady propulsion of ciliated microorganisms and their response to external gradients.

Granular flow in a silo demonstrates multiple non-local rheological phenomena due to the finite size of grains. We solve the non-local granular fluidity continuum model in quasi-two-dimensional silo geometries and evaluate its ability to predict these non-local effects, including flow spreading and, importantly, clogging (arrest) when the opening is small enough. The model is augmented to include a free-separation criterion and is implemented numerically with an extension of the trans-phase granular flow solver described in Dunatunga & Kamrin (J. Fluid Mech., vol. 779, 2015, pp. 483–513), to produce full-field solutions. The implementation is validated against analytical results of the model in the inclined chute geometry, such as the solution for the critical thickness for flow arrest, and the velocity profile as a function of layer height. We then implement the model in the silo geometry and vary the apparent grain size. The model predicts a clogging criterion when the opening competes with the scale of the mean grain size, which agrees with previous experimental studies. For larger openings, the flow within the silo obtains a diffusive characteristic whose spread depends on the model's non-local amplitude and the mean grain size. The numerical tests are controlled for grid effects and a comparison study of coarse vs refined numerical simulations shows agreement in the pressure field, the shape of the arch in a clogged silo configuration and the velocity field in a flowing configuration.

Interfacial waves between two superimposed dielectric fluid layers under a horizontal electric field are investigated from asymptotic and numerical aspects. The fluid is taken to be inviscid, incompressible and non-conducting in each layer. The competing forces resulting from gravity, surface tension and electric field are all considered. A systematic procedure is proposed to derive model equations of multiple scales in various possible limits from the electrified Euler equations in the framework of the Zakharov–Craig–Sulem formulation. Based on thorough analyses of the Dirichlet–Neumann operators in the long-wave approximation, classic weakly nonlinear models – including the Boussinesq-type system, the Korteweg–de Vries (KdV) equation and its variants, and the Benjamin-type equation – are obtained under different scaling assumptions. In addition, strongly nonlinear models (without the smallness assumption on the wave amplitude) in the Benjamin and Barannyk–Papageorgiou–Petropoulos regimes are derived. In these models, the electric effects are shown to produce dispersive regularisations of long and short waves. A modified boundary integral equation method is developed to compute solitary waves in the original electrified Euler equations. Through comparisons with solitary-wave solutions in the Euler equations, it is found that in various asymptotic regimes, weakly nonlinear models are in overall good agreement when wave amplitudes are small. In contrast, the range of validity of the strongly nonlinear model is much broader. It is shown that the horizontal electric field plays a significant role in the physical system: it expands the range of parameters for the existence of progressive waves, changes the qualitative characteristics of solitary waves and leads to a new type of solitary wave, namely the KdV–wavepacket mixed type.

A numerical investigation of turbulent flows in straight pipes with a cross-section in the form of a circular sector at different values of the apex angle ${\alpha }$ is carried out. Main attention is paid to the cases ${\alpha }>{\rm \pi}$ when the cross-section boundary contains a convex external corner. An analytical solution to the problem of laminar flow in the geometry under consideration is given. The law of resistance is determined, and velocity distributions over the pipe cross-section are obtained. The singularity of wall shear stress $\tau _w\sim r^{{\rm \pi} /{\alpha }-1}$ at ${\alpha }>{\rm \pi}$ is shown which persists in turbulent flows as well. Turbulent flows are simulated at $Re=2000$ and four apex-angle values ${\alpha }=5{\rm \pi} /4$, $3{\rm \pi} /2$, $7{\rm \pi} /4$ and $2{\rm \pi}$, as well as at a larger $Re=4000$ and ${\alpha }=3{\rm \pi} /2$. The characteristic features of the mean-velocity distributions are outlined, and their relationship with secondary flows is shown. The velocity of the secondary flow in the vicinity of the external corner reaches the value $6.3\,\%$ of the bulk flow velocity at the maximum ${\alpha }=2{\rm \pi}$. A characteristic feature of the considered flows is the presence of intense transverse velocity fluctuations in the region above the apex corner. It is hypothesized that the cause of these fluctuations may be the linear instability of the mean flow field. The studies of linear stability confirm this hypothesis. Considerable attention is paid to the study of secondary flows in the vicinity of the external corner. In general, the formation of these flows fits into the scheme proposed earlier (Nikitin, J. Fluid Mech., vol. 917, 2021, A24; Nikitin et al., Fluid Dyn., vol. 56, issue 4, 2021, pp. 513–538), according to which the main mechanism is the centrifugal force arising from the fluctuating flow over the corner in the transverse plane. It is shown that the shape of secondary flows is reproduced to a certain extent by the vortical part of the Reynolds-stress force field. The latter may be found from the Helmholtz decomposition. The features of the mean pressure distribution associated with the secondary flow and with the presence of a region of concentrated fluctuations above the external corner are explained.