This paper is primarily concerned with the turbulence generated by the interaction of random entropy fluctuations with non-uniform mean flows. The results are obtained by using rapid distortion theory in conjunction with a high frequency solution of a previously developed wave equation that governs the small amplitude unsteady vortical and entropic motion on steady potential flows (Goldstein 1978). The analysis is applied to symmetric contractions or expansions (or combinations of the two) and comparisons are made with a corresponding theory of Batchelor & Proudman (1954) for the rapid distortion of upstream turbulence by a contraction of this type. It is shown that the energy of the entropy-generated turbulence increases much more rapidly with contraction ratio than that of the imposed upstream turbulence. Turbulence of the former type can therefore dominate the latter even when the upstream entropy fluctuations are weak relative to the imposed turbulent intensities. Moreover the structure of the entropy-generated turbulence is found to be quite different from that of the contracted upstream turbulence.

A secondary purpose of the paper is to discuss some effects of compressibility on rapid distortion theory.

The results are presented of an experimental investigation of the flow of mercury along straight, circular and rectangular non-conducting ducts situated in a magnetic field that is uniform except over a short length of the duct where its value decreases by 50%. Magnitudes of the field strength and mean velocity are such that the Hartmann number M is large, the interaction parameter N ≈ M½ and the magnetic Reynolds number Rm [Lt ] 1. In all but one respect this is the prototype problem analysed by Holroyd & Walker (1978): their analysis required that N [Gt ] M½.

Distributions of pressure, electric potential and velocity are measured, the latter by hot-film probes. Qualitative agreement with the theoretical predictions is obtained in so far as a pressure drop of O(duct radius × fully-developed flow pressure gradient × M½) occurs over the non-uniform field region and, in the circular duct, the fluid can be seen to migrate towards the centre of the duct upstream and downstream of the non-uniform field region but in that region this tendency is reversed.

Similar effects appear to occur in the rectangular duct.

Velocity measurements in a 51 mm diameter turbulent jet are presented. The measurement programme is conducted in two parts. The first part is devoted to the validation of laser velocimeter (LV) data. This consists of comparative measurements with the LV and a hot-wire anemometer. The second part consists of a survey of the jet flow field at Mach 0·28, 0·90, and 1·37 under ambient temperature conditions. Radial and centre-line distributions of the axial and radial, mean and fluctuating velocities are obtained. The distributions indicate a decrease in the spreading rate of the mixing layer with increasing Mach number and a corresponding lengthening of the potential core. The results further indicate that these two parameters vary with the square of the jet Mach number. Radial distributions collapse when plotted in terms of ση*, where σ = 10.7/(1 - 0.273 MJ2) and η* = (r − r0·5)/x. This is true for distributions in planes located as far downstream as two potential core lengths. The collapsed data of mean velocity can be approximated by a Görtler error function profile: \[ U/U_J = 0.5[1-{\rm erf}(\sigma\eta^{*})]. \] Centre-line distributions at various Mach numbers also collapse if plotted in terms of x/xc, xc being the potential core length. A general equation for the collapsed data of mean velocity is given by: U/UJ = 1 - exp{1.35/(1 - x/xc)}, for the range of Mach numbers 0·3-1·4, where xc = 4.2 + 1.1 MJ2.

The dispersion relations for infinitesimal internal gravity waves (A) and axisymmetric waves in swirling streams (B) are considered. In both cases the mainstream may be sheared and density stratified in the transverse (vertical in case A, radial in case B) direction. The following results are proved for either case: If the maximum speed Wmax (or minimum speed Wmin) (in a meridian plane in case B) of the mainstream occurs at an interior point in the fluid, then the phase speed of any mode takes all values from the Wmax (or Wmin) to +∞ ( —∞) as the overall Richardson number λ2 varies from 0 to ∞. If Wmax(Wmin) is attained at a boundary point with finite rate of strain, there is a positive non-zero critical Richardson number below which one or both branches of the dispersion relation terminate. These results employ variational methods and correct erroneous results concerning problem B stated in Chandrasekhar's treatise on hydrodynamic stability. Furthermore, bounds are given on the group velocity for both branches of the dispersion relation. From these bounds it is shown that in the absence of reversals of the mainstream (Wmin > 0) upstream propagation of wave energy is impossible whenever upstream propagation of constant phase surfaces is impossible.

An externally applied d.c. electric field is known to produce instability in a plane layer of dielectric liquid heated from above. The stationary linear instability of a unipolar charge injection equilibrium for which carrier mobility depends linearly on temperature is investigated. It is found that the sign of the temperature gradient in relation to the emitting electrode determines whether or not such instability can occur, and that two types of instability can be distinguished: (i) a space charge modified Bénard mode; and (ii) a thermally modified space charge mode. It is shown that the critical voltage is highly dependent upon the absolute value of mobility and its variation across the layer.

Detailed measurements in the wakes behind two-dimensional square section blocks (height h) mounted in thick rough wall boundary layers (height δ) are presented for cases in which h/δ [Lt ] 1. The data provides some insight into the relaxing flow downstream of reattachment, confirming the conclusion of Bradshaw & Wong (1972) that reattaching flows are surprisingly complicated and involve considerable distortion of the separated shear layer. In particular, the measurements show that eddy length scales are considerably reduced and, since the flow eventually relaxes to a boundary layer similar to that upstream, turbulence models based on eddy viscosity concepts cannot, in principle, be expected to be satisfactory. Using the present data this is demonstrated by a more detailed comparison with the theoretical predictions of Counihan, Hunt & Jackson (1974) than has been previously possible. It is shown that, whilst their theory does not predict the behaviour of the turbulent stresses, it does give reasonable agreement with the mean velocity perturbations at least in the near wake −10 < x/h < 30. Except in the near wall region, where the roughness provides the dominant length scale, it is argued that the rate at which the perturbation flow decays is governed largely by the amount by which the separated shear layer is distorted prior to reattachment, which in turn is determined by, say, a turbulence Reynolds number of the body, (hU/v0)h, or, in other words, by the characteristics of the upstream flow at, say, the body height.

By establishing that the length scale governing the detachment of a shock wave from a wedge is the distance from the leading edge to the sonic line, and by considering the view of observers with different length scales, it is predicted that the detachment distance increases gradually with wedge angle for relaxing flow and more rapidly in a perfect gas. Both of these features are confirmed by experiments in the free-piston shock tunnel. The influence of other length scales is discussed. The phenomenon is related to a relaxation effect in which a subsonic layer grows from the translational-rotational shock as the wedge inclination is increased beyond the frozen sonic point.

Oscillations of impinging flows, which date back to the jet-edge phenomenon (Sondhaus 1854), have been observed for a wide variety of impingement configurations. However, alteration of the structure of the shear layer due to insertion of an impingement edge (or surface) and the mechanics of impingement of vortical structures upon an edge have remained largely uninvestigated. In this study, the impingement of a shear layer upon a cavity edge (or corner) is examined in detail. Water is used as a working fluid and laser anemometry and hydrogen bubble flow visualization are used to characterize the flow dynamics. Reynolds numbers (based on momentum thickness at separation) of 106 and 324 are employed. Without the edge, the shear layer produces the same sort of non-stationary (variable) velocity autocorrelations observed by Dimotakis & Brown (1976). When the edge is inserted, the organization of the flow is dramatically enhanced as evidenced by a decrease in variability of autocorrelations and appearance of well-defined peaks in the corresponding spectra. This enhanced organization is not locally confined to the region of the edge but extends along the entire length of the shear layer, thereby reinforcing the concept of disturbance feedback. Comparison of spectra with and without insertion of the edge reveals a remarkable similarity to those of a non-impinging shear layer with and without application of sound at a discrete frequency (Browand 1966; Miksad 1972); with enhanced organization at the fundamental frequency, simultaneous enhancement occurs also at the sub- and higher-harmonics.

This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Padé approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.

From a series of experiments using simplified mechanical models we suggest certain minor modifications to the Weis-Fogh (1973)–Lighthill (1973) explanation of the so-called ‘clap and fling’ mechanism for the generation of large lift coefficients by insects in hovering flight. Of particular importance is the production and motion of a leading edge, separation vortex that accounts for virtually all of the circulation generated during the initial phase of the ‘fling’ process. The magnitude of this circulation is substantially larger than that calculated using inviscid theory. During the motion that subsequently separates the wings, the vorticity over each of them is convected and combined to become a tip vortex of uniform circulation spanning the space between them. This combined vortex moves downwards as a part of a ring, of large impulse, that is then continuously fed from quasi-steady separation bubbles that move with the wings as they continue to open at a large angle of attack. Such effects are able to account for the large lift forces generated by the insect.

The generation of initial wavelets, which appear at the initial stage of the generation and growth processes of wind waves after the abrupt start of the wind on a still water surface, has been investigated by systematic experiments together with theoretical analyses. The energy of the initial wavelets, measured by a resistance-type wave gauge of 50 μm diameter, grew exponentially with time at a constant frequency. The frequency and the growth rate were independent of the fetch but did depend on the friction velocity u*a of the air. The phase velocity of the initial wavelets, measured by a shadowgraph-photography technique, was nearly constant, independent of u*a. A coupled shear flow model in the air and water was examined, to explain the observed characteristics of the initial wavelets in terms of the instability mechanism. The theoretical analysis showed that, for each shear flow pattern observed in the experiments, there exist waves whose growth rate is maximum. The frequency, the growth rate and the phase velocity of these critical waves were virtually coincident with those properties of the observed initial wavelets. It is concluded that the generation of wind waves, whose initial stage is called the initial wavelets, is caused by the selective amplification, by the instability mechanism, of the small perturbations which inevitably occur in the flow.

The limitation of the linear instability theory as applied to the process of further growth of the wind waves is also discussed. From some facts recognized through detailed observations, it is inferred that the phenomena controlled by the linear mechanism last for only about 10 s, and that these evolve to the wind waves which are characterized by inherent nonlinearity.

A time similarity formulation of the flow equations for unsteady plumes is shown to exist only when the buoyancy flux at the source varies as a power function of time. The time similarity equations for unsteady plumes are solved numerically. It is shown that the velocity of the leading edge of the plume is less (at most the 0·42 fraction) than the velocity inside the plume behind its leading edge; this observation is consistent with Turner's (1962) results on the behaviour of a starting plume with constant buoyancy flux at the source. Finally, experimental results of axial temperature histories in the buoyant plume generated by a fast-growing fire are compared with the theoretical predictions.

Our analysis of 18th and 19th century cannon firings shows that knowledge of sphere drag can be substantially extended into the region of 0·3 ≤ M∞ ≤ 2·0 and Re∞d up to 107. Bashforth’s chronographic measurements (1868) are of a quality comparable to modern measurements. The data of Mayevski (chronograph, 1868), Hutton (ballistic pendulum, 1787-1791), and Didion (ballistic pendulum, 1839-1840) are of lesser accuracy but in agreement with Bashforth’s. These cannon data are combined with modern data to provide the most extensive curves available of CD vs. Re∞d in this region. Interesting features of these curves for M∞ ≤ 1·0 are briefly described.

In nematic homeotropic films (director n perpendicular to the horizontal limiting plates) heated from below, the distortion of the director which is coupled to the ordinary heat convection mechanism responsible for the Rayleigh–Bénard instability exerts a strongly stabilizing influence. Owing to the difference in time scales, an oscillatory instability results whose characteristics are investigated experimentally here. An inverted bifurcation with an associated hysteresis is also obtained and this was studied in some detail. A vertical magnetic field H is also used to align the sample. The decrease of the orientational time constant when H increases leads to marked changes in the overstable regime, which are well described by a simple analysis.

The motion of a sphere in the presence of a fluid-fluid interface is studied. First, a solution is derived for a point force near a plane interface. Then the solution is extended to include the higher-order terms which are required to describe the motion of a solid sphere. Singularities of higher orders at the centre of the sphere are obtained by using the method of reflexions. For a fluid–fluid interface with an arbitrary viscosity ratio, the drag force and the hydrodynamic torque are calculated for the special cases of motion of a sphere perpendicular and parallel to the interface. In addition, the rotational motion of a sphere is also investigated.

This paper investigates a class of bead–rod and bead–spring models which have been proposed to describe the dynamics of an isolated macromolecule in a flowing solution. Hassager (1974a) has pointed out a surprising result in regard to these models: the statistical conformation of a molecule (and hence its influence on the flow) apparently depends upon whether a very stiff-springed model structure or a rigid one is used. This paradox is examined and resolved. It is shown that a unique answer is obtained by regarding the system as the classical limit of a quantum-mechanical one. The extent of the quantum influence can be characterized by a dimensionless group Q. For a ‘hot’ or ‘large’ system (for which Q → 0) the classical (stiff spring) results are recovered. The effects of the parameter Q on the size of the molecules and the rheology of the solution are calculated in detail for a simple model, and the gross features are identified for a more realistic Rouse chain model, each in both weak and strong flows.

A final section considers weak, rapidly varying flows. It is shown that, within the context of classical (non-quantum) physics, for sufficiently rapid changes any model structure will tend to move with the applied flow, and therefore exert no stresses on the fluid. This explains the theoretical observation of Fixman & Evans (1976) that, in regard to the particle stress, the limits of rigidity and infinitely high frequency do not commute.

The initial development of turbulence in the shear layer of a circular jet is observed to show disturbances of increasing scale at discrete frequencies in an approximate 4:2:1 sequence. These are completely confined within the laminar shear layer and convect at 0·59 of the jet velocity. Such relatively regular behaviour was not observed once the disturbances became larger in transverse dimension than the laminar shear layer.

In the development of the subsequent turbulent shear layer it was found that the fluctuating turbulent shear did not scale with local mean shear, but rather scaled more closely with the minus half power of distance from the apparent origin of the laminar shear layer emanating from the nozzle. The scale of the shear fluctuations departed from growth in proportion to shear layer thickness, remaining almost constant. In these aspects it appears that the turbulent shear layer is not well described by a similar growth with axial distance.

The shear fluctuations convected at a speed closer to the local mean velocity than do velocity fluctuations and showed a relatively more patchy distribution with a distinct rotational sense and no reversal of skewness across the layer. Velocity fluctuations showed phase lags approaching $\frac{1}{3}\pi$ relative to shear fluctuations suggesting that dominant velocity disturbances are those associated with entrainment behind concentrations of rotation.

The variations in refractive index in stratified liquid flows have been a major impediment to the use of laser-Doppler anemometry in these situations. This paper describes a method whereby these refractive-index variations can be drastically reduced while retaining the dynamically important density differences. The method uses two solutes to produce the density differences and it is shown that double-diffusive convection (of the salt-finger type) can be avoided by using a suitable pair of solutes. A theoretical model of the lateral wander of a single laser beam propagating through a turbulent medium is developed and this explains the success of the method.

Local wall shear rates in steady flow in the entry region of a curved tube have been measured by the electrochemical limiting current method. A semi-circular rigid tube of circular cross-section with radius ratio 1/7 has been employed for a range of Dean number between 139 and 2868. The circumferential and axial distributions of the wall shear rates have been measured at 20° circumferential increments at five different sections of the entry region.

The steady streaming induced by oscillatory viscous flow of small amplitudes over a wavy wall has been analysed, and the computed flow patterns have been found to agree well with the flow patterns visualized experimentally in a tube. When the first parameter, α/δ (the ratio of the wavelength of the wavy wall to the thickness of Stokes layer), becomes larger than about 26, the streaming has a double structure consisting of regions of upper and lower pairs of recirculations. As the second parameter, L/δ (the ratio of the amplitude of the wavy wall to the thickness of Stokes layer), is increased, the upper pair of recirculations squeezes in a gap between the lower recirculations above the troughs of the wall. A similar double structure of steady streamings was also observed above ripple marks formed under oscillatory viscous flow. A bearing is suggested of this phenomenon on the determination of stationary profiles of ripple marks.