The steady-state equations of motion are solved for a fluid sphere translating in a quiescent medium. A semi-analytical series truncation method is employed in conjunction with a cubic finite-element scheme. The range of Reynolds numbers investigated is from 0.5 to 50. The range of viscosity ratios is from 0 (gas bubble) to 107 (solid sphere). The flow structure and the drag coefficients agree closely with the limited available experimental measurements and also compare favourably with published finite-difference solutions. The strength of the internal circulation was found to increase with increasing Reynolds number. The flow patterns and the drag coefficient show little variation with the interior Reynolds number. Based on the numerical results, predictive equations for drag coefficients are recommended for both moderate- and low-Reynolds-number flows.

An asymptotic theory of solid cylindrical wind-tunnel-wall interference about subsonic slender bodies has been developed. The basic approximation used is one of large wall-radius to body-length ratio. Matched asymptotic expansions show that in contrast to the analogous two-dimensional problem of a confined airfoil, three regions exist. Besides the incompressible crossflow and nearly axisymmetric zones, a wall layer exists where reflection in the wall of the line source representing the body becomes of dominant importance. From the theory, the interference pressures are shown to be approximately constant for closed bodies. Also demonstrated is that D'Alembert's paradox holds for interference drag of such shapes. Numerical studies comparing the exact theory to the asymptotic model which provides drastic simplifications, show that the latter can be used with reasonable accuracy to describe flows, even where the characteristic tunnel-radius to body-length ratio is as low as 1.5.

A slow moving flow in a duct emerging into a quiescent negatively buoyant environment may separate from its inner wall prior to the lip. Buoyancy accelerates the flow, curving the streamlines within the duct away from the walls. The resulting deceleration at the wall may be sufficient to provoke separation. The problem of the location of this separation point in a two-dimensional channel is studied. A potential-flow model is examined first to explore the large-Reynolds-number behaviour. The form of the potential-flow description in the vicinity of the assumed location of separation is characterized by the presence of a square-root singularity in the pressure gradient at the wall. This permits use of the ideas of viscous-inviscid interaction, proposed by Sychev (1972), to determine the separation location as a function of Froude and Reynolds numbers. Results obtained in the high-Reynoldsnumber limit show that the channel flow separates at shorter distances from the entrance as Froude number is reduced.

The three-dimensional wave pattern generated by a moving pressure distribution of finite extent acting on the surface of water of depth h is studied. It is shown that, when the pressure distribution travels at a speed near the linear-long-wave speed, the response is governed by a forced nonlinear Kadomtsev-Petviashvili (KP) equation, which describes a balance between linear dispersive, nonlinear and three-dimensional effects. It is deduced that, in a channel of finite width 2w, three-dimensional effects are negligible if w [Lt ] h2/a, a being a typical wave amplitude; in such a case the governing equation reduces to the forced Korteweg-de Vries equation derived in previous studies. For aw/h2 = O(1), however, three-dimensional effects are important; numerical calculations based on the KP equation indicate that a series of straight-crested solitons are radiated periodically ahead of the source and a three-dimensional wave pattern forms behind. The predicted dependencies on channel width of soliton amplitude and period of soliton formation compare favourably with the experimental results of Ertekin, Webster & Wehausen (1984). In a channel for which aw/h2 [Gt ] 1, three-dimensional, unsteady disturbances appear-ahead of the pressure distribution.

An experiment on the Saffman-Taylor instability with wetting fluids is presented that explores a greater range of capillary numbers than did the original experiment of Saffman and Taylor. It turns out that no clear one-half plateau for the finger size is observed, and that the ensemble of experiments cannot be analysed in terms of a single control parameter. The effect of the film of oil left behind the finger is important, and we measure its thickness. A qualitative discussion of the instabilities of the fingers for large capillary numbers is presented, the first instability leading to asymmetrical fingers. Tip splitting appears for larger values of 1/B. The 1/B value for the onset of instabilities is shown to be noise dependent.

The possibility of an excitation of individual subharmonic perturbations in each of the shear layers forming the far wake is investigated numerically. Principal considerations allow for the existence of two equivalent subharmonic modes which by opposite routes can lead to a doubling of the wavelength in the wake. Since vortical disturbances in the far wake are amplified only convectively, the simultaneous existence of both modes in the flow field is possible, which could provide an explanation for the group structure observed experimentally in the far wake. These considerations also provide a logical explanation of the finding of a very regular vortex pairing process in forced wakes.

Two-dimensional numerical simulations assuming incompressible flow and almost inviscid dynamics illustrate the opposite developments of regions dominated by the two different modes and also confirm the possibility of a resulting group structure. As an important result it is demonstrated that, if vortex pairing plays an important role in the growth of the far-wake structure, this does not have to be related to the excitation of the subharmonic peak in the frequency spectrum. Quite the contrary, it is to be expected that the subharmonic itself is of minor importance and that instead a small frequency and its multiples related to the group structure of the flow dominate the spectrum. In the light of these considerations measurements by Cimbala (1984) are discussed and frequency spectra recorded by him are analysed more closely. Various properties of these spectra seem to indicate that vortex pairing might be significant with respect to the evolution of the far-wake structure.

A novel technique is presented for determining the coefficient of shear-induced particle self-diffusion in concentrated suspensions of solid spheres, which relies on the fact that this coefficient can be computed from the measured variations in the time taken by a single marked particle in the suspension to complete successive circuits in a Couette device. Since this method does not involve the direct measurement of the lateral position of the marked particle, it requires a much simpler experiment than that used by Eckstein, Bailey & Shapiro (1977) which is shown to be constrained by wall effects at high particle concentration. The diffusion coefficient thus determined was found to be proportional to the product γa2, where γ is the shear rate and a the particle radius, and to have the asymptotic form 0.5γa2ϕ2 in the dilute limit when the particle concentration ϕ → 0.

A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centreline velocity and channel half-width, with about 4 × 106 grid points (192 × 129 × 160 in x, y, z). All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behaviour of turbulence correlations near the wall. In addition, a number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

Measurements of surface pressure-fluctuation spectra and wave speeds are reported for a well-documented separating turbulent boundary layer. Two sensitive instrumentation microphones were used in a new technique to measure pressure fluctuations through pinhole apertures in the flow surface. Because a portion of the acoustic pressure fluctuations is the same across the nominally two-dimensional turbulent flow, it is possible to decompose the two microphone signals and obtain the turbulent flow contributions to the surface pressure spectra. In addition, data from several earlier attached-flow surface-pressure-fluctuation studies are re-examined and compared with the present measurements.

The r.m.s. of the surface pressure fluctuation p′ increases monotonically through the adverse-pressure-gradient attached-flow region and the detached-flow zone. Apparently p′ is proportional to the ratio α of streamwise lengthscale to lengthscales in other directions. For non-equilibrium separating turbulent boundary layers, α is as much as 2.5, causing p′ to be higher than equilibrium layers with lower values of α.

The maximum turbulent shearing stress τM appears to be the proper stress on which to scale p′; p′/τM from available data shows much less variation than when p′ is scaled on the wall shear stress. In the present measurements p′/τM increases to the detachment location and decreases downstream. This decrease is apparently due to the rapid movement of the pressure-fluctuation-producing motions away from the wall after the beginning of intermittent backflow. A correlation of the detached-flow data is given that is derived from velocity- and lengthscales of the separated flow.

Spectra Φ (ω) for ωδ*/U∞ > 0.001 are presented and correlate well when normalized on the maximum shearing stress τM. At lower frequencies, for the attached flow Φ (ω) ∼ ω−0.7 while Φ(ω) ∼ (ω)−3 at higher frequencies in the strong adverse-pressuregradient region. After the beginning of intermittent backflow, Φ(ω) varies with ω at low frequencies and ω−3 at high frequencies; farther downstream the lower-frequency range varies with ω1.4.

The celerity of the surface pressure fluctuations for the attached flow increases with frequency to a maximum; at higher frequencies it decreases and agrees with the semi-logarithmic overlap equation of Panton & Linebarger. After the beginning of the separation process, the wave speed decreases because of the oscillation of the instantaneous wave speed direction. The streamwise coherence decreases drastically after the beginning of flow reversal.

Density currents and density wedges are two observed manifestations of interactions between an ambient flow and a horizontal buoyant intrusion. In a density current the buoyant pressure force is primarily balanced by the local form drag of the current head which has a blunt shape and abrupt depth change. In a density wedge a distributed interfacial drag is the primary balancing force, leading to a stretched-out shape and long-distance intrusions. A perturbation analysis of the approach flow to the inclined front of a density current shows that slight momentum changes caused by viscous effects in the ambient flow determine which of these two flow types is established. In a uniform ambient channel flow, any momentum deficit relative to the inviscid case will lead to a local flattening of the front and ultimate breakdown into a density wedge. On the other hand, a momentum surplus will support a steady-state density current. Several exploratory experiments on control of the ambient boundary layer through local non-uniformities were performed with the objective of achieving stable density-current forms with limited intrusion lengths. These methods include a small step, a barrier and suction and are applied for intrusions at either the bottom or surface of an ambient water flow. In all cases, good agreement is found with the force balances predicted by Benjamin's (1968) theory and its extension by Britter & Simpson (1978) which accounts for entrainment in the wake zone of the head.

We report observations of the nonlinear growth of an unstable interface in, a large Hele-Shaw cell in which it is possible, in the most extreme case, to follow the emergence of a single ‘finger’ from approximately thirty initial wavelets. The larger ‘fingers’ that emerge undergo further instability to form a highly contorted interface. We have measured a number of the averaged characteristics of this interface and can relate the various cases studied through length and time scales constructed from the independent parameters of the problem. We show that the most distorted interfaces may have a fractal dimension at scales larger than the instability wavelength and discuss the significance of this possibility.

Laser-Doppler velocity measurements were performed on the entry flow in a 90° bend of circular cross-section with a curvature ratio a/R = 1/6. The steady entry velocity profile was parabolic, having a Reynolds number Re = 700, with a corresponding Dean number κ = 286. Both axial and secondary velocities were measured, enabling a detailed description of the complete flow field. The secondary flow at the entrance of the bend was measured to be directed completely towards the inner bend. Significant disturbance of the axial velocity field was not measured until a downstream distance (aR)½. Maximum secondary velocities were measured at 1.7 (aR)½ downstream from the inlet. The development of the axial flow field can be quite well explained from the secondary velocity field.

An investigation of an oblique shock wave/laminar boundary layer interaction is presented. The Mach number was 2.15, the Reynolds number was 105 and the overall pressure ratio was 1.55. The interation has been demonstrated to be laminar and nominally two-dimensional. Experimental results include pressure distributions on the plate and single component laser-Doppler velocimetry velocity measurements both in the attached and separated regions.

The numerical results have been obtained by solving the full compressible Navier-Stokes equations with the implicit approximate factorization algorithm by Beam & Warming (1980). Comparison with experimental data shows good agreement in terms of pressure distributions, positions of separation and reattachment and velocity profiles.

Combustion instability is investigated in the case of a multiple inlet combustor with dump. It is shown that low-frequency instabilities are acoustically coupled and occur at the eigenfrequencies of the system. Using spark-schlieren and a special phase-average imaging of the C2-radical emission, the fluid-mechanical processes involved in a vortex-driven mode of instability are investigated. The phase-average images provide maps of the local non-steady heat release. From the data collected on the combustor the processes of vortex shedding, growth, interactions and burning are described. The phases between the pressure, velocity and heat-release fluctuations are determined. The implications of the global Rayleigh criterion are verified and a mechanism for low-frequency vortex-driven instabilities is proposed.

To understand the imaging of the sea surface by radar, it is useful to know the theoretical variations in the wavelength and steepness of short gravity waves propagated over the surface of a train of longer gravity waves of finite amplitude. Such variations may be calculated once the orbital accelerations and surface velocities in the longer waves have been accurately determined – a non-trivial computational task.

The results show that the linearized theory used previously for the longer waves is generally inadequate. The fully nonlinear theory used here indicates that for longer waves having a steepness parameter AK = 0.4, for example, the short-wave steepness can be increased at the crests of the longer waves by a factor of order 8, compared with its value at the mean level. (Linear theory gives a factor less than 2.)

The calculations so far reported are for free, irrotational gravity waves travelling in the same or directly opposite sense to the longer waves. However, the method of calculation could be extended without essential difficulty so as to include effects of surface tension, energy dissipation due to short-wave breaking, surface wind-drift currents, and to arbitrary angles of wave propagation.

The two-dimensional motion of a cylinder of fluid released from rest into a flow that is uniform far upstream of the cylinder is studied. We consider cases where the cylinder is initially of circular cross-section and the fluid is either inviscid or viscous. For the inviscid fluid, we use analytical methods to determine the motion for small and large times after release and three numerical methods, the vortex-sheet method, the vortex-blob method and the vortex-in-cell method, to determine the intermediate-time motion. For the viscous-fluid problem we use the vortex-in-cell method with random walks to compute both the initial flow around the cylinder and the motion of the released fluid at a Reynolds number of 484. In the inviscid case, the released fluid deforms into a structure that resembles a vortex pair that propagates down stream at a speed less than the onset flow speed. In the viscous case, after a wake representative of a Kármán vortex street has developed, the released fluid usually deforms into an elongated horseshoe shape that travels downstream at a speed greater or less than the incident flow speed (depending on when in the vortex-shedding cycle the cylinder is released). The results of the numerical calculations are compared with some simple experiments in a water channel.

This investigation is concerned with the numerical calculation of multiple solutions for a mixed-convection flow problem in horizontal rectangular ducts. The numerical results are interpreted in terms of recent observations by Benjamin (1978a) on the bifurcation phenomena for a bounded incompressible fluid. The observed mutations of cellular flows are discussed in terms of dynamic interchange processes. Each cellular flow may be represented by a solution surface in the parametric space of Grashof number Gr and aspect ratio γ, which is delimited by stability boundaries. Such a stability map has been generated for each type of cellular flow by a series of numerical experiments. Once these boundaries are crossed one cellular flow mutates into another via a certain dynamical process. Although the nature of the singular points on this map have not been determined precisely, a plausible general structure of the cellular-flow exchange process emerges from this map with several features in common with the Taylor-Couette flow. The primary modes appear to exchange roles via the formation of tilted cusp. Other salient features such as primary-mode hysteresis and quasi-critical range for cellular development appear to be present. However no anomolous modes have been observed.

A theoretical study is made of the disturbance produced by an oscillating, shallow topographical feature in horizontal relative motion in a rapidly rotating, linearly stratified, unbounded fluid. For a sinusoidal surface oscillation, an explicit solution is obtained in terms of wavenumber spectra of the topography. The oscillating far-field behaviour is shown to consist of a large-scale, cyclonic component above the topography and a system of inertial waves behind the caustics, which spreads predominantly in the downstream direction. A significant property of the flow field is its dependence on a frequency threshold familiar from classical works on internal gravity waves in the absence of rotation, determined by the Brunt-Väisälä value. When the frequency is supercritical, a prominent circle of maximum disturbance appears in the far field, which provides the transition boundary between two distinct cyclonic structures and an upstream barrier to the propagating waves ahead of the obstacle. The circle has a radius depending on the relative magnitude of the pulsating frequency and the Brunt-Väisälä value, and is distinctly marked also by a phase jump in pressure and velocities. These features are substantiated by numerical examples of the full solution at a large but finite distance above the obstacle at supercritical frequencies. The circle of maximum disturbance signifies a preferential direction for energy propagation unaccounted for by group velocity. Its relation to the classical result of Görtler in the homogeneous case and that in the classical internal-gravity-wave theory are examined.

The influence of rotation upon internal solitary waves is studied in a (10 m × 2 m × 0.6 m) channel located on the large rotating platform at Grenoble University. We observe an intumescence which moves along the right-hand side of the channel with respect to its direction of propagation. Along the side, once the intumescence reaches its equilibrium shape, the height variation of the interface with time is correctly described by the sech2 function, and the characteristic KdV scaling law linking the maximum amplitude and the wavelength along the side is fulfilled. The intumescence is a stable phenomenon which moves as a whole without deformation apart from the viscous damping. For identical experimental conditions, the amplitude of the intumescence along the side increases with increasing Coriolis parameter, and at a given period of rotation of the platform, the celerity along the side increases with increasing amplitude. But for identical conditions, we found that the celerity along the side is equal to the celerity that the wave would have for such conditions without rotation. The amplitude of the intumescence in a plane perpendicular to the wall decreases exponentially with increasing distance from the side, but the crest of the wave is curved backward.

The basis of the conformal-mapping method for topographic-wave problems of Johnson (1985) is discussed in greater detail by considering the invariance under conformal mapping of the linear, barotropic, potential-vorticity equation, noted in Davis (1983). A method is presented for using this property to construct further solutions for waves propagating over varying topography. Results are given for semi-infinite channels and elongated basins. A coordinate system is constructed that approaches a Cartesian system exponentially fast with distance from end-walls. For exponentially sloping topography the solutions for infinite channels, semi-infinite channels, and basins have the same structure and dispersion relation as waves in an elliptical basin, discussed in Johnson (1987). The structures presented there can thus be considered as in some sense universal for exponentially sloping topography.