A generalized similarity formulation extending the work of Terrill (1967) for Couette–Poiseuille flow in the annulus between concentric cylinders of infinite extent is given. Boundary conditions compatible with the formulation allow a study of the effects of inner and outer cylinder transpiration, rotation, translation, stretching and twisting, in addition to that of an externally imposed constant axial pressure gradient. The problem is governed by η, the ratio of inner to outer radii, a Poiseuille number, and nine Reynolds numbers. Single-cylinder and planar problems can be recovered in the limits η→0 and η→1, respectively. Two coupled primary nonlinear equations govern the meridional motion generated by uniform mass flux through the porous walls and the azimuthal motion generated by torsional movement of the cylinders; subsidiary equations linearly slaved to the primary flow govern the effects of cylinder translation, cylinder rotation, and an external pressure gradient. Steady solutions of the primary equations for uniform source/sink flow of strength F through the inner cylinder are reported for 0[les ]η[les ]1. Asymptotic results corroborating the numerical solutions are found in different limiting cases. For F<0 fluid emitted through the inner cylinder fills the gap and flows uniaxially down the annulus; an asymptotic analysis leads to a scaling that removes the effect of η in the pressure parameter β, namely β=π2R*2, where R*=F(1−η)/(1+η). The case of sink flow for F>0 is more complex in that unique solutions are found at low Reynolds numbers, a region of triple solutions exists at moderate Reynolds numbers, and a two-cell solution prevails at large Reynolds numbers. The subsidiary linear equations are solved at η=0.5 to exhibit the effects of cylinder translation, rotation, and an axial pressure gradient on the source/sink flows.

In this paper, we apply aeration with oxygen microbubbles to tap water; the intent is to quantitatively evaluate whether nitrogen gas originally dissolved in the water under the atmosphere is purged by the aeration with oxygen microbubbles. Oxygen microbubbles are continuously injected into the circulation system of tap water open to the atmosphere. While the concentration of dissolved oxygen (DO) can be detected by a commercial DO meter, that of dissolved nitrogen (DN) is unavailable. To detect the DN level, we observe the growth of millimetre-sized gas bubbles nucleated at glass surfaces in contact with the aerated water and compare it with the multi-species theory of Epstein and Plesset where the (unknown) DN concentration is treated as a fitting parameter. In the theory, we solve binary diffusion of each gas species (oxygen or nitrogen) in the water independently, under the assumption that the dissolved gases are sufficiently dilute. Comparisons between the experiment and the theory suggest that the DN in the water is effectively purged by the oxygen aeration. The supplemental experiment of aeration with nitrogen microbubbles is also documented to show that the DO can be effectively purged as well.

A series of direct numerical simulations were performed of Taylor–Couette (TC) flow, the flow between two coaxial cylinders, with the outer cylinder rotating and the inner one fixed. Three cases were considered, where the Reynolds number of the outer cylinder was $Re_{o}=5.5\times 10^{4}$, $Re_{o}=1.1\times 10^{5}$ and $Re_{o}=2.2\times 10^{5}$. The ratio of radii ${\it\eta}=r_{i}/r_{o}$ was fixed to ${\it\eta}=0.909$ to mitigate the effects of curvature. Axially periodic boundary conditions were used, with the aspect ratio of vertical periodicity ${\it\Gamma}$ fixed to ${\it\Gamma}=2.09$. Being linearly stable, TC flow with outer cylinder rotation is known to have very different behaviour than TC flow with pure inner cylinder rotation. Here, we find that the flow nonetheless becomes turbulent, but the torque required to drive the cylinders and level of velocity fluctuations was found to be smaller than those for pure inner cylinder rotation at comparable Reynolds numbers. The mean angular momentum profiles showed a large gradient in the bulk, instead of the constant angular momentum profiles of pure inner cylinder rotation. The near-wall mean and fluctuation velocity profiles were found to coincide only very close to the wall, showing large deviations from both pure inner cylinder rotation profiles and the classic von Karman law of the wall elsewhere. Finally, transport of angular velocity was found to occur mainly through intermittent bursts, and not through wall-attached large-scale structures as is the case for pure inner cylinder rotation.

When a sphere settles through the free surface of a viscous fluid, the interface is deformed and assumes a funnel shape behind the sphere. If the fluid is viscoelastic and the settling process is fast compared to the relaxation time of the fluid, elastic effects are dominant and an instability occurs. The interface loses its original axisymmetry and buckles, leading to a particular mode of pinch-off unseen in Newtonian fluids. We present experimental evidence that stress boundary layers form in this type of flow, and argue that a physical mechanism for this instability can be recovered, at least qualitatively, by considering the stability of a stretched anisotropic elastic membrane in a pressure field.

Wave run-up phenomena driven by nonlinear wave interactions with a fixed rectangular box are investigated. Experiments are carried out in different types of uni-directional waves with normal incidence. Significant wave run-ups featuring tertiary interaction effects, similar to those reported by Molin et al. (J. Fluid Mech., vol. 528, 2005, pp. 323–354) for a fixed vertical plate, are observed in regular wave tests. Transient wave group tests are conducted for comparison, to facilitate the analysis of the tertiary interactions in irregular waves. The most striking observation is that the wave surface elevations at the centre of the front face of the fixed box can reach $4\times$ the incident waves even in irregular waves, much larger than the ${\sim}2\times$ predicted from linear theory and observed for the transient groups. The extra amplification builds up slowly and is localized on the weather side of the box. It is believed to result from tertiary interactions between the incident and reflected wave fields upstream, which induce a local lensing effect and thus wave focusing on the weather side. These interactions, though a nonlinear process, occur at the first harmonic quantities rather than high harmonics. Supporting evidence is extracted from random wave runs using NewWave analysis, where surface amplifications and phase lag – both key characteristics of tertiary wave interactions – are identified. The identification of these tertiary interactions in irregular waves is new, and may be of practical importance.

The endothelial glycocalyx layer (EGL) is a macromolecular layer that lines the inner surface of blood vessels. It is believed to serve a number of physiological functions in the microvasculature, including protection of the vessel walls from potentially harmful levels of fluid shear, as a molecular sieve that acts to regulate transendothelial mass transport, and as a transducer of mechanical stress from the vessel lumen. To best fulfil some of its roles, it has been suggested that the EGL redistributes, so that it is thickest at the cell–cell junctions. It has also been suggested that the majority of mechanotransduction occurs through the solid phase of the EGL, rather than via its fluid phase. The difficulties associated with measuring the distribution of the EGL in vivo make these hypotheses difficult to confirm experimentally. Consequently, to gauge the impact of EGL redistribution from a theoretical standpoint, we compute the flow through a porous-lined microvessel, the endothelial surface of which has been informed by confocal microscopy images of a postcapillary venule. Following earlier studies, we model the poroelastohydrodynamics of the EGL using biphasic mixture theory, taking advantage of a recently developed boundary integral representation of these equations to solve the coupled poroelastohydrodynamics using the boundary element method. However, the low permeabilities of the EGL mean that viscous effects are confined to thin layers, thereby also enabling an asymptotic treatment of the dynamics in this limit. In this asymptotic regime, we also consider a two-layer Stokes flow model for the lumen flow to approximate the effect of red blood cells within the lumen. We demonstrate that redistribution of the EGL can have a substantial impact upon microvessel haemodynamics. We also confirm that the bulk of the mechanical stress is indeed carried through the solid phase of the EGL.

Flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via solution of the pertinent global (BiGlobal) partial differential equation (PDE)-based eigenvalue problem. Subsequently, a simple extension of the extended Görtler–Hämmerlin ordinary differential equation (ODE)-based polynomial model proposed by Theofilis et al. (2003) for orthogonal flow, which includes previous models as special cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the analysis results and unravel the limits of validity of the basic flow model analysed. The effect of the angle of attack, , on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from (orthogonal flow) up to values close to which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at are shown to be recoverable from those of orthogonal flow, via a simple algebraic transformation involving .

In this study we consider particle-laden turbulent flows with significant heat transfer between the two phases due to sustained heating of the particle phase. The sustained heat source can be due to particle heating via an external radiation source as in the particle-based solar receivers or an exothermic reaction in the particles. Our objective is to investigate the effects of fluid heating by a dispersed phase on the turbulence evolution. An important feature in such settings is the preferential clustering phenomenon which is responsible for non-uniform distribution of particles in the fluid medium. Particularly, when the ratio of particle inertial relaxation time to the turbulence time scale, namely the Stokes number, is of order unity, particle clustering is maximized, leading to thin regions of heat source similar to the flames in turbulent combustion. However, unlike turbulent combustion, a particle-laden system involves a wide range of clustering scales that is mainly controlled by particle Stokes number. To study these effects, we considered a decaying homogeneous isotropic turbulence laden with heated particles over a wide range of Stokes numbers. Using a low-Mach-number formulation for the fluid energy equation and a Lagrangian framework for particle tracking, we performed numerical simulations of this coupled system. We then applied a high-fidelity framework to perform spectral analysis of kinetic energy in a variable-density fluid. Our results indicate that particle heating can considerably influence the turbulence cascade. We show that the pressure-dilatation term introduces turbulent kinetic energy at a range of scales consistent with the scales observed in particle clusters. This energy is then transferred to high wavenumbers via the energy transfer term. For low and moderate levels of particle heating intensity, quantified by a parameter $\unicode[STIX]{x1D6FC}$ defined as the ratio of eddy time to mean temperature increase time, turbulence modification occurs primarily in the dilatational modes of the velocity field. However, as the heating intensity is increased, the energy transfer term converts energy from dilatational modes to divergence-free modes. Interestingly, as the heating intensity is increased, the net modification of turbulence by heating is observed dominantly in divergence-free modes; the portion of turbulence modification in dilatational modes diminishes with higher heating. Moreover, we show that modification of divergence-free modes is more pronounced at intermediate Stokes numbers corresponding to the maximum particle clustering. We also present the influence of heating intensity on the energy transfer term itself. This term crosses over from negative to positive values beyond a threshold wavenumber, showing the cascade of energy from large scales to small scales. The threshold is shown to shift to higher wavenumbers with increasing heating, indicating a growth in the total energy transfer from large scales to small scales. The fundamental energy transfer analysis presented in this paper provides insightful guidelines for subgrid-scale modelling and large-eddy simulation of heated particle-laden turbulence.

Direct numerical simulations of turbulent suspension flows are carried out with the force-coupling method in plane Couette and pressure-driven channel configurations. Dilute to moderately concentrated suspensions of neutrally buoyant finite-size spherical particles are considered when the Reynolds number is slightly above the laminar–turbulent transition. Tests performed with synthetic streaks, in both turbulent channel and Couette flows, show clearly that particles trigger the instability in channel flow whereas the plane Couette flow becomes laminar. Moreover, we have shown that particles have a pronounced impact on pressure-driven flow through a detailed temporal and spatial analysis whereas they have no significant impact on the plane Couette flow configuration. The substantial difference between the two flow configurations is related to the spatial preferential distribution of particles in the large-scale rolls (inactive motion) in Couette flow, whereas they are accumulated in the ejection (active motion) regions in pressure-driven flow. Through investigation of particle modification in two distinct flow configurations, we were able to show the specific response of turbulent structures and the modulation of the fundamental mechanisms composing the regeneration cycle in the buffer layer of the near-wall turbulence. Especially for pressure-driven flow, the particles enhance the lift-up and let it act continuously whereas the particles do not significantly alter the streak breakdown process. The reinforcement of the streamwise vortices is attributed to the vorticity stretching term by the wavy streaks. The smaller and more numerous wavy streaks enhance the vorticity stretching and consequently strengthen the circulation of large-scale streamwise vortices in suspension flow.

In this paper, we analyse the dispersion of a dye by a Landau–Squire plume, generated by a jet flow emerging from a nanocapillary into a reservoir. We demonstrate analytically that the dye concentration profile exhibits a long-range profile decaying as the inverse of the distance to the origin, whereas the plume shape is only a function of a Péclet number defined in terms of the flow characteristics inside the nanocapillary. These predictions are successfully compared with experiments on fluorescent dye dispersion from nanocapillaries under pressure-driven flow. The plume shape allows extraction of the nanojet force characterizing the Landau–Squire velocity profile for a given pressure drop, with results in full agreement with direct velocimetry measurements and finite-element calculations. The peculiarities of the Landau–Squire plume make it a sensitive probe of the flow properties inside the seeding nanocapillary.

We derive here Lagrangian fluctuation–dissipation relations for advected scalars in wall-bounded flows. The relations equate the dissipation rate for either passive or active scalars to the variance of scalar inputs from the initial values, boundary values and internal sources, as those are sampled backward in time by stochastic Lagrangian trajectories. New probabilistic concepts are required to represent scalar boundary conditions at the walls: the boundary local-time density at points on the wall where scalar fluxes are imposed and the boundary first hitting time at points where scalar values are imposed. These concepts are illustrated both by analytical results for the problem of pure heat conduction and by numerical results from a database of channel-flow turbulence, which also demonstrate the scalar mixing properties of near-wall turbulence. As an application of the fluctuation–dissipation relation, we examine for wall-bounded flows the relation between anomalous scalar dissipation and Lagrangian spontaneous stochasticity, i.e. the persistent non-determinism of Lagrangian particle trajectories in the limit of vanishing viscosity and diffusivity. In Part I of this series, we showed that spontaneous stochasticity is the only possible mechanism for anomalous dissipation of passive or active scalars, away from walls. Here it is shown that this remains true when there are no scalar fluxes through walls. Simple examples show, on the other hand, that a distinct mechanism of non-vanishing scalar dissipation can be thin scalar boundary layers near the walls. Nevertheless, we prove for general wall-bounded flows that spontaneous stochasticity is another possible mechanism of anomalous scalar dissipation.

This experimental study investigates the effect of a uniform lateral inflow on the aerodynamic characteristics of flapping wings. Seven designated sideward ratios in the hovering condition and in the presence of a contralateral wing and a body were taken into account as variables in order to secure a better understanding of wing–wing and/or wing–body interactions under the lateral inflow. Our results from the single-wing cases clarified that an inflow running from the wingroot strengthened the leading-edge vortex, thereby augmenting the aerodynamic force/moment. The inflow running in the opposite direction drastically bent the leading-edge vortex to the trailing edge, but the cycle-averaged aerodynamic force/moment was barely changed. This led to substantial imbalances in the force/moment on the two wings. The roll moment on a centre of gravity and the static margin suggested flight instability in the lateral direction, similar to previous studies. We found that the wing–wing interaction was not completely negligible overall under a lateral inflow. A massive downwash induced by the wing on the windward side nearly neutralized the aerodynamic force/moment augmentations on the other wing with lower effective angles of attack. The wing–wing interaction also gave rise to a low-lift high-drag situation during the pitching-up wing rotation, resulting in greater side force derivatives than the theory of flapping counterforce. Further calculations of the roll moment and the static margin with the centre of gravity showed that the wing–wing interaction can improve static stability in the lateral direction. This mainly stemmed from both the attenuation of the lift augmentation and the elimination of the positive roll moment of the flapping-wing system.

A two-dimensional Galerkin formulation of the three-dimensional Oberbeck-Boussinesq equations is used to describe the onset of convection in an infinite rigid horizontal channel uniformly heated from below. The dependence of the critical Rayleigh number on the channel aspect ratio is determined and results are compared with those of an idealized model studied by Davies-Jones (1970). Asymptotic results are derived for both narrow and wide channels, corresponding to limits of small and large aspect ratios respectively. In the latter case the main core flow, consisting of two-dimensional rolls with axes perpendicular to the vertical walls of the channel, can be represented by the solution of an amplitude equation. Close to the walls, however, the motion remains fully three-dimensional and a reversal of the vertical flow is associated with a local subdivision of each main roll into a pair of co-rotating rolls.

The present direct numerical simulation (DNS) study, the first of its kind, explores the effect that the location of a cylinder, immersed in the turbulent wake of a grid-element, has on heat transfer. An insulated single square grid-element is used to generate the turbulent wake upstream of the heated circular cylinder. Due to fine-scale resolution requirements, the simulations are carried out for a low Reynolds number. Three locations downstream of the grid-element, inside the production, peak and decay regions, respectively, are considered. The turbulent flow in the production and peak regions is highly intermittent, non-Gaussian and inhomogeneous, while it is Gaussian, homogeneous and fully turbulent in the decay region. The turbulence intensities at the location of the cylinder in the production and decay regions are almost equal at 11 %, while the peak location has the highest turbulence intensity of 15 %. A baseline simulation of heat transfer from the cylinder without oncoming turbulence was also performed. Although the oncoming turbulent intensities are similar, the production region increases the stagnation point heat transfer by 63 %, while in the decay region it is enhanced by only 28 %. This difference cannot be explained only by the increased approaching velocity in the production region. The existing correlations for the stagnation point heat transfer coefficient are found invalid for the production and peak locations, while they are satisfied in the decay region. It is established that the flow in the production and peak regions is dominated by shedding events, in which the predominant vorticity component is in the azimuthal direction. This leads to increased heat transfer from the cylinder, even before vorticity is stretched by the accelerating boundary layer. The frequency of oncoming turbulence in production and peak cases also lies close to the range of frequencies that can penetrate the boundary layer developing on the cylinder, and therefore the latter is very responsive to the impinging disturbances. The highest Nusselt number along the circumference of the cylinder is shifted 45 degrees from the front stagnation point. This shift is due to the turbulence-generating grid-element bars that result in the prevalence of intense events at the point of maximum Nusselt number compared to the stagnation point.