A bubble translating through a continuous liquid (i.e. Newtonian) phase moves as a sphere when inertial and viscous forces are small relative to capillary forces. Spherical bubbles with stress-free interfaces do not retain wakes at their trailing ends as inertial forces become important (increasing Reynolds number). This is in contrast to translating spheres with immobile interfaces in which flow separation and wake formation occurs at order-one Reynolds number. Surfactants present in the continuous phase adsorb onto a bubble surface as it translates, and affect the interfacial mobility by creating tension gradient forces. Adsorbed surfactant is convected to the trailing end of the bubble, lowers the tension there relative to the front, and creates a tension gradient which reduces the surface flow. For low bulk concentrations of surfactant (or if kinetic exchange between bulk and surface is slow relative to convection), diffusion towards the surface is much slower than convection, and surfactant is swept into an immobile cap at the trailing end. As with solid spheres, these caps entrain wakes at order-one Reynolds number. In adsorptive bubble technologies where solutes transfer between the bubble and the continuous phase, usually through thin boundary layers around the bubble surface (high Péclet number), these wakes generally form owing to the presence of surfactant impurities. The wake presence retards the interphase transfer displacing the thin boundary layer towards the front end of the bubble; as mass transfer through the wake is much slower than through the boundary layer, the mass transfer is reduced.

Our recent theoretical research has demonstrated that at low Reynolds numbers, the mobility of a surfactant-retarded bubble interface can be increased by raising the bulk concentration of a surfactant which kinetically rapidly exchanges between the surface and the bulk. At high bulk concentrations the interface saturates with surfactant, effectively removing the tension gradient. In this paper, we demonstrate theoretically that this interfacial control is still realized at order-one Reynolds numbers, and, more importantly, we show that the control can be used to manipulate the formation, size and ultimately the disappearance of a wake. This wake removal mechanism has the potential to dramatically increase the interphase transfer in adsorptive bubble technologies.

A theory is constructed for rotating plane Couette flow of ferrofluid that is subject to the field generated by a periodic array of magnets. The system that is analysed contains a substantial lateral magnetic buoyancy, or magnetic gravity, allowing the configuration to be used in experimental studies of stratified shear flows in a connected geometry.

However, the spatial variation of the magnetic vector field of the magnet stack leads to magnetically generated wavy flows via the action of flow vorticity on the particle orientation in the suspension. The basic rotating Couette flow instabilities may also be affected by the same mechanism, which is sometimes referred to as rotational or ‘magnetic viscosity’. Theoretical calculations show that the directly excited wavy flows are generally small, for anticipated experimental conditions, except when they resonate with the natural linear instabilities of the Couette flow. A weakly nonlinear analysis is carried out in order to predict the behaviour in these cases. Magnetic effects stabilize the fundamental roll instability of rotating Couette flow by about 10% for a typical laboratory realization.

The flow resulting from suddenly heating a semi-infinite, vertical wall immersed in a stationary fluid has been described in the following way: at any fixed position on the plate, the flow is initially described as one-dimensional and unsteady, as though the plate is doubly infinite; at some later time, which depends on the position, a transition occurs in the flow, known as the leading-edge effect (LEE), and the flow becomes two-dimensional and steady. The transition is characterized by the presence of oscillatory behaviour in the flow parameters, and moves with a speed greater than the maximum fluid velocities present in the boundary layer. A stability analysis of the one-dimensional boundary layer flow performed by Armfield & Patterson (1992) showed that the arrival times of the LEE determined by numerical experiment were predicted well by the speed of the fastest travelling waves arising from a perturbation of the initial one-dimensional flow. In this paper, we describe an experimental investigation of the transient behaviour of the boundary layer on a suddenly heated semi-infinite plate for a range of Rayleigh and Prandtl numbers. The experimental results confirm that the arrival times of the LEE at specific locations along the plate, relatively close to the leading edge, are predicted well by the Armfield & Patterson theory. Further, the periods of the oscillations observed following the LEE are consistent with the period of the maximally amplified waves calculated from the stability result. The experiments also confirm the presence of an alternative mechanism for the transition from one-dimensional to two-dimensional flow, which occurs in advance of the arrival of the LEE at positions further from the leading edge.

We present a new mechanism for generation of near-wall streamwise vortices – which dominate turbulence phenomena in boundary layers – using linear perturbation analysis and direct numerical simulations of turbulent channel flow. The base flow, consisting of the mean velocity profile and low-speed streaks (free from any initial vortices), is shown to be linearly unstable to sinuous normal modes only for relatively strong streaks, i.e. for wall inclination angles of streak vortex lines exceeding 50°. Analysis of streaks extracted from fully developed near-wall turbulence indicates that about 20% of streak regions in the buffer layer exceed the strength threshold for instability. More importantly, these unstable streaks exhibit only moderate (twofold) normal-mode amplification, the growth being arrested by self-annihilation of streak-flank normal vorticity due to viscous cross-diffusion. We present here an alternative, streak transient growth (STG) mechanism, capable of producing much larger (tenfold) linear ampliflcation of x-dependent disturbances. Note the distinction of STG – responsible for perturbation growth on a streak velocity distribution U(y, z) – from prior transient growth analyses of the (streakless) mean velocity U(y). We reveal that streamwise vortices are generated from the more numerous normal-mode-stable streaks, via a new STG-based scenario: (i) transient growth of perturbations leading to formation of a sheet of streamwise vorticity ωx (by a ‘shearing’ mechanism of vorticity generation), (ii) growth of sinuous streak waviness and hence ∂u/∂x as STG reaches nonlinear amplitude, and (iii) the ωx sheet’s collapse via stretching by ∂u/∂x (rather than rollup) into streamwise vortices. Significantly, the three-dimensional features of the (instantaneous) streamwise vortices of x-alternating sign generated by STG agree well with the (ensemble-averaged) coherent structures educed from fully turbulent flow. The STG-induced formation of internal shear layers, along with quadrant Reynolds stresses and other turbulence measures, also agree well with fully developed turbulence. Results indicate the prominent – possibly dominant – role of this new, transient-growth-based vortex generation scenario, and suggest interesting possibilities for robust control of drag and heat transfer.

Movies of the breakup of viscous and viscoelastic drops in the high-speed airstream behind a shock wave in a shock tube have been reported by Joseph, Belanger & Beavers (1999). They performed a Rayleigh–Taylor stability analysis for the initial breakup of a drop of Newtonian liquid and found that the most unstable Rayleigh–Taylor wave fits nearly perfectly with waves measured on enhanced images of drops from the movies, but the effects of viscosity cannot be neglected. Here we construct a Rayleigh–Taylor stability analysis for an Oldroyd-B fluid using measured data for acceleration, density, viscosity and relaxation time λ1. The most unstable wave is a sensitive function of the retardation time λ2 which fits experiments when λ2/λ1 = O(10-3). The growth rates for the most unstable wave are much larger than for the comparable viscous drop, which agrees with the surprising fact that the breakup times for viscoelastic drops are shorter. We construct an approximate analysis of Rayleigh–Taylor instability based on viscoelastic potential flow which gives rise to nearly the same dispersion relation as the unapproximated analysis.

The problem of the spreading of a granular mass released at the top of a rough inclined plane was investigated. The evolution of the avalanche was measured experimentally from the initiation up to the deposit using a Moiré image-processing technique. The results are quantitatively compared with the prediction of an hydrodynamic model based on depth-averaged equations. In the model, the interaction between the flowing layer and the rough bottom is described by a non-trivial friction force whose expression is derived from measurements on steady uniform flows. We show that the spreading of the mass is quantitatively predicted by the model when the mass is released on a plane free of particles. When an avalanche is triggered on an initially static layer, the model fails in quantitatively predicting the propagation but qualitatively captures the evolution.

We consider the problem of a thin liquid layer falling down an inclined plate that is subjected to non-uniform heating. The plate temperature is assumed to be linearly distributed and both directions of the temperature gradient with respect to the flow are investigated. The film flow is not only influenced by gravity and mean surface tension, but in addition by the thermocapillary force acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. Applying the long-wave theory, a nonlinear evolution equation is derived. When the plate temperature is decreasing in the downstream direction, linear stability analysis exhibits a film stabilization, compared to a uniformly heated film. In contrast, for increasing temperature along the plate, the film becomes less stable. Numerical solution of the evolution equation indicates the existence of permanent finite-amplitude waves of different kinds. The shape of the waves depends mainly on the mean flow and the mean surface tension, but their amplitudes and phase speeds are influenced by thermocapillarity.

Oblique transition was experimentally investigated in a Blasius boundary layer formed on a flat plate. This transition mechanism was provoked by exciting a pair of oppositely oriented oblique Orr–Sommerfeld (O–S) modes given by (ω/ωts, ±β/βts) = (1, ±1) in the frequency-wavenumber (spanwise) space. Surface waviness with height Δh and a well-defined wavenumber spectrum that is synchronized with the neutral O–S wavenumber at Branch I, (αw, ±βw) = (αts,I, ±βts,I), was used to provide a steady velocity perturbation in the near-wall region. A planar downstream-travelling acoustic wave of amplitude ε was created to temporally excite the flow near the resonance frequency, ωts(= 2πfo), of an unstable eigenmode corresponding to kts = kw (where k =±[α2+β2]1/2). Possible mechanisms leading to laminar-to-turbulent breakdown were examined for various forcing combinations, εΔh. For small values of εΔh, a peak-valley structure corresponding to a spanwise wavenumber of 2βw was observed. As expected, the maximum r.m.s. narrow-band streamwise velocity fluctuations, ut(fo), occur at peak locations, which correspond to regions with mean streamwise velocity, U, deficits. For the largest value of εΔh, significant mean-flow distortion was observed in the spanwise profiles of U. Large spanwise velocity gradients, [mid ]dU/dζ[mid ], exist between peaks and valleys and appear to generate an explosive growth in the velocity fluctuations. The maximum values of ut no longer occur at peak locations of the stationary structure but at locations of spanwise inflection points. The magnitude of ut scales with [mid ]dU/dζ[mid ]. A nonlinear interaction of two non-stationary modes was conjectured as a possible mechanism for the enhancement of the streak ampliflcation rate.

Large-eddy simulations of a compressible turbulent square duct flow at low Mach number are described. First, we consider the isothermal case with all the walls at the same temperature: good agreement with previous incompressible DNS and LES results is obtained both for the statistical quantities and for the turbulent structures. A heated duct with a higher temperature prescribed at one wall is then considered and the intensity of the heating is varied widely. The increase of the viscosity with temperature in the vicinity of the heated wall turns out to play a major rôle. We observe an amplification of the near-wall secondary flows, a decrease of the turbulent fluctuations in the near-wall region and, conversely, their enhancement in the outer wall region. The increase of the viscous thickness with heating implies a significant augmentation of the size of the characteristic flow structures such as the low- and high-speed streaks, the ejections and the quasi-longitudinal vorticity structures. For strong enough heating, the size limitation imposed by the lateral walls leads to a single low-speed streak located near the duct central plane surrounded by two high-speed streaks on both sides. Violent ejections of slow and hot fluid from the heated wall are observed, linked with the central low-speed streak. A selective statistical sampling of the most violent ejection events reveals that the entrainment of cold fluid, originated from the duct core, at the base of the ejection and its subsequent expansion amplifies the ejection intensity.

In many geophysical, environmental and industrial situations, a finite volume of fluid with a density different to the ambient is released on a sloping boundary. This leads to the formation of a gravity current travelling up, down and across the slope. We present novel laboratory experiments in which the dense fluid spreads both down-slope (and initially up-slope) and laterally across the slope. The position, shape and dilution of the current are determined through video and conductivity measurements for moderate slopes (5° to 20°). The entrainment coefficient for different slopes is calculated from the experimental results and is found to depend very little on the slope. The value agrees well with previously published values for entrainment into gravity currents on a horizontal surface. The experimental measurements are compared with previous shallow-water models and with a new wedge integral model developed and presented here. It is concluded that these simplified models do not capture all the significant features of the flow. In the models, the current takes the form of a wedge which travels down the slope, but the experiments show the formation of a more complicated current. It is found that the wedge integral model over-predicts the length and width of the gravity current but gives fair agreement with the measured densities in the head. The initial stages of the flow, during which time the wedge shape develops, are studied. It is found that although the influence of the slope is seen relatively quickly for moderate slopes, the time taken for the wedge to develop is much longer. The implications of these findings for safety analysis are briefly discussed.

The effect of random wave fields on passive tracer spatial variations is studied. We derive a closed-form expression for the spatial autocorrelation function (or power spectrum) of the tracer fluctuations that is quantitatively accurate so long as wave field nonlinearities are small. The theory is illustrated for the case of long internal gravity waves in the ocean. We find that even if the (rear face of the) spectrum of the advecting velocity field is a pure power law, the tracer spectrum has two separate power law subranges. Most important to oceanographic applications, in the larger scale subrange, the effective horizontal compressibility of the wave velocity field becomes a dominant factor of the tracer variations. In such cases, the concentration spectrum becomes approximately proportional to the spectrum of the wave potential energy. The latter, which decays with increasing wavenumber much more rapidly than that known for two-dimensional eddy turbulence, is confirmed by satellite observations in wave-dominated ocean regions. As an additional confirmation of the theory, we demonstrate the occurrence of spectral peaks at wavenumbers corresponding to the semi-diurnal tide frequency.

This paper analyses the generation of sound and Tollmien–Schlichting (T–S) waves in a compressible boundary layer that is subject to unsteady suction and injection. An asymptotic approach based on the triple-deck formulation has been developed to calculate the sound field. It is shown that in addition to the three familiar asymptotic regions that govern the near-field hydrodynamic motion, an extra outer region controlling the sound radiation must be introduced. The near-field solution is sought via an asymptotic expansion in ascending powers of ε = R−1/8, where R is the global Reynolds number. The first three terms in the asymptotic series are found to act as quadrupole, dipole and monopole sources respectively, and make equal order-of-magnitude contributions to the acoustic far field. The analysis also allows the amplitude of the excited T–S waves to be determined to O(ε) accuracy. It is believed that the flow structure and solution procedure may be used to solve a range of aeroacoustic problems.

The transition to unsteady flow and the dynamics of moderate-Reynolds-number flows in unbounded and wall-bounded periodic arrays of aligned cylinders are examined using lattice-Boltzmann simulations. The simulations are compared to experiments, which necessarily have bounding walls. With bounding walls, the transition to unsteady flow is accompanied by a loss of spatial periodicity, and the temporal fluctuations are chaotic at much smaller Reynolds numbers. The walls, therefore, affect the unsteady flows everywhere in the domain. Consistency between experiments and simulations is established by examining the wake lengths for steady flows and the fundamental frequencies at higher Reynolds numbers, both as a function of the Reynolds number. Simulations are used to examine the velocity fluctuations, flow topologies, and the fluctuating forces on the cylinders.

This article presents an analytical and experimental study of magnetohydrodynamic Rayleigh–Bénard convection in a large aspect ratio, 20[ratio ]10[ratio ]1, rectangular box. The test fluid is a eutectic sodium potassium Na22K78 alloy with a small Prandtl number of Pr≈0:02. The experimental setup covers Rayleigh numbers in the range 103< Ra<8×104 and Chandrasekhar numbers 0[les ]Q[les ]1.44×106 or Hartmann numbers 0[les ]M[les ]1200, respectively.

When a horizontal magnetic field is imposed on a heated liquid metal layer, the electromagnetic forces give rise to a transition of the three-dimensional convective roll pattern into a quasi-two-dimensional flow pattern in such a way that convective rolls become more and more aligned with the magnetic field. A linear stability analysis based on two-dimensional model equations shows that the critical Rayleigh number for the onset of convection of quasi-two-dimensional flow is shifted to significantly higher values due to Hartmann braking at walls perpendicular to the magnetic field. This finding is experimentally confirmed by measured Nusselt numbers. Moreover, the experiments show that the convective heat transport at supercritical conditions is clearly diminished. Adjacent to the onset of convection there is a significant region of stationary convection with significant convective heat transfer before the flow proceeds to time-dependent convection. However, in spite of the Joule dissipation effect there is a certain range of magnetic field intensities where an enhanced heat transfer is observed. Estimates of the local isotropy properties of the flow by a four-element temperature probe demonstrate that the increase in convective heat transport is accompanied by the formation of strong non-isotropic time-dependent flow in the form of large-scale convective rolls aligned with the magnetic field which exhibit a simpler temporal structure compared to ordinary hydrodynamic flow and which are very effective for the convective heat transport.

The constant initial speed of propagation (V) of heavy gravity currents, of density ρC, released from behind a lock and along the bottom boundary of a tank containing a linearly stratified fluid has been measured experimentally and calculated numerically. The density difference, bottom to top, of the stratification is (ρb−ρ0) and its intrinsic frequency is N. For a given ratio of the depth of released fluid (h) to total depth (H) it has been found that the dimensionless internal Froude number, Fr = V/NH, is independent of the length of the lock and is a logarithmic function of a parameter R = (ρC−ρ0)/(ρb−ρ0), except at small values of h/H and R close to unity. This parameter, R, is one possible measure of the relative strength of the current (ρC−ρ0) and stratification (ρb−ρ0). The distance propagated by the current before this constant velocity regime ended (Xtr), scaled by h, has been found to be a unique function of Fr for all states tested. After this phase of the motion, for subcritical values of Fr, i.e. less than 1/π, internal wave interactions with the current resulted in an oscillation of the velocity of its leading edge. For supercritical values, velocity decay was monotonic for the geometries tested. A two-dimensional numerical model incorporating a no-slip bottom boundary condition has been found to agree with the experimental velocity magnitudes to within ±1:5%.

An experimental investigation of a homogeneous swarm of rising bubbles is presented. The experimental arrangement ensures that all the bubbles have the same equivalent radius, a = 1.25 mm. This particular size corresponds to high-Reynolds-number ellipsoidal rising bubbles. The gas volume fractions α is small, ranging from 0.5 to 1.05%. The results are compared with the reference situation of a single rising bubble, which was investigated in a previous work. From the use of conditional statistics, the existence of two regions in which the liquid velocity fluctuations are of a different nature are distinguished. In the vicinity of the bubbles, the liquid fluctuations are the same as those measured close to a single rising bubble. They therefore do not depend on α. Far from the bubble, the liquid fluctuations are controlled by the nonlinear interactions between the wakes of all the bubbles. Their probability density function scales as α0.4, exhibiting a self-similar behaviour. The total fluctuation combines the contributions of these two regions weighted by the fraction of the liquid volume they occupy. The contribution of the bubble vicinity is thus shown to vary linearly with α while the wake contribution does not. Both are non-isotropic since strong upward vertical fluctuations are more probable.

We apply a new analytic technique, namely the homotopy analysis method, to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate. An explicit analytic solution of the temperature distributions is obtained in general cases and recurrence formulae of the corresponding constant coefficients are given. In the cases of constant plate temperature distribution and constant plate heat flux, the first-order derivative of the temperature on the plate at the 30th order of approximation is given. The convergence regions of these two formulae are greatly enlarged by the Padé technique. They agree well with numerical results in a very large region of Prandtl number 1[les ]Pr[les ]50 and therefore can be applied without interpolations.

We present an experimental and theoretical description of the kinetics of coalescence of two water drops on a plane solid surface. The case of partial wetting is considered. The drops are in an atmosphere of nitrogen saturated with water where they grow by condensation and eventually touch each other and coalesce. A new convex composite drop is rapidly formed that then exponentially and slowly relaxes to an equilibrium hemispherical cap. The characteristic relaxation time is proportional to the drop radius R* at final equilibrium. This relaxation time appears to be nearly 107 times larger than the bulk capillary relaxation time tb = R*η/σ, where σ is the gas–liquid surface tension and η is the liquid shear viscosity.

In order to explain this extremely large relaxation time, we consider a model that involves an Arrhenius kinetic factor resulting from a liquid–vapour phase change in the vicinity of the contact line. The model results in a large relaxation time of order tb exp(L/[Rscr ]T) where L is the molar latent heat of vaporization, [Rscr ] is the gas constant and T is the temperature. We model the late time relaxation for a near spherical cap and find an exponential relaxation whose typical time scale agrees reasonably well with the experiment.