Receptivity of a high-speed boundary layer on a flat plate to acoustic disturbances is investigated using a combined numerical and asymptotic approach. The leading-edge receptivity problem is discussed with emphasis on physical mechanisms associated with scattering and diffraction of acoustic waves. Analytical solutions provide insight into the interplay of these mechanisms as a function of the angle of incidence of external acoustic waves. The theoretical predictions are in good agreement with the wind-tunnel experimental data of Maslov et al. obtained at free-stream Mach number 6. The leading-edge receptivity model is incorporated into the multiple-modes method to account for the inter-modal exchange downstream from the leading edge. This combined modelling resembles basic features of the direct numerical simulation of Ma & Zhong. A comparative analysis of the leading-edge receptivity and the inter-modal exchange associated with non-parallel effects is presented. The theory allows fast evaluation of the receptivity coefficients and clarifies the physics of the receptivity process. The theoretical results may guide further direct numerical simulations and experimental studies of boundary layer receptivity at supersonic and hypersonic speeds.

A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately.

It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.

The influence of large variations of viscosity on convection in a layer of fluid heated from below has been investigated. Solutions for the flow and temperature fields were obtained numerically assuming infinite Prandtl number, free-surface boundary conditions, and two-dimensional motion of fixed horizontal wavelength. The effects of a temperature-dependent and a depth-dependent viscosity were each studied; calculations were also carried out using a temperature- and depth-dependent viscosity model appropriate to the earth's mantle.

Direct numerical simulations of decaying high-Reynolds-number turbulence are presented at resolutions up to 8002 for general periodic flows and 20482 for periodic flows with large-scale symmetries. For turbulence initially excited at large scales, we characterize a transition of the inertial energy-spectrum exponent from n ≈ − 4 at early times to n ≈ − 3 when the turbulence becomes more mature. In physical space, the first regime is associated with isolated vorticity-gradient sheets, as predicted by Saffman (1971). The second regime, which is essentially statistical, corresponds to an enstrophy cascade (Kraichnan 1967; Batchelor 1969) and reflects the formation of layers resulting from the packing of vorticity-gradient sheets. In addition to these small-scale structures, the simulation displays vorticity macro-eddies which will survive long after the vorticity-gradient layers have been dissipated (McWilliams 1984). We validate the linear description of two-dimensional turbulence suggested by Weiss (1981), which predicts that coherent vortices will survive in regions where vorticity dominates strain, while vorticity-gradient sheets will be formed in regions where strain dominates. We show that this analysis remains valid even after vorticity-gradient sheets have been formed.

The stability of natural convection of a viscous fluid in a vertical slot having isothermal side walls of different temperatures is investigated analytically. Both the conduction and boundary-layer régimes are found to be unstable with respect to stationary disturbances in the form of multicellular secondary flows. Theoretical predictions of the critical Rayleigh number and of the form of the secondary flow are verified by experimental measurements.

The performance of an electromagnetic flowmeter head is assessed in terms of a weight vector W such that the output voltage ∝ ∫ v. Wdτ, where v is the velocity and τ the flowmeter volume. The condition curl W = 0 with W → 0 at ∞ is shown to be necessary and sufficient for the velocity to depend only on the flow rate and not on the flow pattern. A class of such ‘ideal’ meters is described. It is shown that meters with point electrodes can never be ideal but may, with considerable complication of the magnetic field, be made immune to asymmetric velocity-profile variations if the flow is rectilinear.

Particle image velocimetry experiments were performed to study the impact of realistic roughness on the spatial structure of wall turbulence at moderate Reynolds number. This roughness was replicated from an actual turbine blade damaged by deposition of foreign materials and its features are quite distinct from most roughness characterizations previously considered as it is highly irregular and embodies a broad range of topographical scales. The spatial structure of flow over this rough surface near the outer edge of the roughness sublayer is contrasted with that of smooth-wall flow to identify any structural modifications due to roughness. Hairpin vortex packets are observed in the outer layer of the rough-wall flow and are found to contribute heavily to the Reynolds shear stress, consistent with smooth-wall flow. While similar qualitative consistency is observed in comparisons of smooth- and rough-wall two-point correlations, some quantitative differences are also apparent. In particular, a reduction in the streamwise extent of two-point correlations of streamwise velocity is noted which could be indicative of a roughness-induced modification of outer-layer vortex organization. Proper orthogonal decomposition analysis reveals the streamwise coherence of the larger scales to be most sensitive to roughness while the spatial characteristics of the smaller scales appear relatively insensitive to such effects.

Nonlinear oscillations and other motions of large axially symmetric liquid drops in zero gravity are studied numerically by a boundary-integral method. The effect of small viscosity is included in the computations by retaining first-order viscous terms in the normal stress boundary condition. This is accomplished by making use of a partial solution of the boundary-layer equations which describe the weak vortical surface layer. Small viscosity is found to have a relatively large effect on resonant-mode coupling phenomena.

This paper is concerned with the behaviour of buoyant plumes driven by a source of bubbles. It is shown experimentally that, when a bubble plume rises through a stratified environment, fluid can be transported vertically for some distance and then some of this fluid can leave the plume and spread out horizontally at its own density level. A simple plume model which regards the plume as a single entity is discussed in order to make a first assessment of the effects of gas expansion and bubble slip velocity in this stratified case. However, the experiments reveal a more complicated plume structure in which the bubbles remain in the centre part of the plume, and only the outer part of the plume spreads out into the environment at certain levels. On the basis of these observations a double-plume model is proposed which regards the plume as being composed of two parts: an inner circular plume (which contains all the bubbles of gas) and an outer annular plume.

Results of laboratory experiments are used to determine the morphology and the ascent rate of growing buoyant plumes in a homogeneous, viscous fluid. The plumes were formed by injecting a glucose solution through a small orifice into another glucose solution of different density. Two classes of creeping (low-Reynolds-number) plumes are investigated: (i) diapiric plumes, for which the plume viscosity is approximately equal to the ambient-fluid viscosity, and (ii) cavity plumes, for which the plume fluid is much less viscous than the ambient fluid. Fully developed diapirs consist of a tapered cylindrical stem capped by a mushroom-shaped vortex at its leading edge. Fully developed cavity plumes consist of a nearly spherical chamber connected to the source by a narrow umbilical conduit. It is observed that the ascent velocity of cavity plumes increases with time as t⅖. The ascent velocity of diapirs is found to be proportional to the terminal velocity of a cylinder moving parallel to its axis. The presence of pre-existing conduits alters the morphology of cavity plumes and greatly increases their ascent rate. Fossil conduits act as plume guides by offering low-resistance ascent paths. Finally, a series of experiments have been made on the interaction between cavity plumes and a large-scale background circulation. A low-viscosity plume generated by a source towed steadily through a highly viscous fluid breaks into a chain of regularly spaced, individual cavities, as first demonstrated by Skilbeck & Whitehead. The cavities ascend as an inclined linear array of Stokes droplets. Dimensional analysis is used to derive scaling laws for the cavity volumes and their replication rate in terms of the source parameters and the tow speed. The qualitative results from these experiments generally lend support to the hypothesis that buoyant plumes in the Earth's mantle are the source of hot-spot volcanism. In particular the experiments suggest an explanation for the observation that hot spots remain nearly fixed in the presence of mantle convection.

The paper presents the results of a detailed experimental examination of fully developed asymmetric flow between parallel planes. The asymmetry was introduced by roughening one of the planes while the other was left smooth; the ratio of the shear stresses at the two surfaces was typically about 4:1.

The main emphasis of the research has been on establishing the turbulence structure, particularly in the central region of the channel where the two dissimilar wall flows (generated by the smooth and rough surfaces) interact. Measurements have included profiles of all non-zero double and triple velocity correlations; spectra of the same correlations at several positions in the channel; skewness and flatness factors; and lateral two-point space correlations of the streamwise velocity fluctuation.

The region of greatest interaction is characterized by strong diffusional transport of turbulent shear stress and kinetic energy from the rough towards the smooth wall region, giving rise, inter alia, to an appreciable separation between the planes of zero shear stress and maximum mean velocity. The profiles of length scales of the larger-scale motion are, in contrast to the turbulent velocity field, nearly symmetric. Moreover, it appears that at high Reynolds numbers the small-scale motion may in many respects be treated as isotropic.

This article gives a review of six areas of current activity and importance in aero-acoustics, including (i) the generation of sound and vorticity by vorticity and sound, respectively, (ii) the basis for, and consequences of, the application of a Kutta condition in unsteady leading- and trailing-edge flows, and (iii) the suppression or amplification of broadband hydrodynamic and acoustic fields in a jet under the influence of weak discrete tone forcing. The intention is also to promote acceptance once again of acoustics as a serious branch of fluid mechanics.

We investigate the flow induced by a localized insoluble surfactant on a thin film. This problem is intended to model the behaviour of the lung's thin-film lining after an aerosol droplet lands on its surface. The surfactant-induced surface-tension gradients drive convection (Marangoni convection) within the film, disrupting the film surface and causing the surfactant to spread. The surfactant may also spread on the film's surface by surface diffusion without inducing convection. Gravity provides a restoring force that decreases film disturbances.

Lubrication theory is employed to derive equations that describe the evolution of the film thickness and surfactant concentration. A nonlinear surface-tension equation of state describes the relationship between the surfactant concentration and the surface tension. Solutions of the evolution equations are found numerically using the method of lines and analytically under limiting cases of small and large surface diffusivity. The results elucidate the behaviour of the thin-film/surfactant system.

We find that surface-tension-induced convection creates film disturbances that increase the film thickness near the surfactant's leading edge, and thins the film in the central region. Surface diffusion causes more rapid spreading of the surfactant, and decreases the film disturbances. Gravity decreases the film disturbances by creating bi-directional flow in the form of a ring vortex. This behaviour may have implications for the delivery of medications or toxins by aerosol inhalation.

Boundary-forced stratified turbulence is studied in the prototypical case of turbulent channel flow subject to stable stratification. The large-eddy simulation approach is used with a mixed subgrid model that involves a dynamic eddy viscosity component and a scale-similarity component. After an initial transient, the flow reaches a new balanced state corresponding to active wall-bounded turbulence with reduced vertical transport which, for the cases in our study with moderate-to-large levels of stratification, coexists with internal wave activity in the core of the channel. A systematic reduction of turbulence levels, density fluctuations and associated vertical transport with increasing stratification is observed. Countergradient buoyancy flux is observed in the outer region for sufficiently high stratification.

Mixing of the density field in stratified channel flow results from turbulent events generated near the boundaries that couple with the outer, more stable flow. The vertical density structure is thus of interest for analogous boundary-forced mixing situations in geophysical flows. It is found that, with increasing stratification, the mean density profile becomes sharper in the central region between the two turbulent layers at the upper and lower walls, similar to observations in field measurements as well as laboratory experiments with analogous density-mixing situations.

Channel flow is strongly inhomogeneous with alternative choices for the Richardson number. In spite of these complications, the gradient Richardson number, Rig, appears to be the important local determinant of buoyancy effects. All simulated cases show that correlation coefficients associated with vertical transport collapse from their nominal unstratified values over a narrow range, 0.15 < Rig < 0.25. The vertical turbulent Froude number, Frw, has an O(1) value across most of the channel. It is remarkable that stratified channel flow, with such a large variation of overall density difference (factor of 26) between cases, shows a relatively universal behaviour of correlation coefficients and vertical Froude number when plotted as a function of Rig. The visualizations show wavy motion in the core region where the gradient Richardson number, Rig, is large and low-speed streaks in the near-wall region, typical of unstratified channel flow, where Rig is small. It appears from the visualizations that, with increasing stratification, the region with wavy motion progressively encroaches into the zone with active turbulence; the location of Rig ≃ 0.2 roughly corresponds to the boundary between the two zones.

A general theory is put forward for the effect of wall proximity on the Stokes resistance of an arbitrary particle. The theory is developed completely for the case where the motion of the particle is parallel to a principal axis of resistance. In this case, the wall-effect correction can be calculated entirely from a knowledge of the force experienced by the particle in an unbounded fluid, providing (i) that the wall correction is already known for a spherical particle and (ii) that the particle is small in comparison to its distance from the boundary. Experimental data are cited which confirm the theory. The theory is extended to the wall effect on a particle rotating near a boundary.

The regions associated with high levels of vorticity and energy dissipation are studied in numerically simulated isotropic turbulence at $Re_\lambda = 168$. Their geometry and spatial distribution are characterized by means of box-counting methods. No clear scaling is observed for the box counts of intense strain rate and vorticity sets, presumably due to the limited inertial range, but it is shown that, even in that case, the box-counting method can be refined to characterize the shape of the intense structures themselves, as well as their spatial distribution. The fractal dimension of the individual vorticity structures, $D_\omega \rightarrow 1.1 \pm 0.1$, suggests that they tend to form filamentary vortices in the limit of high vorticity threshold. On the other hand, the intense dissipation structures have dimensions $D_{s} \simeq 1.7 \pm 0.1$, with no noticeable dependence on the threshold, suggesting structures in the form of sheets or ribbons. Statistics of the associated aspect ratios for different thresholds support these observations. Finally box counting is used to characterize the spatial distribution of the baricentres of the structures. It is found that the intense structures are not randomly distributed in space, but rather form clusters of inertial-range extent, implying a large-scale organization of the small-scale intermittent structures.

Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as $\psi = U^2_{\infty}tg(\xi, \eta) $ in conical similarity co-ordinates ζ = x/U∞t and η = y/U∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U∞. A second stable focus with celerity 0·64U∞ also appears near the wall at the rear of the spot.

Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Görtler type in the sublayer.

A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.

The present investigation considers the vortex wakes behind finite-length yawed cylinders that are stationary or vibrating transversly in a uniform flow. In the Reynolds-number range 160–103 a number of three-dimensional and nominally two-dimensional wake flows are observed and attributed to the dominance of end conditions over rather large spans of the cylinder (aspect ratios up to 100).

A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to surface-wave instabilities that couple the interfacial deflection to the underlying shear flow. These instabilities are found to be directly related to the two-dimensional waves on an isothermal layer subject to wind shear as described by Miles and by Smith & Davis. Hence the surface-tension gradients are important only in that they drive the basic shear flow. The surface-wave stability characteristics for liquid layers with and without return-flow profiles are presented, and special attention is paid to long-wave instabilities. Comparisons are made with available experimental observations.