Radko’s recent article (J. Fluid Mech., vol. 805, 2016, pp. 147–170) entitled Thermohaline layering in dynamically and diffusively stable shear flows, is slated to become a seminal reference in the field of fluid dynamics. It proposes an elegant solution to the long-standing question of why thermohaline staircases form in the high-latitude oceans. Equally importantly, it provides a rare and interesting example of how two physical processes that are both strongly stable when considered individually, can trigger a linear instability when they interact.

We present a novel analytical solution for hydro-acoustic waves in a weakly compressible fluid flow over a slowly varying bottom. Application of a multiple-scale perturbation technique and matched asymptotic analysis leads to a uniform analytical solution of the depth-averaged governing equations in three dimensions. We show that the slow depth variation has a leading-order effect on the evolution of the normal mode amplitude and direction. This dynamics is much richer than the two-dimensional limit analysed in previous studies. For tsunamigenic disturbances, we show that the hydro-acoustic wave field is made up by longshore trapped and offshore propagating components, which were not explicated in previous work. For a plane beach, we find an exact analytical solution of the model equation in terms of integrals of Bessel functions. Our model offers a physical insight into the evolution of hydro-acoustic waves of interest for the design of tsunami early warning systems.

When suspended in a liquid solution, chemically active colloids may self-propel due to an asymmetry in either particle shape or the interfacial distribution of solute absorption. We here consider a chemically homogeneous spherical particle which undergoes self-diffusiophoresis due to the presence of nearby inert wall. In particular, we focus upon the near-contact limit where it was recently observed (Yariv, Phys. Rev. Fluids, vol. 1 (3), 2016, 032101) that the solute-concentration profile within the narrow gap separating the particle and the wall cannot be uniquely determined by a gap-scale analysis. We here revisit this near-contact limit using matched asymptotic expansions, the inner region being the gap domain and the outer region being on the particle scale. Asymptotic matching with the Hankel-transform representation of the outer distribution of solute concentration serves to determine both the scaling and magnitude of the corresponding inner profile. The ensuing gap-scale pressure field, set by a lubrication mechanism, gives rise to an anomalous particle–wall interaction, scaling as an irrational power of the gap clearance.

In this communication, we offer a theoretical explanation for the results of recent experiments that examine the stress response of a dilute suspension of bacteria (wild-type E. coli) subjected to step changes in the shear rate (Lopez et al., Phys. Rev. Lett., vol. 115, 2015, 028301). The observations include a regime of negative apparent shear viscosities. We start from a kinetic equation that describes the evolution of the single-bacterium orientation probability density under the competing effects of an induced anisotropy by the imposed shear, and a return to isotropy on account of stochastic relaxation mechanisms (run-and-tumble dynamics and rotary diffusion). We then obtain analytical predictions for the stress response, at leading order, of a dilute bacterial suspension subject to a weak but arbitrary time-dependent shear rate profile. While the predicted responses for a step-shear compare well with the experiments for typical choices of the microscopic parameters that characterize the swimming motion of a single bacterium, use of actual experimental values leads to significant discrepancies. The incorporation of a distribution of run times leads to a better agreement with observations.

This paper continues a series of works developing a model for a high-speed boiling flow capable of describing different fluxes with no change in the model coefficients. Refining the interfacial area transport equation in partial derivatives, we test the ability of the model to describe phenomena that cannot be simulated by models that average the interfacial interaction. In the previous version, the possibility for bubble fragmentation was considered, which permitted us to reproduce an explosive boiling in rarefaction shocks moving at a speed of ${\sim}10~\text{m}~\text{s}^{-1}$ fixed in experiments on hot water decompression. The shocks were shown to be caused by a chain bubble fragmentation leading to a sharp increase in the interphase area (Ivashnyov et al., J. Fluid Mech., vol. 413, 2000, pp. 149–180). With no change in the free parameters (the initial number of boiling centres in the flow bulk and the critical Weber number) chosen for a tube decompression, the model gave close predictions for critical flows in long nozzles, $L/D\sim 100$. The formation of a boiling shock in the nozzle was shown to be the reason for the onset of autovibrated regimes (Ivashnyov & Ivashneva, J. Fluid Mech., vol. 710, 2012, pp. 72–101). However, the previous model does not simulate the phenomenon of a vapour explosion at a primary stage of a hot water decompression, when the first rarefaction wave is followed by an extended, 1 m width, several MPa amplitude compression wave in which the pressure reaches a plateau below a saturation value. The model proposed assumes initial boiling centre origination at the channel walls. Due to overflowing, the wall bubbles break up, with their fragments passing into the flow. On growing up, the flow bubbles can break up in their turn. It is shown that an extended compression wave is caused by the fragmentation of wall bubbles, which leads to the increase in the interphase area, boiling intensification and the pressure rise. The pressure reaches a plateau before a saturation state is reached due to flow momentum loss accelerating the fragments of wall bubbles. The phenomenon of pressure ‘oscillation’ fixed in some experimental oscillograms when the pressure in the compression wave increases up to a saturation pressure and then drops to the plateau value has been explained as well. The ‘illposedness’ defect of the generally accepted model for two-phase two-velocity flow with a compressible carrying phase, which lies in its complex characteristics, has been rectified. The calculations of a stationary countercurrent liquid-particle flow in a diffuser with the improved hyperbolic model predicts a critical regime with a maximal liquid mass flux, while the old non-hyperbolic model simulates the supercritical regimes with ‘numerical instabilities’. Calculations of a transient upward flow of particles have shown the formation of a superslow ‘creeping’ shock wave of particles compacting.

An analytical theory has been developed for properties of a steady, axisymmetric liquid–gas capillary bridge that is present between two identical, perfectly wettable, rigid spheres. In this theory the meridional profile of the capillary bridge surface is represented by a part of an ellipse. Parameters in this geometrical description are determined from the boundary conditions at the three-phase contact circle at the sphere and at the neck (i.e. in the middle between the two spheres) and by the condition that the mean curvature be equal at the three-phase contact circle and at the neck. Thus, the current theory takes into account properties of the governing Young–Laplace equation, contrary to the often-used toroidal approximation. Expressions have been developed analytically that give the geometrical parameters of the elliptical meridional profile as a function of the capillary bridge volume and the separation between the spheres. A rupture criterion has been obtained analytically that provides the maximum separation between the spheres as a function of the capillary bridge volume. This rupture criterion agrees well with a rupture criterion from the literature that is based on many numerical solutions of the Young–Laplace equation. An expression has been formulated analytically for the capillary force as a function of the capillary bridge volume and the separation between the spheres. The theoretical predictions for the capillary force agree well with the capillary forces obtained from the numerical solutions of the Young–Laplace equation and with those according to a comprehensive fit from the literature (that is based on many numerical solutions of the Young–Laplace equation), especially for smaller capillary bridge volumes.

This paper describes the three-dimensional destabilization characteristics of an annular liquid sheet when subjected to the combined action of Rayleigh–Taylor (RT) and Kelvin–Helmholtz (KH) instability mechanisms. The stability characteristics are studied using temporal linear stability analysis and by assuming that the fluids are incompressible, immiscible and inviscid. Surface tension is also taken into account at both the interfaces. Linearized equations governing the growth of instability amplitude have been derived. These equations involve time-varying coefficients and have been analysed using two approaches – direct numerical time integration and frozen-flow approximation. From the direct numerical time integration, we show that the time-varying coefficients evolve on a slow time scale in comparison with the amplitude growth. Therefore, we justify the use of the frozen-flow approximation and derive a closed-form dispersion relation from the appropriate governing equations and boundary conditions. The effect of flow conditions and fluid properties is investigated by introducing dimensionless numbers such as Bond number ($Bo$), inner and outer Weber numbers ($We_{i}$, $We_{o}$) and inner and outer density ratios ($Q_{i}$, $Q_{o}$). We show that four instability modes are possible – Taylor, sinuous, flute and helical. It is observed that the choice of instability mode is influenced by a combination of both $Bo$ as well as $We_{i}$ and $We_{o}$. However, the instability length scale calculated from the most unstable wavenumbers is primarily a function of $Bo$. We show a regime map in the $Bo,We_{i},We_{o}$ parameter space to identify regions where the system is susceptible to three-dimensional helical modes. Finally, we show an optimal partitioning of a given total energy ($\unicode[STIX]{x1D701}$) into acceleration-induced and shear-induced instability mechanisms in order to achieve a minimum instability length scale (${\mathcal{L}}_{m}^{\ast }$). We show that it is beneficial to introduce at least 90 % of the total energy into acceleration induced RT instability mechanism. In addition, we show that when the RT mechanism is invoked to destabilize an annular liquid sheet, ${\mathcal{L}}_{m}^{\ast }\sim \unicode[STIX]{x1D701}^{-3/5}$.

Trapped waves can exist in the presence of bodies in open water, and also in channels of finite width. Various examples are found for bodies that support trapped waves in channels, including floating and submerged bodies and bottom-mounted cylinders. Different types of trapping are considered where the body is fixed or free to move in response to the oscillatory pressure. In some cases both types are supported by the same body. In most cases for fixed bodies the fluid motion is antisymmetric about the centreline of the channel, but special body shapes exist where the trapped mode is asymmetric. For free bodies the trapping modes and body motions are symmetric about the centreline if the body is floating or antisymmetric if it is submerged.

We explore the two-dimensional flow around a circular cylinder with the aim of elucidating the changes in the topology of the vorticity field that lead to the formation of the Kármán vortex street. Specifically, we analyse the formation and disappearance of extremal points of vorticity, which we consider to be feature points for vortices. The basic vortex creation mechanism is shown to be a topological cusp bifurcation in the vorticity field, where a saddle and an extremum of the vorticity are created simultaneously. We demonstrate that vortices are first created approximately 100 diameters downstream of the cylinder, at a Reynolds number, $Re_{K}$, which is slightly larger than the critical Reynolds number, $Re_{crit}\approx 46$, at which the flow becomes time periodic. For $Re$ slightly above $Re_{K}$, the newly created vortices disappear again a short distance further downstream. As $Re$ is further increased, the points of creation and disappearance move rapidly upstream and downstream, respectively, and the Kármán vortex street persists over increasingly large streamwise distances.

To date, the understanding of the role buoyancy plays in the entrainment process in unstable configurations such as turbulent plumes remains incomplete. Towards addressing this question, we set up a flow in which a plume evolves in time instead of space. We demonstrate that the temporal problem is equivalent to a spatial plume in a strong coflow and address in detail how the temporal plume can be realized via direct numerical simulation. Using numerical data of plume simulations up to $Re_{\unicode[STIX]{x1D706}}\approx 100$, we show that the entrainment coefficient can be determined consistently using a global entrainment analysis in an integral framework as well as via a local approach. The latter is based on a study of the local propagation of the turbulent/non-turbulent interface relative to the fluid. Locally, this process is dominated by small-scale diffusion which is amplified by interface convolutions such that the total entrained flux is independent of viscosity. Further, we identify a direct buoyancy contribution to entrainment by baroclinic torque, which accounts for 8 %–12 % of the entrained flux locally, comparable to the 15 % buoyancy contribution at the integral level. It appears that the baroclinic torque is a mechanism that might explain higher values of the entrainment coefficient in spatial plumes compared with jets.

The wake of polygonal cylinders with side number $N=2\sim \infty$ is systematically studied based on fluid force, hot-wire, particle image velocimetry and flow visualisation measurements. Each cylinder is examined for two orientations, with a flat surface or a corner leading and facing normally to the free stream. The Reynolds number $Re$ is $1.0\times 10^{4}\sim 1.0\times 10^{5}$, based on the longitudinally projected cylinder width. The time-averaged drag coefficient $C_{D}$ and fluctuating lift coefficient on these cylinders are documented, along with the characteristic properties including the Strouhal number $St$, flow separation point and angle $\unicode[STIX]{x1D703}_{s}$, wake width and critical Reynolds number $Re_{c}$ at which the transition from laminar to turbulent flow occurs. It is found that once $N$ exceeds 12, $Re_{c}$ depends on the difference between the inner diameter (tangent to the faces) and the outer diameter (connecting corners) of a polygon, the relationship being approximately given by the dependence of $Re_{c}$ on the height of the roughness elements for a circular cylinder. It is further found that $C_{D}$ versus $\unicode[STIX]{x1D709}$ or $St$ versus $\unicode[STIX]{x1D709}$ for all the tested cases collapse onto a single curve, where the angle $\unicode[STIX]{x1D709}$ is the corrected $\unicode[STIX]{x1D703}_{s}$ associated with the laterally widest point of the polygon and the separation point. Finally, the empirical correlation between $C_{D}$ and $St$ is discussed.

Direct numerical simulations (DNS) are performed to analyse the global transport properties of turbulent Taylor–Couette flow with inner rough wall up to Taylor number$Ta=10^{10}$. The dimensionless torque $Nu_{\unicode[STIX]{x1D714}}$ shows an effective scaling of $Nu_{\unicode[STIX]{x1D714}}\propto Ta^{0.42\pm 0.01}$, which is steeper than the ultimate regime effective scaling $Nu_{\unicode[STIX]{x1D714}}\propto Ta^{0.38}$ seen for smooth inner and outer walls. It is found that at the inner rough wall, the dominant contribution to the torque comes from the pressure forces on the radial faces of the rough elements; while viscous shear stresses on the rough surfaces contribute little to $Nu_{\unicode[STIX]{x1D714}}$. Thus, the log layer close to the rough wall depends on the roughness length scale, rather than on the viscous length scale. We then separate the torque contributed from the smooth inner wall and the rough outer wall. It is found that the smooth wall torque scaling follows $Nu_{s}\propto Ta_{s}^{0.38\pm 0.01}$, in excellent agreement with the case where both walls are smooth. In contrast, the rough wall torque scaling follows $Nu_{r}\propto Ta_{r}^{0.47\pm 0.03}$, very close to the pure ultimate regime scaling $Nu_{\unicode[STIX]{x1D714}}\propto Ta^{1/2}$. The energy dissipation rate at the wall of an inner rough cylinder decreases significantly as a consequence of the wall shear stress reduction caused by the flow separation at the rough elements. On the other hand, the latter shed vortices in the bulk that are transported towards the outer cylinder and dissipated. Compared to the purely smooth case, the inner wall roughness renders the system more bulk dominated and thus increases the effective scaling exponent.

A floating air bag, ballasted in water, expands and contracts as it heaves under wave action. Connecting the bag to a secondary volume via a turbine transforms the bag into a device capable of generating useful energy from the waves. Small-scale measurements of the device reveal some interesting properties, which are successfully predicted numerically. Owing to its compressibility, the device can have a heave resonance period longer than that of a rigid device of the same shape and size, without any phase control. Furthermore, varying the amount of air in the bag is found to change its shape and hence its dynamic response, while varying the turbine damping or the air volume ratio changes the dynamic response without changing the shape.

The production of enstrophy is strongly coupled to the vortex stretching process that is of inherent importance to the cascading process, one of the driving processes of turbulence in a flow. In this work the enstrophy production mechanism is investigated to identify its variation in the wall-normal direction for the case of a turbulent boundary layer. Production is decomposed into its core quantities including the ratio of the principal strains and the alignment of vorticity with the eigenvectors of the strain rate tensor. The strong variations of these quantities with the wall distance are presented and explained. A self-similar shape of the probability distribution of the enstrophy production is found for regions above the buffer layer. Based on these findings we propose a modification to an existing vortex stretch model that accounts for the wall-normal variation in enstrophy production in a boundary layer. A characteristic decomposition is applied on the turbulence field that allows for the study of the individual production mechanisms of the separate structure types. This analysis reveals a potential backscatter mechanism that transfers kinetic energy from smaller scales towards larger ones, for a structure type described as unstable vortices.

The dissolution of a single droplet, containing a mixture of oils, in water is experimentally studied. The oils in the droplet varied in terms of their solubility in water and their hydrophobicity. We demonstrate that the polarity of the droplet constituents strongly influences the dissolution dynamics. A binary-component droplet, containing two polar components (one soluble the other insoluble) exhibits a retarded dissolution as compared to a droplet containing only the soluble component. We argue that in this case the mixture in the droplet can be assumed homogeneous, leading to a smaller effective contact area of the soluble liquid in the droplet with the bulk water, and thus delayed dissolution. On the other hand, it is shown that this is not the case when a polar, soluble component is mixed with an insoluble non-polar component, in which case segregation between the different liquids inside the droplet occurs, leading to Marangoni flows and superspreading of the droplet. The segregation is confirmed by volumetric measurements and by the use of a solvatochromic dye in combination with confocal microscopy, which clearly showed that during dissolution local concentration differences inside the droplet developed.

The purpose of this paper is to provide secondary instability analysis of stationary crossflow vortices on a hypersonic yawed straight circular cone with a $7^{\circ }$ half-angle at $6^{\circ }$ angle of attack, free-stream Mach number 6 and unit Reynolds number $10.09\times 10^{6}~\text{m}^{-1}$. At an angle of attack, a three-dimensional boundary layer is developed between the windward and leeward symmetry planes. Under the action of azimuthal pressure gradients, the flow near the surface is deflected more than the flow near the edge of the boundary layer. This results in an inflectional velocity profile that can sustain the growth of crossflow vortices. The stationary crossflow instability is computed by means of the nonlinear parabolized stability equations, including a methodology to predict the stationary-crossflow marching path and variation of the spanwise number of waves in the marching direction solely from the basic state. Secondary instability analysis is performed using spatial BiGlobal equations based on two-dimensional partial differential equations. The secondary instabilities are calculated at different axial locations along two crossflow vortex trajectories selected to complement experiments conducted in the Mach 6 Quiet Tunnel at Texas A&M University and in the Boeing/AFOSR Mach 6 Quiet Tunnel at Purdue University. The secondary instability analysis captures various instability modes. Similar to observations in the low-speed regime for an infinite swept wing, secondary shear-layer instabilities are amplified as a consequence of the three-dimensional shear layer formed by crossflow vortices. Also, low-frequency travelling crossflow and high-frequency second modes coexist with the shear-layer instabilities. These results are shown to be in good agreement with the two sets of hypersonic yawed cone experiments (one with natural surface roughness and one with artificial discrete roughness) and compare well with experimental measurements of an incompressible swept wing.

The spatial structure of smooth- and rough-wall boundary layers is examined spectrally at approximately matched friction Reynolds number ($\unicode[STIX]{x1D6FF}^{+}\approx 12\,000$). For each wall condition, temporal and true spatial descriptions of the same flow are available from hot-wire anemometry and high-spatial-range particle image velocimetry, respectively. The results show that over the resolved flow domain, which is limited to a streamwise length of twice the boundary layer thickness, true spatial spectra of smooth-wall streamwise and wall-normal velocity fluctuations agree, to within experimental uncertainty, with those obtained from time series using Taylor’s frozen turbulence hypothesis (Proc. R. Soc. Lond. A, vol. 164, 1938, pp. 476–490). The same applies for the streamwise velocity spectra on rough walls. For the wall-normal velocity spectra, however, clear differences are observed between the true spatial and temporally convected spectra. For the rough-wall spectra, a correction is derived to enable accurate prediction of wall-normal velocity length scales from measurements of their time scales, and the implications of this correction are considered. Potential violations to Taylor’s hypothesis in flows above perturbed walls may help to explain conflicting conclusions in the literature regarding the effect of near-wall modifications on outer-region flow. In this regard, all true spatial and corrected spectra presented here indicate structural similarity in the outer region of smooth- and rough-wall flows, providing evidence for Townsend’s wall-similarity hypothesis (The Structure of Turbulent Shear Flow, vol. 1, 1956).

The steady mixed convection non-axisymmetric (Homann, Z. Angew. Math. Mech., vol. 16, 1936, pp. 153–164) stagnation-point flow over a vertical flat wall placed in a viscous and incompressible fluid is considered. A similarity solution is derived which involves the dimensionless parameters $\unicode[STIX]{x1D6FE}$, representing the shear-to-strain-rate ratio, and $\unicode[STIX]{x1D706}$, a mixed convection parameter. Forced convection, $\unicode[STIX]{x1D706}=0$, is treated first where solutions additional to those given previously by Weidman (J. Fluid Mech., vol. 702, 2012, pp. 460–469) are found arising from singularities as $\unicode[STIX]{x1D6FE}\rightarrow \pm 1$. Numerical solutions are obtained for representative values of both $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D706}$. Critical values $\unicode[STIX]{x1D706}_{c}$ of $\unicode[STIX]{x1D706}$ are seen in opposing flow and these are treated in detail. Asymptotic results for large $\unicode[STIX]{x1D706}$ and $\unicode[STIX]{x1D6FE}$ are derived.

Two-dimensional (2D) and three-dimensional (3D) instabilities in the wake of a circular cylinder placed near to a moving wall are investigated using direct numerical simulation (DNS). The study covers a parameter space spanning a non-dimensional gap ratio ($G^{\ast }$) between 0.1 to 19.5 and Reynolds number ($Re$) up to 300. Variations in the flow characteristics with $Re$ and $G^{\ast }$ are studied, and their correlations with the hydrodynamic forces on the cylinder are investigated. It is also found that the monotonic increase of the critical $Re$ for 2D instability ($Re_{cr2D}$) with decreasing $G^{\ast }$ is influenced by variations in the mean flow rate around the cylinder, the confinement of the near-wake flow by the plane wall and the characteristics of the shear layer formed above the moving wall directly below the cylinder. The first factor destabilizes the wake flow at a moderate $G^{\ast }$ while the latter two factors stabilize the wake flow with decreasing $G^{\ast }$. In terms of 3D instability, the flow transition sequence of ‘2D steady $\rightarrow$ 3D steady $\rightarrow$ 3D unsteady’ for small gap ratios is analysed at $G^{\ast }=0.2$. It is found that the 3D steady and 3D unsteady flows are triggered by Mode C instability due to wall proximity. However, the Mode C structure is not sustained indefinitely, since interference with the shear layer leads to other 3D steady and unsteady flow structures.

This paper considers natural Lapwood convection in a shallow porous cavity filled with a binary fluid. The investigation is mainly focused on the nonlinear behaviour of subcritical convection and the bistability phenomenon caused by the combined effects of porous medium form drag and double-diffusive convection. The Dupuit–Darcy model, which includes the effect of the form drag at high Reynolds flow, is used to describe the convective flow in the porous matrix. The enclosure is subject to vertical temperature and concentration gradients. The governing parameters of the problem under study are the Rayleigh number, $R_{T}$, the buoyancy ratio, $\unicode[STIX]{x1D711}$, the Lewis number, $Le$, the form drag coefficient, ($1/P_{r}^{\ast }$), where $P_{r}^{\ast }$ is a modified Prandtl number, and the aspect ratio of the cavity, $A$. An analytical solution, valid for shallow enclosures ($A\gg 1$), is derived on the basis of the parallel flow approximation. Among other things, this work focuses on the effects of the form drag parameter on the convective flows that occur when the thermal and solutal buoyancy forces are opposing each other. For this situation, in the absence of the form drag effect, the onset of motion is known to occur at a subcritical Rayleigh number, $R_{TC}^{sub}$, which depends upon $\unicode[STIX]{x1D711}$ and $Le$ only. The effects of $P_{r}^{\ast }$ on $R_{TC}^{sub}$ and on the subsequent convective heat and mass transfer rates are found to be significant. A new bistability phenomenon arises when the onset of subcritical convection is shifted close to or beyond the threshold of supercritical convection, whether heating or cooling isothermally or upon applying constant heat and solute fluxes, regardless of the enclosure aspect ratio value. It is demonstrated, on the basis of linear stability theory, that the form drag parameter has a stabilizing effect and considerably affects the threshold for Hopf bifurcation, $R_{TC}^{Hopf}$, which characterizes the transition from steady to unsteady convection. In the range of governing parameters considered in this study, the heat, solute and flow characteristics predicted by the analytical model are found to agree well with the numerical study of the full governing equations.