A theoretical model describing the response of a single-phase near-critical fluid to small-amplitude, high-frequency translational vibrations is developed on the basis of the multiple-scale and averaging methods. Additionally to the usual terms of thermal convection, the equations and boundary conditions contain new terms responsible for the generation of pulsating and average flows due to vibrational forcing and fluid compressibility. The effect of compressibility is taken into account both in the boundary layers and in the bulk. A number of classical problems of convection and thermoacoustics are considered on the basis of the new model.

We present a new adaptive control strategy to isolate and stabilize turbulent states in transitional, stably stratified plane Couette flow in which the gravitational acceleration (non-dimensionalized as the bulk Richardson number $Ri$) is adjusted in time to maintain the turbulent kinetic energy (TKE) of the flow. We demonstrate that applying this method at various stages of decaying stratified turbulence halts the decay process and allows a succession of intermediate turbulent states of decreasing energy to be isolated and stabilized. Once the energy of the initial flow becomes small enough, we identify a single minimal turbulent spot, and lower-energy states decay to laminar flow. Interestingly, the turbulent states which emerge from this process have very similar time-averaged $Ri$, but TKE levels different by an order of magnitude. The more energetic states consist of several turbulent spots, each qualitatively similar to the minimal turbulent spot. This suggests that the minimal turbulent spot may well be the lowest-energy turbulent state which forms a basic building block of stratified plane Couette flow. The fact that a minimal spot of turbulence can be stabilized, so that it neither decays nor grows, opens up exciting opportunities for further study of spatiotemporally intermittent stratified turbulence.

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.

Multidimensional instability of planar detonations, leading to cellular structures, is studied analytically near Chapman–Jouguet conditions, in the limit of small heat release, with small (Newtonian) differences between heat capacities, by using an expansion in a small parameter representing the ratio of the heat release to the thermal enthalpy of the fresh mixture. In this limit, the dynamics of detonations is governed by the interaction between the acoustic waves and the heat-release rate inside the inner detonation structure, the entropy–vorticity wave playing a negligible role at leading order. This situation is just opposite from that considered in our 1997 study of strongly overdriven detonations. The present analysis offers a step towards improving our understanding of the cellular structures of ordinary detonations, for which both the entropy–vorticity waves and the acoustic waves are involved in the instability mechanism. The relevant bifurcation parameter is identified, involving the degree of overdrive and the sensitivity of the rate of heat release to temperature at the Neumann state, and the onset of the instability is studied analytically for a realistic model of the inner structure of gaseous detonations.

Being motivated by the recent experiments on instabilities of the two-layer flows in the rotating annulus with super-rotating top, we perform a full stability analysis for such system in the shallow-water approximation. We use the collocation method which is benchmarked by comparison with analytically solvable one-layer shallow-water equations linearized about a state of cyclogeostrophic equilibrium. We describe different kinds of instabilities of the cyclogeostrophically balanced state of solid-body rotation of each layer (baroclinic, Rossby–Kelvin (RK) and Kelvin–Helmholtz (KH) instabilities), and give the corresponding growth rates and the structure of the unstable modes. We obtain the full stability diagram in the space of parameters of the problem and demonstrate the existence of crossover regions where baroclinic and RK, and RK and KH instabilities, respectively, compete having similar growth rates.

A study has been made of baroclinic instability in a differentially heated, rotating fluid annulus whose channel width varies azimuthally. Both laboratory experiments and an a.nalytica1 model employing a linear normal-mode analysis have been used. The experiments show three types of flow. For slow rotation the flow is 'symmetric’, whereas at high rotation speeds baroclinic waves occur at all azimuths. At intermediate rotation speeds it is possible to have a mixed flow which is ‘symmetric’ in the narrow part but has baroclinic waves in the wide part of the annulus. This result suggested the analytical investigation of the stability of a barocIinic flow whose meridional scale varies downstream. It was found that this model also permits three possible types of flow: everywhere stable, everywhere unstable, and also a mixed flow which is locally unstable where the meridional scale is largest but locally stable where the scale is smallest.

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer-thickness Reynolds number were 4 and 105, respectively. The adverse pressure gradient was induced by an externally generated, conical shock wave.

Mean and time-averaged fluctuating-flow data, including the experimental Reynolds shear stresses and experimental turbulent heat-transfer rates, are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed.

From the results of the investigation, it is concluded that the shock-wave/boundary-layer interaction significantly alters the shear-stress characteristics of the boundary layer.

Free-surface flow over a bottom topography with an asymptotic depth change (a ‘step’) is considered for different ranges of Froude numbers varying from subcritical, transcritical, to supercritical. For the subcritical case, a linear model indicates that a train of transient waves propagates upstream and eventually alters the conditions there. This leading-order upstream influence is shown to have profound effects on higher-order perturbation models as well as on the Froude number which has been conventionally defined in terms of the steady-state upstream depth. For the transcritical case, a forced Korteweg–de Vries (fKdV) equation is derived, and the numerical solution of this equation reveals a surprisingly conspicuous distinction between positive and negative forcings. It is shown that for a negative forcing, there exists a physically realistic nonlinear steady state and our preliminary results indicate that this steady state is very likely to be stable. Clearly in contrast to previous findings associated with other types of forcings, such a steady state in the transcritical regime has never been reported before. For transcritical flows with Froude number less than one, the upstream influence discovered for the subcritical case reappears.

The governing equations for the two-point correlations of the turbulent fluctuating velocity in the temporally evolving wake were analysed to determine whether they could have equilibrium similarity solutions. It was found that these equations could have such solutions for a finite-Reynolds-number wake, where the two-point velocity correlations could be written as a product of a time-dependent scale and a function dependent only on similarity variables. It is therefore possible to collapse the two-point measures of all the scales of motions in the temporally evolving wake using a single set of similarity variables. As in an earlier single-point analysis, it was found that the governing equations for the equilibrium similarity solutions could not be reduced to a form that was independent of a growth-rate dependent parameter. Thus, there is not a single ‘universal’ solution that describes the state of the large-scale structures, so that the large-scale structures in the far field may depend on how the flow is generated.

The predictions of the similarity analysis were compared to the data from two direct numerical simulations of the temporally evolving wakes examined previously. It was found that the two-point velocity spectra of these temporally evolving wakes collapsed reasonably well over the entire range of scales when they were scaled in the manner deduced from the equilibrium similarity analysis. Thus, actual flows do seem to evolve in a manner consistent with the equilibrium similarity solutions.

The subject of this note is the behaviour of three-dimensional small disturbances to plane parallel flows, which have a variation in the direction normal to the plane of mean flow, in relation to two-dimensional disturbances which vary in the plane of mean flow only. It was pointed out by Squire (1933) that, in linearized theory, the disturbancewhichisneutrallystable at the criticalReynolds number R, is two-dimensional in form. More recently interest has turned to the question as to which kind of disturbance is most rapidly amplified at a given Reynolds number above the critical. Jungclaus (1957) pointed out that for certain values of R and of the resolved wavelength in the plane of mean flow, three-dimensional disturbances may be more unstable than plane ones. Recently, Watson (1960) has shown further that a two-dimensional disturbance is the one most rapidly amplified in a certain range of R starting from the critical. In thi8 note we take a slightly different view of the problem which enables us to define specifically the upper end of this range of R, when it exists.

We simulate shear flow past a stationary monolayer of spherical particles embedded in a flat gas–liquid interface. This problem is relevant to the understanding of the microhydrodynamics of particle-laden interfacial structures, including particle-laden drops, bubbles and foams. The combination of the free-shear condition at the gas–liquid interface and the no-slip condition at the particle surfaces gives rise to a velocity slip at the particle-laden interface. We study the characteristics of the flow near the monolayer, focusing on slip velocity, slip length and interfacial shear stress. Two microstructures are compared: a square array, and a reticulated array mimicking a percolating network of aggregated particles. We demonstrate that the scaling laws for the dependence of the slip length on solid area fraction developed for flow past superhydrophobic microstructured surfaces apply to the case of interfacial particles. The calculated slip lengths are in general smaller that those reported for microstructured superhydrophobic surfaces. This difference, which is due to the significant protrusion of the spherical particles in the liquid, can be accounted for in the case of the square array by an approximate argument. For a given area fraction, the reticulated array yields a larger slip length than the square array. We analyse the hydrodynamic forces acting on the particles, and the corresponding tangential stress exerted by the bulk ‘subphase’.

Intermittency effects are numerically studied in turbulent bubbling Rayleigh–Bénard (RB) flow and compared to the standard RB case. The vapour bubbles are modelled with a Euler–Lagrangian scheme and are two-way coupled to the flow and temperature fields, both mechanically and thermally. To quantify the degree of intermittency we use probability density functions, structure functions, extended self-similarity (ESS) and generalized extended self-similarity (GESS) for both temperature and velocity differences. For the standard RB case we reproduce scaling very close to the Obukhov–Corrsin values common for a passive scalar and the corresponding relatively strong intermittency for the temperature fluctuations, which are known to originate from sharp temperature fronts. These sharp fronts are smoothed by the vapour bubbles owing to their heat capacity, leading to much less intermittency in the temperature but also in the velocity field in bubbling thermal convection.