In order to understand how free-stream turbulence affects the vortex-pairing mechanism in free-mixing layers, water-flume experiments have been performed on the interaction between single vortex pairs (with circulation Γp) and also vortex rings propelled towards the rolling-up vortices (of circulation Γh) in a two-dimensional separated shear layer. The Reynolds number of an obstacle generating the shear layer is about 103 and of the vortex pairs and rings about 10–100. Our observations show that, if the ratio Γp/Γh exceeds about 1.4, the vortex pairs break away any shear-layer vortices in their path and if Γp/Γh is less than about 0.5 the shear-layer vortices destroy the vortex pair. But if Γp/Γh = 1.0 ± 0.4 the vortex pairs and shed vortices interact strongly, for example by a pairing between one vortex of the pair and the shed vortex, by the vortex pair eliminating coalescence of vortices in the shear layer, or by combining with the rolling-up vortices to generate large vortices. Qualitatively similar effects are observed with the vortex rings.

Numerical calculations of the interaction between an array of vortices on a line and a vortex pair are described. The results are similar to those of the physical experiments, in particular displaying the same sensitivity to Γp/Γh at Γp/Γh ≈ 1.0. It is suggested that these results demonstrate one important way in which free-stream turbulence interacts with shear layers and how shear layers interact with other vortices.

The influence of buoyancy on the pressure–strain term is calculated approximately by an analytical theory. It is shown that the buoyancy contribution to (ϕij + ϕji)1, the fluctuation part of the pressure–strain term, is approximately equal to the buoyancy contribution which comes from the mean-field part of the pressure–strain term, provided that the mean buoyancy does not vary rapidly in space or time. The latter, but not the former, buoyancy contribution was previously obtained by Launder (1975) and by Zeman & Lumley (1976). Both contributions are shown to be accounted for by use of a single numerical coefficient Cθ*. The value of Cθ* predicted from purely theoretical considerations is 0.7, and a value determined from an experiment is 0.9. The theoretical method has some generality and can be applied to higher than second-order correlations of velocity and temperature fluctuations.

In the critical Reynolds-number range (Re = 3−4 × 105) the structure of the flow around a circular cylinder undergoes drastic changes that are coupled with a break in symmetry manifested by the occurrence of a steady lift force having unpredictable sign. Between the stable states the time functions of lift exhibit chaotic behaviour. Sensitivity to small perturbations is demonstrated by experiments showing that in principle it is possible to trip all transition jumps in the critical range by a perturbation localized in space and time. The structural changes of the flow, in particular the symmetry breaks, are visualized by oil-flow photographs. Furthermore the transition jumps were recorded in the time domain, thus the characteristic time for the jumps was obtained.

Oscillating flow in a tapered channel was studied experimentally by observing the deformation of a dye streak within a Plexiglas channel during piston induced, volume-cycled oscillations. The observed steady streaming was compared to theoretical calculations. Both the theoretical and experimental results show bi-directional drift for all frequencies, with characteristics dependent upon the value of the Womersley parameter, α = b(ω/ν)½. For large values of α, e.g. α > 10, the fluid near the walls and along the centreline drifted towards the narrow end of the channel, while fluid in an intermediate region drifted towards the wide end of the channel. For small values of α, e.g. α < 5, the fluid drifted towards the narrow end at the wall and the wide end of the channel along the centreline. Applications to mass transport in the lung are discussed.

Experiments on and calculation methods for flow and pollutant spreading in meandering channels are reviewed. The shortcomings of existing calculation methods are discussed in the light of the complex three-dimensional nature of the flow situation. A mathematical model is presented which takes full account of the three-dimensionality of the flow and pollutant concentration fields. This model is based on the solution of the momentum equations governing the flow in the lateral, vertical and longitudinal directions with a three-dimensional numerical procedure together with the continuity equation. The turbulent stresses appearing in the momentum equations are calculated with a version of the k-ε turbulence model that accounts for streamline curvature effects on turbulence. The pollutant concentration field is subsequently obtained from a solution to its transport equation. The model is tested by application to three different meander situations for which velocity and concentration measurements are available from the literature, with channel width-to-depth ratios in the range 4–20, smooth and rough beds and various pollutant-discharge locations. Detailed comparisons of the velocity and concentration fields show generally good agreement. The effect of streamline curvature on the turbulent mass fluxes was found to be important only in the narrow channel with a smooth bed. Bed-generated turbulence appears to overrule this in the other two cases of a wide channel with a smooth bed and a narrow channel with a rough bed. The flow patterns show the presence of a single large eddy at most cross-sections in these cases, whereas the predictions indicate the presence of usually more than one eddy in the former case.

Experiments were performed to examine the structure of a chemically reacting, gas-phase, two-stream plane mixing layer. Temporally and spatially resolved measurements of streamwise velocity and of the concentrations of a reactant and product species and a conserved scalar were recorded across the mixing layer at streamwise locations between Redelta; = 730–2520. Non-reacting flow experiments were conducted to establish the entrainment and mixing characteristics of the layer. Reacting flow experiments were performed using dilute concentrations of the reactants, NO and O3, to ensure that the flow field remained isothermal. The probability density functions (p.d.f.s) and associated statistical quantities of the conserved and reactive scalars are compared with results from previous analytical and experimental studies. The data suggest, in concert with the Broadwell-Breidenthal model, that fluid in the mixing layer exists in three states: tongues of unmixed free-stream fluid which, on occasion, stretch across the layer; finite-thickness interfacial diffusion zones of mixed fluid which border the parcels of unmixed fluid; and regions comprising fluid of nearly homogeneous composition. The data also confirm previously reported asymmetry in entrainment rates from the two feed streams and show the important role of molecular diffusion in the mixing process. A fast-chemistry assumption, applied to predict reactive-species concentrations from the measured conserved-scalar p.d.f.s, overestimates the extent of reaction, indicating the importance of finite-rate chemistry for the present conditions. A Damköhler number, based on large-scale mixing times, is shown to be useful in determining the applicability of a fast-chemistry analysis to reacting mixing layers.

A subsonic air jet impinging upon a cavity is studied to explain the resultant heating phenomenon. Flow visualization within the cavity shows a large central vortex dominating the flow pattern. Velocity measurements inside the cavity are made using a hot-wire anemometer. Temperature is measured with a copper-constantan thermocouple. The velocity field within the cavity is described by a modified Rankine combined vortex. An uncommon form of the energy equation is used to account for turbulent heating in adverse pressure gradients. A theoretical solution is developed to model the temperature field in the cavity. There is a good agreement between the calculated and measured temperatures. The heating effect is related to Ranque-Hilsch tubes.

A mathematical model is constructed to represent the diffraction of plane harmonic waves through a gap between two semi-infinite breakwaters in water of constant depth. The boundary-value problem corresponding to this model is formulated and then specialized to the case of waves that are long relative to the gap width. A solution to the long-wave problem is found using the method of matched asymptotic expansions. A selection of results are presented and, where possible, comparisons are made with previous work.

The nonlinear evolution of perturbed equilibrium configurations of constant-vorticity vortices is calculated. To illustrate a variety of nonlinear behaviour, we consider the following relatively simple configurations: the corotating configurations of N vortices whose linear stability has been treated in a previous study; the elliptical vortex; and the annular vortex. Our calculations test for nonlinear stability as well as categorize the possible forms of stability and instability. The energy ideas announced in the previous study are found to greatly constrain vortex evolution. In particular, we show that two vortices and an elliptical vortex may evolve into each other, and that an annular vortex may break cleanly into five co-rotating vortices.

The dispersion of continuous emissions from a line-source in a reversed-flow layer is analysed by means of diffusion equations; a family of exact solutions is found in the form of infinite series and/or integrals. It is shown that the concentration within the layer decays exponentially with the streamwise distance in the direction of reversed flow. The ground-level concentration near the source is found to be governed largely by the local mean flow; the value of the diffusivity affects the position of the maximum of ground-level concentration, but has little influence upon its magnitude. A useful upper limit is deduced for the background concentration due to recirculation effects. Further, a simple formula is given for the maximum value of the ground-level concentration for cases where the source is not too near the ground. The predictions for ground-level concentration are validated against experimental data for the particular case of a line source in the recirculating wake behind a two-dimensional backward-facing step. The extension of the analysis to the case of a point source is also discussed.

In the self-preserving region of a slightly heated turbulent plane jet, conventional isocorrelation contours of velocity and temperature fluctuations support the existence of organized large-scale structures. Temperature fronts associated with these structures were visually detected using a spanwise rake of cold wires. This method of detection was then used to condition velocity and temperature fluctuations and products of these fluctuations. Ensemble-averaged velocity vectors, constructed in the plane of main shear, suggest a topology for the organized motion in which the temperature front is identified with the diverging separatrix connecting adjacent structures on the same side of the centreline. Coherent stresses and heat fluxes are particularly significant near the diverging separatrix. Contributions by the coherent and random motions to the averaged momentum and heat transports are generally of the same order of magnitude.

A plane, isothermal, chemically reacting mixing layer has been experimentally investigated to analyse the origin and the development of three-dimensional stream-wise vorticity. The results show that early in its evolution, the plane, free shear layer is composed of counter-rotating pairs of streamwise vortices superimposed upon the spanwise ones. This coherent, streamwise vortical structure was found to be the result of the unstable response of the layer to three-dimensional perturbations in the upstream conditions. Depending on the magnitude and location of the upstream disturbances, the location of the transition to three-dimensionality varied. However, the concentrated streamwise vorticity was always seen to form first on the braids between consecutive spanwise vortices and then to propagate into their cores.

For the low and moderate Reynolds numbers of this study, it was found that the onset of the so-called ‘mixing transition’ does not necessarily coincide with that of the formation of concentrated streamwise vorticity. These vortices were observed to have a scale, as measured by the size of their cores, somewhat smaller than but comparable with that of the spanwise ones, thus contributing substantially to the entrainment process in the early stages of mixing-layer development.

The average thickness of the wetting film left behind during the slow passage of an air bubble in a water-filled capillary tube of circular cross-section has been determined experimentally as a function of bubble speed and bubble length. For bubbles of length many times the tube radius, the ratio of film thickness to tube radius is found to be a function of the capillary number only, in agreement with previous experimental studies. As has been found previously, the asymptotic result of Bretherton (1961) significantly underpredicts the film thickness, the discrepancy being greatest at the lowest speeds. For bubbles of length less than about 20 tube radii, on the other hand, good agreement with the Bretherton theory is obtained over two orders of magnitude in bubble speed. The theoretical profile of long bubbles is shown to be unstable; however the explanation of the observed behaviour is, as yet, incomplete.

We consider the linearized stability of interfacial progressive waves in a two-layer inviscid fluid, for the case when there is a basic current shear in either, or both, of the fluids. For this configuration the basic wave has been calculated by Pullin & Grimshaw (1983b). Our results here are mainly restricted to two-space-dimensional instabilities (i.e. one-dimensional in the propagation space), and are obtained both analytically and numerically. The analytical results are for the long-wavelength modulational instability of small-amplitude waves. The numerical results are restricted to the case when the lower fluid is infinitely deep, and for the Boussinesq approximation. They are obtained by solving the linearized stability problem with truncated Fourier series, and solving the resulting eigenvalue problem for the growth rate. For small values of the basic current shear, and for small or moderate basic wave amplitude, the instabilities are determined by a set of low-order resonances; for larger basic wave amplitude, these are dominated by the onset of a local wave-induced Kelvin–Helmholtz instability. For larger values of the basic current shear, this interpretation is modified owing to the appearance of a number of new effects.

Direct numerical simulations of sink-flow boundary layers, with acceleration parameters K between 1.5 × 10−6 and 3.0 × 10−6, are presented. The three-dimensional, time-dependent Navier–Stokes equations are solved numerically using a spectral method, with about 106 degrees of freedom. The flow is assumed to be statistically steady, and self-similar. A multiple-scale approximation and periodic conditions are applied to the fluctuations. The turbulence is studied using instantaneous and statistical results. Good agreement with the experiments of Jones & Launder is observed. Two effects of the favourable pressure gradient are to extend the logarithmic layer, and to alter the energy balance of the turbulence near the edge of the boundary layer. At low Reynolds number the logarithmic layer is shortened and slightly displaced, but wall-layer streaks are present even at the lowest values of Rθ for which turbulence can be sustained. Large quiescent patches appear in the flow. Relaminarization occurs at K = 3.0 × 10−6, corresponding to a Reynolds number Rθ ≈ 330.

Using both Monte Carlo and numerical techniques, Taylor dispersion in a curved tube at low Dean numbers has been evaluated and the results are in qualitative agreement with those found by Janssen (1976): Dn2Sc is the controlling parameter with Df falling to about 0.2 of its straight-tube value at high values of Dn2Sc. Agreement with available experimental data is generally good. Further, we find that for large Dn2Sc, the transition from convective to diffusive dispersion occurs earlier than in straight-tube flow, but only by a factor of two.

The Burgers equation, in spherical and cylindrical symmetries, is studied numerically using pseudospectral and implicit finite difference methods, starting from discontinuous initial (N wave) conditions. The study spans long and varied regimes–embryonic shock, Taylor shock, thick evolutionary shock, and (linear) old age. The initial steep-shock regime is covered by the more accurate pseudospectral approach, while the later smooth regime is conveniently handled by the (relatively inexpensive) implicit scheme. We also give some analytic results for both spherically and cylindrically symmetric cases. The analytic forms of the Reynolds number are found. These give results in close agreement with those found from the numerical solutions. The terminal (old age) solutions are also completely determined. Our analysis supplements that of Crighton & Scott (1979) who used a matched asymptotic approach. They found analytic solutions in the embryonic-shock and the Taylor-shock regions for all geometries, and in the evolutionary-shock region, leading to old age, for the spherically symmetric case. The numerical solution of Sachdev & Seebass (1973) is updated in a comprehensive manner; in particular, the embryonic-shock regime and the old-age solution missed by their study are given in detail. We also study numerically the non-planar equation in the form for which the viscous term has a variable coefficient. It is shown that the numerical methods used in the present study are sufficiently versatile to tackle initial-value problems for generalized Burgers equations.

A source of light water was started along the outside vertical wall of a cylindrical tank in uniform rotation. Like wall gravity currents studied previously, it had a nose which detrained eddies as it propagated. The gravity current then impinged upon a sloping bottom with the following effects: (i) the gravity current became more laminar; the detrainment of eddies at the nose and off the side of the current ceased; (ii) the gravity current became wider; (iii) the gravity current suddenly slowed and then continued to decelerate; (iv) when the gravity current was slower than the first-mode barotropic shelf wave, a shelf wave was radiated ahead of the gravity current; and (v) the deceleration was significantly greater than the deceleration of a gravity current next to a vertical wall. This is probably attributable to shelf-wave radiation drag, viscous effects and a finite energy source, although the relative importance of each remains an open question.

The fluid flow types observed in a new rotating cylindrical annulus configuration are presented in regime diagrams. This new annulus has radial temperature gradients imposed on plane, horizontal, thermally conducting endwalls and the cylindrical sidewalls are insulators. This configuration is to be contrasted with the classical cylindrical annulus which has differentially heated conducting sidewalls and insulating endwalls. Studies of the flows occurring in the classical annulus have contributed much to our understanding of basic atmospheric dynamics. Unlike the classical annulus the new configuration permits a measure of control over the internal vertical temperature gradient. To observe the flow from above (and below) and to satisfy the conduction requirement, transparent sapphire disks are used for the endwalls. The fluid used was water. Qualitative observations of the flow types were made using a small amount of rheoscopic concentrate added to the water.

As well as the axisymmetric flow and non-axisymmetric baroclinic wave flow which occur in the classical annulus, two additional non-axisymmetric flow types, boundary-layer thermal convection and deep thermal convection, are observed in the new annulus. Three flow regime diagrams for three different values of the imposed vertical temperature difference are presented. The flows are described and explanations for the flow transitions are offered.

It is argued that the new annulus configuration is more relevant to real atmospheric flows than the original annulus. Another motivation for this research was to provide scientific backup for the Atmospheric General Circulation Experiment (AGCE). The AGCE is a true spherical baroclinic flow experiment which can only be realized in a low gravity environment and which has been proposed for space flight.

We study the chaotic mixing in two periodic model flows, the ‘tendril–whorl’ flow and the ‘Aref-blinking-vortex’ flow, with the objective of supplying evidence for the primary mechanisms responsible for mixing in two-dimensional deterministic flows. The analysis is based on tools of dynamical systems theory but it is clear that the mixing problem generates several questions of its own: low periodic points and horseshoes dominate the picture, since we want to achieve mixing quickly; Poincaré sections, popular in dynamical systems analyses, might give misleading information with regard to dispersion at short times. Our analysis shows that both flows are able to stretch and fold material lines well below the lengthscale of the flows themselves. The inner workings of the two systems are revealed by studying the local and global bifurcations. Computations for the blinking-vortex system indicate the existence of an optimum period at which the average efficiency is maximized, whereas the intensity of segregation – a classical parameter in mixing studies – decays rapidly to an asymptotic value in the globally chaotic region. Even though our flows are not turbulent the results might have some implications for pointing to the limits of similar studies in actual turbulent flows (e.g. line stretching).