This paper addresses shear-induced self-diffusion in a monodisperse suspension of non-Brownian particles in Couette flow by two-dimensional computer simulations following the lattice-Boltzmann method. This method is suited for the study of (many-particle) particulate suspensions and can not only be applied for Stokes flow, but also for flow with finite Reynolds number. At relatively low shear particle Reynolds numbers (up to 0.023), shear-induced diffusivity exhibited a linear dependence on the shear rate, as expected from theoretical considerations. Simulations at shear particle Reynolds numbers between 0.023 and 0.35, however, revealed that in this regime, shear-induced diffusivity did not show this linear dependence anymore. Instead, the diffusivity was found to increase more than linearly with the shear rate, an effect that was most pronounced at lower area fractions of 0.10 and 0.25. In the same shear regime, major changes were found in the flow trajectories of two interacting particles in shear flow (longer and closer approach) and in the viscosity of the suspension (shear thickening). Moreover, the suspended particles exhibited particle clustering. The increase of shear-induced diffusivity is shown to be directly correlated with this particle clustering. As for shear-induced diffusivity, the effect of increasing shear rates on particle clustering was the most intensive at low area fractions of 0.10 and 0.25, where the radius of the clusters increased from about 4 to about 7 particle radii with an increase of the shear Reynolds number from 0.023 to 0.35. The importance of particle clustering to shear-induced diffusion might also indicate the importance of other factors that can induce particle clustering, such as, for example, colloidal instability.

The stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries is investigated using numerical calculations in three-dimensional rectangles. At low Rayleigh numbers (Ra < 20000) calculations of the stability of two-dimensional rolls to cross-roll disturbances are in agreement with the predictions of Bolton & Busse for a fluid with a large but finite Prandtl number. Within the range 2 × 104 < Ra [les ] 5 × 105, steady rolls with basic wavenumber α > 2.22 (aspect ratio < 1.41) are stable solutions. Two-dimensional rolls with basic wavenumber α < 1.96 (aspect ratio > 1.6) are time dependent for Ra > 4 × 104. For every case in which the initial condition was a time-dependent large-aspect-ratio roll, two-dimensional convection was found to be unstable to three-dimensional convection. Time-dependent rolls are replaced by either bimodal or knot convection in cases where the horizontal dimensions of the rectangular box are less than twice the depth. The bimodal planforms are steady states for Ra [les ] 105, but one case at Ra = 5 × 105 exhibits time dependence in the form of pulsating knots. Calculations at Ra = 105 in larger domains resulted in fully three-dimensional cellular planforms. A steady-state square planform was obtained in a 2.4 × 2.4 × 1 rectangular box. started from random initial conditions. Calculations in a 3 × 3 × 1 box produced steady hexagonal cells when started from random initial conditions, and a rectangular planform when started from a two-dimensional roll. An hexagonal planform started in a 3.5 × 3.5 × 1 box at Ra = 105 exhibited oscillatory time dependence, including boundary-layer instabilities and pulsating plumes. Thus, the stable planform in three-dimensional convection is sensitive to the size of the rectangular domain and the initial conditions. The sensitivity of heat transfer to planform variations is less than 10%.

Shock reflections over a convex and a concave wedge were investigated by using a 5 × 7 cm ordinary pressure-driven shock tube. Dry air was used for both the driving and driven gases. The large difference between the transition from regular (RR) to Mach reflection (MR) and that from MR to RR was observed, confirming the results obtained by Ben-Dor, Takayama & Kawauchi (1980). These results contradict all of the previous theoretical transition criteria. A new theory on the transition between RR and MR was developed by applying Whitham's ‘ray shock’ theory. This new theory agrees quite well with the experimental results.

The valveless impedance pump is a simple design that allows the producion or amplification of a flow without the requirement for valves or impellers. It is based on fluid-filled flexible tubing, connected to tubing of different impedances. Pumping is achieved by a periodic excitation at an off-centre position relative to the tube ends. This paper presents a comprehensive study of the fluid and structural dynamics in an impedance pump model using numerical simulations. An axisymmetric finite-element model of both the fluid and solid domains is used with direct coupling at the interface. By examining a wide range of parameters, the pump's resonance nature is described and the concept of resonance wave pumping is discussed. The main driving mechanism of the flow in the tube is the reflection of waves at the tube boundary and the wave dynamics in the passive tube. This concept is supported by three different analyses: (i) time-dependent pressure and flow wave dynamics along the tube, (ii) calculations of pressure–flow loop areas along the passive tube for a description of energy conversion, and (iii) an integral description of total work done by the pump on the fluid. It is shown that at some frequencies, the energy given to the system by the excitation is converted by the elastic tube to kinetic energy at the tube outlet, resulting in an efficient pumping mechanism and thus significantly higher flow rate. It is also shown that pumping can be achieved with any impedance mismatch at one boundary and that the outlet configuration does not necessarily need to be a tube.

A gas in a tube is excited by a reciprocating piston operating at or near a resonant frequency. Damping is introduced into the system by two means: radiation of energy from one end of the tube and rate dependence of the gas. These define a lumped damping coefficient. It is shown that in the small rate limit the signal in the periodic state suffers negligible distortion in one travel time, and hence its propagation according to acoustic theory is valid. The shape of the signal is determined by a nonlinear ordinary differential equation. The small rate condition provides a test of the applicability of the theory to given experimental conditions. When there is no damping, shocks are a feature of the flow for frequencies in the resonant band. For a given amount of damping an upper bound on the piston acceleration which ensures shockless motion is given. The resonant band is analysed for both damped and undamped cases. The predictions of the theory are compared with experiment.

Measurements of the heat flux and temperature gradient in a layer of saline solution stably stratified by Soret diffusion and heated from below exhibit the onset of convection by the growth of very small oscillations which eventually trigger finite amplitude convection. The critical Rayleigh numbers and periods of oscillation are consistent with published theoretical calculations. Several non-linear modes are observed, even for the same heat flux, near the point of onset.

The paper deals with the problem of estimating the sound field generated by a limited region of turbulence in an infinitely long, straight, hard-walled pipe. The field is analysed in a co-ordinate system moving with the assumed uniform mean flow, and the possibility of eddy convection relative to that reference system is considered. Large-scale turbulence is shown to induce plane acoustic waves of intensity proportional to the sixth power of flow velocity. The same is true of small-scale turbulence of low characteristic frequency. In both cases convective effects increase the acoustic output and distribute the bulk of the energy in a mode propagating upstream against the mean flow. Small-scale turbulence of higher frequency excites more modes, the sound increasing with very nearly the eighth power of velocity (U7.7) as soon as the second mode is excited. In the limit, when more than about 20 modes are excited, the energy output is unaffected by the constraint of the pipe walls, increasing with the eighth power of velocity, and being substantially amplified by convective motion.

The evolution of a bidimensional foam submitted to continuous quasi-static shearing isinvestigated both experimentally and numerically. We extract, from the images of the sheared foam, the plastic flow profiles as well as the local statistical properties of the stress field. When the imposed strain becomes larger than the yield strain, the plastic events develop large spatial and temporal correlations, and the plastic flow becomes confined to a narrow shear band. This transition and the steady-state regime of flow are investigated by first focusing on the elastic deformation produced by an elementary plastic event. This allows us to understand (i) the appearance of long-lived spatial heterogeneities of the stress field, which we believe are at the origin of the shear-banding transition, and (ii) the statistics of the dynamic fluctuations of the stress field induced by plastic rearrangements in the steady-state regime. Movies are available with the online versionof the paper.

Vortex-induced vibration (VIV) of a sphere represents one of the most generic fundamental fluid–structure interaction problems. Since vortex-induced vibration can lead to structural failure, numerous studies have focused on understanding the underlying principles of VIV and its suppression. This paper reports on an experimental investigation of the effect of imposed axial rotation on the dynamics of vortex-induced vibration of a sphere that is free to oscillate in the cross-flow direction, by employing simultaneous displacement and force measurements. The VIV response was investigated over a wide range of reduced velocities (i.e. velocity normalised by the natural frequency of the system): $3\leqslant U^{\ast }\leqslant 18$, corresponding to a Reynolds number range of $5000<Re<30\,000$, while the rotation ratio, defined as the ratio between the sphere surface and inflow speeds, $\unicode[STIX]{x1D6FC}=|\unicode[STIX]{x1D714}|D/(2U)$, was varied in increments over the range of $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 7.5$. It is found that the vibration amplitude exhibits a typical inverted bell-shaped variation with reduced velocity, similar to the classic VIV response for a non-rotating sphere but without the higher reduced velocity response tail. The vibration amplitude decreases monotonically and gradually as the imposed transverse rotation rate is increased up to $\unicode[STIX]{x1D6FC}=6$, beyond which the body vibration is significantly reduced. The synchronisation regime, defined as the reduced velocity range where large vibrations close to the natural frequency are observed, also becomes narrower as $\unicode[STIX]{x1D6FC}$ is increased, with the peak saturation amplitude observed at progressively lower reduced velocities. In addition, for small rotation rates, the peak amplitude decreases almost linearly with $\unicode[STIX]{x1D6FC}$. The imposed rotation not only reduces vibration amplitudes, but also makes the body vibrations less periodic. The frequency spectra revealed the occurrence of a broadband spectrum with an increase in the imposed rotation rate. Recurrence analysis of the structural vibration response demonstrated a transition from periodic to chaotic in a modified recurrence map complementing the appearance of broadband spectra at the onset of bifurcation. Despite considerable changes in flow structure, the vortex phase ($\unicode[STIX]{x1D719}_{vortex}$), defined as the phase between the vortex force and the body displacement, follows the same pattern as for the non-rotating case, with the $\unicode[STIX]{x1D719}_{vortex}$ increasing gradually from low values in Mode I of the sphere vibration to almost $180^{\circ }$ as the system undergoes a continuous transition to Mode II of the sphere vibration at higher reduced velocity. The total phase ($\unicode[STIX]{x1D719}_{total}$), defined as the phase between the transverse lift force and the body displacement, only increases from low values after the peak amplitude response in Mode II has been reached. It reaches its maximum value (${\sim}165^{\circ }$) close to the transition from the Mode II upper plateau to the lower plateau, reminiscent of the behaviour seen for the upper to lower branch transition for cylinder VIV. Hydrogen-bubble visualisations and particle image velocimetry (PIV) performed in the equatorial plane provided further insights into the flow dynamics near the sphere surface. The mean wake is found to be deflected towards the advancing side of the sphere, associated with an increase in the Magnus force. For higher rotation ratios, the near-wake rear recirculation zone is absent and the flow is highly vectored from the retreating side to the advancing side, giving rise to large-scale shedding. For a very high rotation ratio of $\unicode[STIX]{x1D6FC}=6$, for which vibrations are found to be suppressed, a one-sided large-scale shedding pattern is observed, similar to the shear-layer instability one-sided shedding observed previously for a rigidly mounted rotating sphere.

Under steady flow conditions, the topological complexity inherent to all random three-dimensional (3D) porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a 3D fluid mechanical analogue of the baker’s map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence, pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW), which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that the chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with the longitudinal advection, whereas the topological constraints associated with two-dimensional porous media limit the mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.

When a steadily moving load is applied to a floating ice plate, the disturbance will generally approach a steady state (relative to the load) as time t → ∞. However, for certain ‘critical’ load speeds the disturbance may grow continuously with time, which represents some danger to vehicles driving on ice. To understand this phenomenon and the overall time development of the ice response, this paper analyses the problem of an impulsively applied, concentrated line load on a perfectly elastic homogeneous floating ice plate. An exact expression for the ice deflection is derived, and then interpreted by means of asymptotic expansions for large t in the vicinity of the source. The spatial development of the disturbance is analysed by considering asymptotic expansions as t → ∞ near an observer moving away from the load. Theoretical results are compared with field measurements, and some hitherto unexplained features can be understood.

Couder & Fort (Phys. Rev. Lett., vol. 97, 2006, 154101) demonstrated that when a droplet walking on the surface of a vibrating bath passes through a single or a double slit, it is deflected due to the distortion of its guiding wave field. Moreover, they suggested the build-up of statistical diffraction and interference patterns similar to those arising for quantum particles. Recently, these results have been revisited (Andersen et al., Phys. Rev. E, vol. 92 (1), 2015, 013006; Batelaan et al., J. Phys.: Conf. Ser., vol. 701 (1), 2016, 012007) and contested (Andersen et al. 2015; Bohr, Andersen & Lautrup, Recent Advances in Fluid Dynamics with Environmental Applications, 2016, Springer, pp. 335–349). We revisit these experiments with a refined experimental set-up that allows us to systematically characterize the dependence of the dynamical and statistical behaviour on the system parameters. The system behaviour is shown to depend strongly on the amplitude of the vibrational forcing: as this forcing increases, a transition from repeatable to unpredictable trajectories arises. In all cases considered, the system behaviour is dominated by a wall effect, specifically the tendency for a drop to walk along a path that makes a fixed angle relative to the plane of the slits. While the three dominant central peaks apparent in the histograms of the deflection angle reported by Couder & Fort (2006) are evident in some of the parameter regimes considered in our study, the Fraunhofer-like dependence of the number of peaks on the slit width is not recovered. In the double-slit geometry, the droplet is influenced by both slits by virtue of the spatial extent of its guiding wave field. The experimental behaviour is well captured by a recently developed theoretical model that allows for a robust treatment of walking droplets interacting with boundaries. Our study underscores the importance of experimental precision in obtaining reproducible data.

The electrohydrodynamic stability of a liquid bridge was studied in steady and oscillatory axial electric fields with a novel apparatus aboard a space shuttle. To avoid interphase transport, which complicates matters in terrestrial, matched-density systems, the experiments focused on a liquid column surrounded by a dielectric gas. The micro-gravity acceleration level aboard the spacecraft kept the Bond number small; so interface deformation by buoyancy was negligible. To provide microgravity results for comparison with terrestrial data, the behaviour of a castor oil bridge in a silicone oil matrix liquid was studied first. The results from these experiments are in excellent agreement with earlier work with isopycnic systems as regards transitions from a perfect cylinder to the amphora shape and the separation of an amphora into drops. In addition, the location of the amphora bulge was found to be correlated with the field direction, contrary to the leaky dielectric model but consistent with earlier results from terrestrial experiments. Next, the behaviour of a bridge surrounded by a dielectric gas, sulphur hexa fluoride (SF6), was investigated. In liquid–gas experiments, electrohydrodynamic ejection of liquids from ‘Taylor cones’ was used to deploy fluid and form bridges by remote control. Experiments with castor oil bridges in SF6 identified the conditions for two transitions: cylinder–amphora, and pinch-off. In addition, new behaviour was uncovered with liquid–gas interfaces. Contrary to expectations based on perfect dielectric behaviour, castor oil bridges in SF6 could not be stabilized in AC fields. On the other hand, a low-conductivity silicone oil bridge, which could not be stabilized by a DC field, was stable in an AC field.

Measurements of the aerodynamic pressure distribution at the interface between air and simple progressive water waves are obtained with the use of a pressure sensor that follows the water surface. The theory of Miles (1957, 1959) and Benjamin (1959) on shear flows past a wavy boundary predicts a phase shift between the pressure distribution along the boundary and the boundary itself. An experimental verification of this theory is sought especially. A wind–wave facility 115 ft. long, 6 ft. high and 3 ft. wide was used. The facility is equipped with an oscil-lating-plate wave-generator which is capable of generating sinusoidal or arbitrary wave-forms, and a suction fan which can produce wind velocities up to 80 ft./sec when the water is at a nominal depth of 3 ft. The pressure sensor used for the measurements of pressure, was mounted on an oscillating device such that the sensor could be maintained at a fixed small distance (within 1/4 in.) above a propagating wavy surface at all times. The perturbation pressure over progressive waves is extracted from recorded data sensed by the moving sensor. The results compare favourably with the theoretical predictions of Miles (1959).

We examine discrete vortex dynamics in two-dimensional flow through a network-theoretic approach. The interaction of the vortices is represented with a graph, which allows the use of network-theoretic approaches to identify key vortex-to-vortex interactions. We employ sparsification techniques on these graph representations based on spectral theory to construct sparsified models and evaluate the dynamics of vortices in the sparsified set-up. Identification of vortex structures based on graph sparsification and sparse vortex dynamics is illustrated through an example of point-vortex clusters interacting amongst themselves. We also evaluate the performance of sparsification with increasing number of point vortices. The sparsified-dynamics model developed with spectral graph theory requires a reduced number of vortex-to-vortex interactions but agrees well with the full nonlinear dynamics. Furthermore, the sparsified model derived from the sparse graphs conserves the invariants of discrete vortex dynamics. We highlight the similarities and differences between the present sparsified-dynamics model and reduced-order models.

This paper presents the results of investigations into particular features of laminar-to-turbulent transition of pipe flows. The first part considers transitional flows that occur ‘naturally’, i.e. without any forcing, when a critical Reynolds number is reached. Measurements are reported that were carried out to study the intermittent nature of pipe flows before they become fully turbulent. The second part of the paper concentrates on forced laminar-to-turbulent transition where the forcing was achieved by ring-type obstacles introduced into the flow close to the pipe inlet. The influence of the ring height was investigated and the results showed a dependence of the critical Reynolds number on the normalized height of the disturbances. The laminar-to-turbulent transition was also investigated when caused by partially closing an iris diaphragm that permitted the flow to be forced to turbulence over short time intervals. Investigations of controlled intermittency became possible in this way and corresponding results are presented.

We report high-precision measurements of the Nusselt number as a function of the Rayleigh number in water-filled rectangular Rayleigh–Bénard convection cells. The horizontal length and width of the cells are 50.0 and 15.0 cm, respectively, and the heights , 25.0, 12.5, 6.9, 3.5, and 2.4 cm, corresponding to the aspect ratios , , , , , and . The measurements were carried out over the Rayleigh number range and the Prandtl number range . Our results show that for rectangular geometry turbulent heat transport is independent of the cells’ aspect ratios and hence is insensitive to the nature and structures of the large-scale mean flows of the system. This is slightly different from the observations in cylindrical cells where is found to be in general a decreasing function of , at least for and larger. Such a difference is probably a manifestation of the finite plate conductivity effect. Corrections for the influence of the finite conductivity of the top and bottom plates are made to obtain the estimates of for plates with perfect conductivity. The local scaling exponents of are calculated and found to increase from 0.243 at to 0.327 at .

Measurements of wall pressure and streamwise velocity fluctuations in a turbulent boundary layer on a cylinder in an axial air flow (δ/a = 5.04, Reθ = 2870) have been used to investigate the turbulent flow structures in the cylindrical boundary layer that contribute to the fluctuating pressure at the wall in an effort to deduce the effect of transverse curvature on the structure of boundary layer turbulence. Wall pressure was measured at a single location with a subminiature electret condenser microphone, and the velocity was measured throughout a large volume of the boundary layer with a hotwire probe. Auto- and cross-spectral densities, cross-correlations, and conditional sampling of the pressure and streamwise velocity indicate that two primary groups of flow disturbances contribute to the fluctuating pressure at the wall: (i) low-frequency large-scale structures with dynamical significance across the entire boundary layer that are consistent with a pair of large-scale spanwise-oriented counter-rotating vortices and (ii) higher frequency small-scale disturbances concentrated close to the wall that are associated with the burst-sweep cycle and are responsible for the short-duration large-amplitude wall pressure fluctuations. A bidirectional relationship was found to exist between both positive and negative pressure peaks and the temporal derivative of u near the wall. Because the frequency of the large-scale disturbance observed across the boundary layer is consistent with the bursting frequency deduced from the average time between bursts, the burst-sweep cycle appears to be linked to the outer motion. A stretching of the large-scale structures very near the wall, as suggested by space-time correlation convection velocity results, may provide the coupling mechanism. Since the high-frequency disturbance observed near the wall is consistent with the characteristic frequency deduced from the average duration of bursting events, the bursting process provides the two characteristic time scales responsible for the bimodal distribution of energy near the wall. Because many of the observed structural features of the cylindrical boundary layer are similar to those observed in flat-plate turbulent boundary layers, transverse curvature appears to have little effect on the fundamental turbulent structure of the boundary layer for the moderate transverse curvature ratio used in this investigation. From differences that exist between the turbulence intensity, skewness, and spectra of the streamwise velocity, however, it appears that transverse curvature may enhance (i.e. energize) the large-scale motion owing to the reduced constraint imposed on the flow by the smaller cylindrical wall.