The convective circulation driven by a surface buoyancy flux in a dead-end open channel is analysed. On the assumption of similarity profiles for velocity and temperature, the governing partlial differential are reduced to two nonlinear ordinary differential equations by integrating over the flow depth. A closed-form solution of the differential equations is presented. The solution is a function of the Grashof number G and the modified Prandtl–Grashof number PmG½ defined ih (21). The velocity and temperature along the channel vary linearly as the distance and as the square of the distance respectively. Analytical expressions for the rate of total heat loss from the channel and the rateof flow in the channel are derived. The analytical results compare well with the available experimental data.

Conditionally sampled hot-wire and ‘cold-wire’ (resistance-thermometer) measure- ments confirm the general flow picture advanced by Falco (1974, 1977, 1980; see also Smith & Abbott 1978) and by Head & Bandyopadhyay (1981; see also Smith & Abbott) on the basis of smoke observations and more limited hot-wire measurements. The probability density function of turbulent-zone lengths in the intermittent region varies rapidly with Reynolds number, supporting the above authors’ finding that the hairpin-vortex ‘typical eddies’ in the viscous superlayer scale on the viscous length ν/uτ, rather than on boundary-layer thickness. However the average turbulent-zone length, deduced as an integral moment of the probability distribution, tends to a constant fraction of the boundary-layer thickness above a momentum-thickness Reynolds number of 5000, which strongly suggests that at high Reynolds numbers the overall shape of the turbulent irrotational interface is controlled by the classical ‘large eddies’ and not by the viscosity-dependent small eddies. The intermittency profile is practically independent of Reynolds number. The second-order structural parameter $\overline{u^2}/\overline{v^2}$ increases strongly with increasing Reynolds number but the triple-product parameters, with the exception of the u-component skewness, vary only slowly with Reynolds number. This behaviour of the intermittency and velocity statistics is most simply explained by supposing that the lengthscale of the large eddies is nearly independent of Reynolds number while their intensity is somewhat lower at low Reynolds number. ‘Typical eddies’ evidently contribute to the Reynolds stresses at low Reynolds number, but it is probable that the large eddies carry most of the triple products at any Reynolds number. Our results confirm the usual finding that the mixing length and dissipation length parameter increase, while the wake component of the velocity profile decreases, as Reynolds number decreases.

Extensive single- and two-point measurements have been made in a high-Reynolds- number single-stream mixing layer growing to encounter a wind-tunnel floor on its high-velocity side. The measurements include detailed conditionally sampled results, which separate the turbulent and irrotational contributions to the two-point covariances. These measurements show that the true (vorticity-bearing) large-scale structure in the isolated mixing layer, well away from the region influenced by the floor, is three-dimensional without a trace of the two-dimensional orderly structure found in some two-stream mixing-layer experiments. The structure appears to be a combination of the classical mixing jet and double-roller eddy (Grant 1958); the circulation in the latter is confined almost exclusively to the (z, z)-plane. The large spanwise scales in the potential motion are attributed to the effect of pressure disturbances and not to two-dimensionality of the turbulent structure, as claimed by previous workers. The first effect of the wall is to stretch the streamwise and spanwise scales of the large eddies. Near the high-velocity edge $\overline{u^2}$ is amplified more than $\overline{w^2}$. The surprising result that the low-wavenumber (large-eddy) contribution to $\overline{v^2}$ is amplified across the whole layer is associated with the nature of the mixing jets and the alteration of the pressure field by the wall. The change in turbulence structure occurs before any significant change in the mean-velocity profile, and the implications for the calculation of the change in boundary conditions are discussed. The measurements made after the mixing layer reached the wind tunnel floor will be presented in part 2.

The source-sink flow within a rapidly rotating annular region, bounded by a pair of concentric circular cylinders and by horizontal end plates, is considered. Fluid is injected into the container at arbitrary locations on the inner radius and withdrawn at one or more locations on either the inner or outer radius, through axisymmetric slots. The upper end wall is maintained at a higher constant temperature than the bottom end plate, while the vertical side walls are thermally insulated; the entire apparatus is rapidly rotating about the common axis of the cylinders. An analysis of the flow and temperature distribution is carried out in the context of the Boussinesq approximation and by assuming that vertical buoyancy effects are negligible to leading order. A method for calculation of the temperature distribution within the container is developed for physical situations where the effects of the imposed thermal gradient and the source-sink flow are of comparable magnitudes; the procedure is applicable for an arbitrary distribution of sources and sinks on the side walls. The temperature problem is an unusual complicated boundary-value problem, and numerical solutions are obtained for a number of different cases. The results reveal a number of interesting flows and temperature fields within the container and indicate how the temperature field is influenced by the placement and temperature of the sources and sinks, as well as by the relative magnitudes of the imposed forced flow and vertical thermal gradient. The possible application of the present theory to centrifuges is indicated.

The cylinder end boundaries, whether they be end plates or simple free ends, alter the vortex-shedding mechanism near these boundaries. This effect has in the past usually been overlooked. In a region near an end plate or a free end (ranging from 6 to 15 cylinder diameters in length), the shedding frequency f2 is found to be 10–15% less than the regular Strouhal frequency fs. The latter frequency is observed over the remaining cylinder length. The simultaneous occurrence of two frequencies results in a beat frequency, which is best observed at the junction of the two regions characterized by fs and f2 respectively. A third frequency f3 with fs > f3 > f2 is observed over the entire cylinder length when the cylinder is bounded by two end plates less than 20 to 30 cylinder diameters apart. Here the critical Reynolds number for the onset of shedding is shifted to about 60 and the laminar Reynolds-number range is extended from about 150 to about 250.

The transition to turbulence in Bénard convection in a layer of air bounded by rigid conducting walls is studied by numerical solution of the three-dimensional time-dependent Boussinesq equations. The wavy instability of rolls is compared with available experimental and theoretical results. The subsequent transition to chaotic convection is shown to occur for Rayleigh numbers larger than about 9000. The role of symmetry-breaking perturbations in the production of chaos is clarified.

Statistical fluid dynamics identifies a functional of the fluid energy spectrum that plays the role of Boltzmann's entropy for fluids. Through a series of two-dimensional flow simulations we confirm the theoretical predictions for the behaviour of this entropy functional. This includes a demonstration of Loschmidt's paradox and an examination of the effects of Rossby waves and viscosity on the behaviour of the entropy.

The gas-flow pattern that occurs when a bubble grows during its passage through a fluidized bed is investigated by applying Davidson's (1961) model in an unsteady manner. It is found that the form of the cloud perceived by an observer of this unsteady motion is significantly different from that predicted by the steady theory. Growth is shown to lead to a reduction in the penetration of the cloud ahead of the bubble and a reduction in the area of overlap between cloud and particles. The cloud boundary also interaepts the bubble boundary, and the gas entering the bubble to sustain its growth does so through its base. There is good agreement with experimental observation of clouds.

A quantitative theory for particle coagulation in continuous particle size distributions is presented and experimentally verified. The analysis, following Friedlander (1960a, b), assumes a local equilibrium in the size distribution maintained by a particle flux through the size distribution, Only particle collisions caused by Brownian motion, fluid shear and differences in settling velocities are considered. For intervals of particle size where only one coagulation mechanism is dominant, dimensional analysis predicts self-similar size distributions that contain only one dimensionless constant for each mechanism. Experiments were designed to test these predictions with clay particles in artificial seawater sheared in the gap between concentric rotating cylinders. Particle-size distributions measured over time were self-similar in shape and agreed with the Brownian- and shear-coagulation prediction in terms of shape and dependence on fluid shear rate and particle volume flux through the size distribution.

Weak coupling between nonlinear internal solitary waves on neighbouring pycnoclines allows resonant energy exchange. The lagging wave increases its energy and speed at the expense of the front-running wave, so that the waves leapfrog about an average position. Analytical estimates for this process agree with the wave-tank experiments described in the companion paper by Weidman & Johnson (1982).

Experiments on the resonant energy transfer between internal gravity-wave solitons travelling along neighbouring pycnoclines have been performed. Measurements of both amplitude and phase oscillations are found to be in qualitative agreement with theoretical predictions given in the companion paper by Liu, Pereira & KO (1982). Using averaged quantities to account approximately for wave-energy dissipation, the theoretical expression correlating the oscillation frequency with the density environ- ment parameters is reasonably well verified. A new three-soliton resonance requiring both upstream and downstream energy transfer has also been observed.

The flow inside a square cavity, generated by a uniform oscillatory motion of the upper cavity wall, is investigated. Numerical solutions of the full unsteady Navier–Stokes equations are computed for a selection of Reynolds’ numbers and frequency parameters in the range 0–600. These results show that the steady streaming component of the flow, in general, comprises two main, equal, contrarotating eddies, situated in the upper half of the cavity (one on either side of the cavity centreline) and two weaker, equal, contrarotating eddies, situated in the lower section of the cavity (again one on either side of the cavity centreline).

The laminar, boundary-layer, natural convection flow adjacent to a vertical, heated or cooled, flat surface submerged in quiescent cold water was studied. The results demonstrate for the first time the existence of multiple steady-state solutions in a natural convection flow. The calculated velocity profiles, over a range of the parameters, are compared with recent corresponding velocity measurements of Wilson & Vyas (1979) and of Carey & Gebhart (1981). The newly found additional steady-state solutions are of considerable practical interest because the heat-transfer rates for a pair of solutions (with determining physical parameters and boundary conditions otherwise identical) are sometimes vastly different. An important consequence of this study is the possible relationship of multiple steady-state solutions to the recently observed unsteadiness in some such flows.

A numerical study of the laminar flow of an incompressible viscous fluid in rotating ducts of rectangular cross-section is conducted. The full time-dependent nonlinear equations of motion are solved by finite-difference techniques for moderate to relatively rapid rotation rates where both the convective and viscous terms play an important role. At weak to moderate rotation rates, a double-vortex secondary flow appears in the transverse planes of the duct whose structure is relatively independent of the aspect ratio of the duct. For Rossby numbers Ro < 100 this secondary flow is shown to lead to substantial distortions of the axial velocity profiles. For more rapid rotations (Ro < l), the Secondary flow (in a duct with an aspect ratio of two) is shown to split into an asymmetric configuration of four counter-rotating vortices similar to that which appears in curved ducts. It is demonstrated mathematically that this effect could result from a disparity in the symmetry of the convective and Coriolis terms in the equations of motion. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration and the axial velocity wumes a Taylor–Proudman configuration in the interior of the duct. Comparisons with existing experimental results are quite favourable.

The general axisymmetric creeping motion of a spherical particle in a stagnation region near a finite surface is modelled by the motion of a sphere of arbitrary size towards a disk for the follodg conditions: (a) pure translation in quiescent fluid, (b) uniform flow past a fixed sphere–disk configuration, and (c) a neutrally buoyant sphere carried by the fluid towards a disk. The combined analytic and numerical solution procedure is similar to that described in Dagan, Weinbaum & Pfeffer (1982b) for the motion of a sphere towards an orifice. The drag force acting on the sphere and on the disk under the flow conditions mentioned above is presented. In addition, the fluid velocity field has been obtained for the case of uniform flow past a fixed sphere–disk configuration. These solutions show the formation and coalescence of separated regions of closed streamlines adjacent to the sphere and the disk.

Hot-film measurements of the streamwise velocity component were carried out in a fully developed turbulent water-channel flow for three different Reynolds numbers (13800, 34600 and 48900). The results for the first four statistical moments complement and extend the results from previous studies of turbulent channel flow. The VITA variance technique waa employed to detect deterministic events in the streamwise velocity. It waa demonstrated that the VITA technique has a band-pass-filter character. The number of events detected was found to decrerrae exponentially with the threshold level and the events occupy a wide range of timescales. This makes it impossible to define one unique frequency of occurrence or one unique duration of the events. However, by using this technique information was obtained on the amplitude and timescale distributions of the events. The chmacteristic features of the conditional iverages were found to be related to the skewness and flatness factors.

A quantitative study of some nonlinear aspects of drop-shape oscillations in a liquid–liquid system has been completed. The results suggest a soft nonlinearity in the fundamental resonant mode frequency as the oscillation amplitude is increased. Indications of an increase in the rate of decay have also been obtained. A study of the internal flow fields has revealed patterns of circulation not present at low amplitude.

An integral-equation and variational formulation for the radiation of swfaee waves from a submerged cylindrical duct is developed. This formulation, which complements that of Simon (1981a) for the corresponding scattering problem, provides variational representations of the radiation impedance of the duct and (through the Green-function identities established by Simon) of the pressure-amplification factor in the scattering problem. An exact solution of the integral equation is obtained for the limiting case of a narrow duct.

The mean circulation of planetary fluids tends to develop uniform potential vorticity q in regions where closed time-mean streamlines or closed isolines of mean potential vorticity exist. This state is established in statistically steady flows by geostrophic turbulence or by wave-induced potential-vorticity flux. At the outer edge of the closed contours the expelled gradients of q are concentrated. Beyond this transition lies motionless fluid, or a different flow regime in which the planetary gradient of q may be dominant. The homogenized regions occur where direct forcing by external stress or heating within the closed isoline is negligible, upon the potential-density surface under consideration. In the stably stratified ocean such regions are found at depths greater than those of direct wind-induced stress or penetrative cooling. In ‘channel’ models of the atmosphere we again find constant q when mesoscale eddies cause the dominant potential-vorticity flux. In the real atmosphere the results here can apply only where internal heating is negligible. The derivations given here build upon the Prandtl–Batchelor theorem, which applies to non-rotating, steady two-dimensional flow. Supporting evidence is found in numerical circulation models and oceanic observations.

In most experimental studies of the shock-wave/boundary-layer interaction at a compression corner the boundary layer upstream of the interaction has developed in zero-pressure-gradient conditions. However, in many practical situations the boundary layer upstream of the interaction is subject to adverse or favourable pressure gradients, and hence is in a non-equilibrium state. This paper presents the results of a series of experiments on the interaction at a compression corner where the boundary layer upstream of the corner is disturbed by air injected through a porous surface. The results are thus of direct interest to the design of transpiration-cooled aerodynamic surfaces. However, the boundary-layer profiles upstream of the interaction also have many similarities to those in an adverse pressure gradient, so that the results also give some indication of the effects of an isentropic compression upstream of the interaction. The results are used to discuss existing correlations for upstream influence and to study conditions for incipient separation. The experiments were made at Mach numbers of 1·8, 2·6, 2·7 and 2·9, with corner angles of 8°, 10°, 12°, 13° and 14°.