Any tilt of a Rayleigh–Bénard convection cell against gravity changes the global flow structure inside the cell, which leads to a change of the heat and momentum transport. Especially sensitive to the inclination angle is the heat transport in low-Prandtl-number fluids and confined geometries. The purpose of the present work is to investigate the global flow structure and its influence on the global heat transport in inclined convection in a cylindrical container of diameter-to-height aspect ratio $\unicode[STIX]{x1D6E4}=1/5$. The study is based on direct numerical simulations where two different Prandtl numbers $Pr=0.1$ and 1.0 are considered, while the Rayleigh number, $Ra$, ranges from $10^{6}$ to $10^{9}$. For each combination of $Ra$ and $Pr$, the inclination angle is varied between 0 and $\unicode[STIX]{x03C0}/2$. An optimal inclination angle of the convection cell, which provides the maximal global heat transport, is determined. For inclined convection we observe the formation of two system-sized plume columns, a hot and a cold one, that impinge on the opposite boundary layers. These are related to a strong increase in the heat transport.

The aeroacoustics of low-Mach-number boundary-layer flow over backward and forward facing steps is studied using large-eddy simulation and Lighthill's theory. The Reynolds number based on the step height and free-stream velocity ranges from 21000 to 328 as the step height is varied from 53% to 0.83% of the unperturbed boundary layer thickness at the step. For the largest step size, statistics of wall pressure fluctuations such as the root mean square values and frequency spectral density yield favourable comparisons with available experimental measurements. A low-frequency Green's function for the step geometry, valid for an acoustically compact step height, is employed to evaluate the volume integral in the solution to Lighthill's equation. Consistent with the result of previous theoretical studies, the steps act primarily as a dipole source aligned in the streamwise direction. The sound from the forward step is shown to be significantly louder than that from the backward step and the underlying reason is analysed in terms of source strength and distribution relative to the Green's function. The forward step generates stronger sources in regions closer to the step corner, which is heavily weighted by the Green's function. A detailed analysis of flow field and Green's function weighted sources reveals that the backward step generates sound mainly through a diffraction mechanism, while the forward step generates sound through a combination of diffraction and turbulence modification by the step. As the step height decreases, the difference in noise level between forward and backward steps is much reduced as turbulence modification becomes less significant.

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for binary fluids with moving contact lines are studied by asymptotic analysis and numerical simulations. The effects of the mobility number as well as a phenomenological relaxation parameter on the boundary condition are considered. In asymptotic analysis, we consider both the cases that the mobility number is proportional to the Cahn number and the square of the Cahn number, and derive the sharp-interface limits for several set-ups of the boundary relaxation parameter. It is shown that the sharp-interface limit of the phase-field model is the standard two-phase incompressible Navier–Stokes equations coupled with several different slip boundary conditions. Numerical results are consistent with the analysis results and also illustrate the different convergence rates of the sharp-interface limits for different scalings of the two parameters.

We call thick those films for which the disjoining pressure and thermal fluctuations are ineffective. Water films with thickness $h$ in the $1{-}100~\unicode[STIX]{x03BC}\text{m}$ range are thick, but are also known, paradoxically, to nucleate holes spontaneously. We have uncovered a mechanism solving the paradox, relying on the extreme sensitivity of the film to surface tension inhomogeneities. The surface tension of a free liquid film is lowered by an amount $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$ over a size $a$ by chemical or thermal contamination. At the same time this spot diffuses (within a time $a^{2}/D$, with $D$ the diffusion coefficient of the pollutant in the substrate), the Marangoni stress $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}/a$ induces an inhomogeneous outward interstitial flow which digs the film within a time $\unicode[STIX]{x1D70F}_{0}\sim \sqrt{\unicode[STIX]{x1D70C}ha^{2}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}}$, with $\unicode[STIX]{x1D70C}$ the density of the liquid. When the Péclet number $Pe=a^{2}/D\unicode[STIX]{x1D70F}_{0}$ is larger than unity, the liquid substrate motion reinforces the surface tension gradient, triggering a self-sustained instability insensitive to diffusional regularisation. Several experimental illustrations of the phenomenon are given, both qualitative and quantitative, including a precise study of the first instants of the unstable dynamics made by controlled perturbations of a Savart sheet at large $Pe$.

We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

The Stokes formula for the resistance force exerted on a sphere moving with constant velocity in a fluid is extended to the case of micropolar fluids. A non-homogeneous boundary condition for the micro-rotation vector is used: the micro-rotation on the boundary of the sphere is assumed proportional to the rotation rate of the velocity field on the boundary.

A theoretical model is developed for the sound generated when a convected disturbance encounters a cambered airfoil at non-zero angle of attack. The model is a generalization of a previous theory for a flat-plate airfoil, and is based on a linearization of the Euler equations about the steady, subsonic flow past the airfoil. High-frequency gusts, whose wavelengths are short compared to the airfoil chord, are considered. The airfoil camber and incidence angle are restricted so that the mean flow past the airfoil is a small perturbation to a uniform flow. The singular perturbation analysis retains the asymptotic regions present in the case of a flat-plate airfoil: local regions, which scale on the gust wavelength, at the airfoil leading and trailing edges; a ‘transition’ region behind the airfoil which is similar to the transition zone between illuminated and shadow regions in optical problems; and an outer region, far away from the airfoil edges and wake, in which the solution has a geometric-acoustics form. For the cambered airfoil, an additional asymptotic region in the form of an acoustic boundary layer adjacent to the airfoil surface is required in order to account for surface curvature effects. Parametric calculations are presented which illustrate that, like incidence angle, moderate amounts of airfoil camber can significantly affect the sound field produced by airfoil–gust interactions. Most importantly, the amount of radiated sound power is found to correlate very well with a single aerodynamic loading parameter, αeff, which is an effective mean-flow incidence angle for the airfoil leading edge.

Laminar–turbulent transition in the boundary layer at supersonic speeds can be initiated by small solid particles present in the free stream. Particulates interacting with the boundary-layer flow generate unstable wavepackets related to Tollmien–Schlichting (TS) waves. The latter grow downstream and ultimately break down to turbulent spots. This scenario of TS-dominated transition is modelled using the Mack amplitude method. A theoretical model describing the receptivity mechanism is developed to predict the initial spectrum of TS waves. With these initial conditions the downstream growth of TS instability is calculated using the linear stability theory. The transition onset is associated with the point where the disturbance amplitude reaches a threshold value. As an example, calculations are carried out for a 14° half-angle sharp wedge flying in the standard atmosphere at altitude 20 km, Mach number 4 and zero angle of attack. It is shown that spherical particles of radius from $10$ to $20~\unicode[.5,0][STIXGeneral,Times]{x03BC} \mathrm{m} $ and density ${\geqslant }1~\mathrm{g} ~{\mathrm{cm} }^{- 3} $ can cause transition onset corresponding to the amplification factor $N= 9{\unicode{x2013}} 10$, which is in the empirical range of flight data. This indicates that atmospheric particulates may be a major source of TS-dominated transition on aerodynamically smooth surfaces at supersonic speeds. The receptivity model provides a foundation for further treatments of different cases associated with transition in dusty environments. It can also be used for predictions of particle-induced transition at subsonic and hypersonic speeds.

The velocity induced by a transversely waving infinite flexible sheet in a viscoelastic liquid is investigated by a method of successive approximation up to second order in the amplitude of oscillation of the sheet. The incompressible second-order fluid model has been used and it is found that the elastic property of the fluid augments self-propulsion (increases the induced velocity) in some range of Reynolds number (based on the phase velocity) and hampers it (reduces the induced velocity) in some other range with higher values of Reynolds number.

This paper presents a comparative analysis of the budgets of acoustic energy and Myers' second-order ‘disturbance energy’ in a simple inhomogeneous flow with heat communication. The flow considered is non-diffusive and one-dimensional, with excitation by downstream-travelling acoustic and entropic disturbances. Two forms of heat communication are examined: a case with only steady heat communication and another in which unsteady heat addition cancels the generation of entropy disturbances throughout the inhomogeneous region.

It is shown that significant entropic disturbances are usually generated at low frequency when a flow with steady heat communication is excited either acoustically or entropically. However, for acoustic excitation and regardless of the form of heat communication, entropic disturbances are not created at high frequency, inferring that all source terms create mainly sound in this limit. A general method is therefore proposed for determining an approximate frequency beyond which the generation of entropy disturbances can be ignored, and the disturbance energy flux then approximates the acoustic energy flux. This frequency is shown to depend strongly on the problem under investigation, which is expected to have practical significance when studying sound generation and propagation in combusting flows in particular. Further, sound is shown to be generated by fluid motion experiencing only steady heat communication, which is consistent with the known mechanism of sound generation by the acceleration of density disturbances.

In experiments recently performed at Melbourne, Pitot-tube mean velocity profiles in a boundary layer disagreed with those obtained with hot wires. The standard MacMillan (1956) correction for the probe displacement effect and a correction for turbulence intensity were both required for obtaining agreement between the two sets of mean velocity data. We were thus motivated to reanalyse the Princeton superpipe data using the same two corrections. The result is a plausible conclusion that the superpipe is rough at the higher Reynolds numbers and its data follow the Colebrook (1939) formula for commercial pipes rather well. It also appears that the logarithmic law of the wall is valid, with a Kármán constant close to that found recently by Österlund (1999) from boundary layer measurements with a hot wire. The smooth regime in the pipe gave almost the same additive constant for the log-law as Österlund's. A comparison between the superpipe data and the pipe data of Perry, Henbest & Chong (1997) suggests that the conventional velocity defect law may be valid down to lower Reynolds numbers than concluded by Zagarola & Smits (1998).

Experiments were made on a pulsating water flow at a mean flow Reynolds number of 3770 in a cylindrical tube of diameter 3·81 cm. Pulsations were produced by a piston oscillating in simple harmonic motion with a period of 12 s. Turbulence was made visible by means of a sheet of dye produced by electrolysis from a fine wire stretched across a diameter. The sheet of dye is contorted by the turbulent eddies, and ciné-photography was used to find the velocity of convection which was shown to be the flow speed except in certain circumstances which are discussed. By subtracting the mean flow velocity profile the profile of the component of the motion oscillating at the imposed frequency was determined.

The Reynolds number of these experiments lies in the turbulent transition range, so that large effects of laminarization are observed. In the turbulent phase, the velocity profile was found to possess a central plateau as does the laminar oscillating profile. The level and radial extent of this were little different from the laminar ones. Near to the wall, the turbulent oscillating profile is well represented by the mean velocity power law relationship, u/U ∝ (y/a)1/n. In the laminarized phase, the turbulent intensity is considerably reduced at this Reynolds number. The velocity profile for the whole flow (mean plus oscillating) relaxes towards the laminar profile. Laminarization contributes appreciably to the oscillating component.

Extrapolation of the results to higher Reynolds numbers and different frequencies of oscillation is suggested.

The results of an experimental investigation into the development of a turbulent plane jet issuing into a parallel moving airstream are described. On the basis of a simple dimensional argument, it is shown that the results for the spread of jets with different ratios of jet nozzle to free-stream velocity can be collapsed into a single universal curve provided the effective origins of the various sets of data can be shifted. Evidence is found of a change in structure of the jet from a self-preserving plane jet flow near the origin of the flow towards a selfpreserving wake type of flow far downstream from the origin. This change of structure is compared with a prediction based on a simple application of Town-send's large-eddy hypothesis. It is shown that the hypothesis does not account for the way in which the jet structure changes and possible reasons for this are briefly discussed. Finally, some comments are made on the usefulness of the various theories of jet spreading.

All components of the fluctuating vorticity vector have been measured in decaying grid turbulence using a vorticity probe of relatively simple geometry (four X-probes, i.e. a total of eight hot wires). The data indicate that local isotropy is more closely satisfied than global isotropy, the r.m.s. vorticities being more nearly equal than the r.m.s. velocities. Two checks indicate that the performance of the probe is satisfactory. Firstly, the fully measured mean energy dissipation rate 〈ε〉 is in good agreement with the value inferred from the rate of decay of the mean turbulent energy 〈q2〉 in the quasi-homogeneous region; the isotropic mean energy dissipation rate 〈εiso〉 agrees closely with this value even though individual elements of 〈ε〉 indicate departures from isotropy. Secondly, the measured decay rate of the mean-square vorticity 〈ω2〉 is consistent with that of 〈q2〉 and in reasonable agreement with the isotropic form of the transport equation for 〈ω2〉. Although 〈ε〉≃〈εiso〉, there are discernible differences between the statistics of ε and εiso; in particular, εiso is poorly correlated with either ε or ω2. The behaviour of velocity increments has been examined over a narrow range of separations for which the third-order longitudinal velocity structure function is approximately linear. In this range, transverse velocity increments show larger departures than longitudinal increments from predictions of Kolmogorov (1941). The data indicate that this discrepancy is only partly associated with differences between statistics of locally averaged ε and ω2, the latter remaining more intermittent than the former across this range. It is more likely caused by a departure from isotropy due to the small value of Rλ, the Taylor microscale Reynolds number, in this experiment.

This experimental study, performed under microgravity conditions, focuses on the evaporation dynamics of ethanol drops and the formation and behaviour of the hydrothermal waves that spontaneously develop on the drop surfaces. The aim of this study is to compare our results to a similar study performed under normal gravity conditions to confirm the purely thermocapillary origin of these instabilities. A scaling law predicts with good agreement the number of instabilities that form, regardless of the gravity level.

Enhancement of heat transport across a fluid layer is of fundamental interest as well as great technological importance. For decades, Rayleigh–Bénard convection has been a paradigm for the study of convective heat transport, and how to improve its overall heat-transfer efficiency is still an open question. Here, we report an experimental and numerical study that reveals a novel mechanism that leads to much enhanced heat transport. When vertical partitions are inserted into a convection cell with thin gaps left open between the partition walls and the cooling/heating plates, it is found that the convective flow becomes self-organized and more coherent, leading to an unprecedented heat-transport enhancement. In particular, our experiments show that with six partition walls inserted, the heat flux can be increased by approximately 30 %. Numerical simulations show a remarkable heat-flux enhancement of up to 2.3 times (with 28 partition walls) that without any partitions.

The ribbing instability, an extremely common cause of non-uniform liquid films in coating operations, is investigated both theoretically and experimentally. The Navier–Stokes system for the two-dimensional flow in symmetric film-splitting in forward roll coating is solved by finite-element analysis. Stability of the flow with respect to three-dimensional disturbances is examined by applying linear stability theory in a consistent finite-element approach, taking Fourier components in the transverse direction. The resulting generalized asymmetric eigenproblem is solved for the growth rates of disturbances as functions of wavenumber. The theory accurately predicts the critical capillary number and wavenumber at the transition to large-amplitude ribs. A sensitive experimental technique for detecting the ribs was developed that relies on low-angle reflection of a focused strip of white light off the meniscus between the rolls. This allowed detection of much smaller amplitude ribs, and much smaller critical capillary numbers were measured. The results indicate that the transition to ribbing is an imperfect bifurcation due to end effects, and clarify earlier discordances in the literature.

Mild to steep standing waves of the fundamental mode are generated in a narrow rectangular cylinder undergoing vertical oscillation with forcing frequencies of 3.15 Hz to 3.34 Hz. A precise, non-intrusive optical wave profile measurement system is used along with a wave probe to accurately quantify the spatial and temporal surface elevations. These standing waves are also simulated by a two-dimensional spectral Cauchy integral code. Experiments show that contact-line effects increase the viscous natural frequency and alter the neutral stability curves. Hence, as expected, the addition of the wetting agent Photo Flo significantly changes the stability curve and the hysteresis in the response diagram. Experimentally, we find strong modulations in the wave amplitude for some forcing frequencies higher than 3.30 Hz. Reducing contact-line effects by Photo-Flo addition suppresses these modulations. Perturbation analysis predicts that some of this modulation is caused by noise in the forcing signal through ‘sideband resonance’, i.e. the introduction of small sideband forcing can generate large modulations of the Faraday waves. The analysis is verified by our numerical simulations and physical experiments. Finally, we observe experimentally a new form of steep standing wave with a large symmetric double-peaked crest, while simulation of the same forcing condition results in a sharper crest than seen previously. Both standing wave forms appear at a finite wave steepness far smaller than the maximum steepness for the classical standing wave and a surface tension far smaller than that for a Wilton ripple. In both physical and numerical experiments, a stronger second harmonic (in time) and temporal asymmetry in the wave forms suggest a 1:2 resonance due to a non-conventional quartet interaction. Increasing wave steepness leads to a new form of breaking standing waves in physical experiments.

The evolution of the cellular structure of the two-dimensional creeping flow induced by a rotating circular cylinder set in the centre of a rectangular channel is studied numerically and experimentally when the aspect ratio A increases from 1 to 7. In the calculations, depending on the value of A, either only series in terms of polar coordinates, or both matched polar and Cartesian coordinates series are employed to represent the stream function and an efficient least-squares method, very easy to program, is selected to satisfy some of the boundary conditions. For the experiments, a special technique which visualizes intermittently the paths of solid tracers during long times of exposure permits us to observe the fluid motion in the whole domain, even in the regions where the velocities are very small. An excellent measure of agreement between the numerical and experimental results is found. Thus it is clearly shown how, in the region beyond the rotating flow directly driven by the cylinder, the two main corner cells visualized at A = 1, develop with increasing A and then coalesce, to finally merge and give rise to a single central cell. This central cell develops in its turn, tending finally to the unbounded channel reference cell, after passing through a maximum length however. Owing to the very high precision of the calculations, many details of the flow development have been clearly shown, in particular the periodicity, with increasing A, of all the different phases, progressively inducing a succession of cells. The prediction that the angle of separation of the fluid boundaries of the cells tends towards the theoretical limit of 58.61° when the aspect ratio becomes large is also confirmed.

The electrification of particles embedded in a turbulent flow may cause hazards such as spark discharges but is also exploited in several industrial applications. Nonetheless, due to its complexity and sensitivity to the initial conditions, the process of build-up of particle charge is currently not well understood. In order to gain a deeper understanding of this phenomenon, we performed fully resolved numerical simulations of particle charging. More specifically, our study concerned the charging process of particles dispersed in a turbulent channel flow at a friction Reynolds number of $Re_{\unicode[STIX]{x1D70F}}=180$. Emphasis was placed on the analysis of the interplay between the different physical mechanisms underlying particle electrification, such as fluid turbulence, particle dynamics and particle collisions. Further, we investigated the influence of some important physical parameters. According to our simulations the charge build-up depends strongly on the particle Stokes number, $Stk$. In particular, at small Stokes numbers, $Stk=0.2$, the turbopheretic drift inhibits particle charging. By contrast, at moderate Stokes numbers, $Stk=2$, and low particle number densities, the electric charge builds up but cannot escape the viscous sublayer due to limited particle migration. However, in the case of high particle number densities, the charge is transported away from the wall via inter-particle charge diffusion. A further increase to $Stk=20$ leads to strong charging and particle-bound charge transport towards the bulk of the channel.