Measurements have been made of the turbulent flow in a rectangular duct of aspect ratio 12:1 at a Reynolds number $\overline{U}h/\nu = 10^5$ (based on duct height h) using conditional-sampling techniques. The lower boundary layer was heated in the entry region, and the fluctuating output of a resistance thermometer was used to distinguish ‘hot’ and ‘cold’ fluid. Thus separate velocity-fluctuation statistics could be obtained for fluid from the upper and lower boundary layers, even after the two layers had merged. The measurements suggest that the interaction region near the centre-line consists of a continuously contorting interface between the ‘hot’ and ‘cold’ layers, shaped by the eruption of large eddies across the centre-line from either side of the duct and surprisingly little affected by the inevitable fine-scale mixing.

In the mean, this time-sharing between ‘hot’ and ‘cold’ fluid gives the impression of two superposed turbulence fields whose mean-square intensities add to give the total intensity. Exact superposition (which cannot take place in a nonlinear system) would imply that one layer had the same turbulent intensity profiles as an isolated boundary layer spreading into a non-turbulent free stream with the same mean velocity profile as the duct flow. The centre-line interaction grows in strength with increasing distance downstream until a steady rate of mutual eddy intrusion and fine-scale mixing is achieved, when the flow is commonly called ‘fully developed’. It is concluded that superposition (timesharing) is a physically reasonable first approximation for use in turbulence models for interacting shear layers: it is argued that better approximations could be obtained if necessary by correlating departures from superposition (i.e. changes in turbulence structure) by means of one or more interaction parameters.

A nonlinear diffusion equation is derived for the longitudinal dispersion of a buoyant pollutant in a slowly varying current. The essential simplifying feature is that the (non-uniform) water depth is assumed to be much less than the channel width. It is found that for small concentration gradients there is a transverse circulation which leads to a marked reduction in the longitudinal dispersion. For large concentration gradients the longitudinal circulation predominates and the longitudinal dispersion increases.

The direct-simulation Monte-Carlo method for the full Boltzmann equation is applied to the problem of rarefied hypersonic flow of rotationally excited N2 past the leading edge of a two-dimensional flat plate aligned with the free stream. An approximate collision model representing rotational–translational energy exchanges is developed for use in the calculations. The effects of this and other inelastic collision models and of the single-parameter Maxwell gas–surface interaction law on the flow in the kinetic/transition regime are discussed.

For practically uniform entry conditions, the features of the steady laminar flow produced by a particular small distortion of the walls of a channel or pipe are shown to alter first from those of the corresponding external situation when the distortion is in an ‘adjustment zone’, sited a large distance O(R⅗l) from the inlet; R ([Gt ] 1) and l signify respectively a typical Reynolds number and length scale of the incompressible fluid motion. The planar channel flow there develops an extended triple-deck structure, with an unknown inviscid core motion bounded by two-tiered boundary layers near the walls. In three-dimensional pipe flow, where a similar structure occurs, the induced secondary motion has a jet-like nature close to the wall. The size and position of the indentation govern the flow properties within this adjustment regime and both can lead to large-scale effects being propagated. The most substantial effects occur if an indentation, interior blockage or bifurcation is sited just downstream of the adjustment stage in a channel. In a pipe, however, such a siting induces much less upstream influence, and instead the most significant long-scale disturbances are generated when the pipe is constricted asymmetrically over a small length. Vortex motion can then be provoked far beyond the constriction, the sense of rotation changing as the fluid moves further downstream, while upstream source-like secondary flow is found.

Axially symmetric motion of a viscous fluid in a cone is considered on the basis of the Stokes assumption. Near the apex of the cone the solution obtained reveals features quite similar to those of that near a sharp corner in two dimensions, which has been discussed already. An infinite sequence of eddies is induced near the apex for values less than about 80·9° of the semi-angle of the cone, which is measured from the symmetry axis lying in the fluid. The solution found by Pell & Payne for a spindle in a uniform stream offers a good illustration of the general discussion. Special attention is paid to the angle 120° for the spindle as well as the cone. The limiting case of zero angle of the cone corresponds to the flow occurring in a circular cylinder.

The effect of compressibility on vertical boundary layers, of thickness E¼ and $E^{\frac{1}{3}}$ respectively (see Stewartson 1957), in a rapidly rotating gas of constant temperature is studied. Such layers have been considered by Nakayama & Usui (1974). However, these authors used a power-series expansion of the basic density field in their calculations, which means that their results are not uniformly valid in the boundary-layer co-ordinate. In this paper, a uniformly valid asymptotic solution and a numerical solution for the velocity field in each layer are computed. The asymptotic solutions are valid for scale heights of the basic density field large in terms of the reference length for the respective boundary layer. The agreement between the asymptotic and numerical solutions is shown to be good. Although the limits considered have no meaning for density scale heights of the order of the respective boundary-layer thickness, one can formally find an exact solution for the E¼-layer for any density scale height. In the limit of large density scale height this solution agrees to third order with the corresponding asymptotic solution. It is shown that for both layers the boundary-layer thickness increases (decreases) if the basic density field decreases (increases) in the direction of the respective boundary-layer co-ordinate.

The parametric instability of a plane internal gravity wave is considered. When the two-dimensional equations of vorticity and mass conservation are linearized in the disturbance quantities, partial differential equations with periodic coefficients result. Substitution of a perturbation of the form dictated by Floquet theory into these equations yields compatibility conditions which, when evaluated numerically, give the curves of neutral stability and constant disturbance growth rate. These results reveal that, for an internal wave of even infinitesimal amplitude, disturbance waves can begin to grow in amplitude. Moreover, these parametric instabilities are shown to reduce to the classical case of the nonlinear resonant interaction in the limit of vanishingly small basic-state amplitude. The fact that these unstable disturbances can exist for an internal wave of any amplitude suggests that this phenomenon may be an important mechanism for extracting energy from an internal gravity wave.

Artificially initiated turbulent spots in a Blasius boundary layer were investi- gated experimentally using hot-wire anemometers. Electrical discharges generated the spots, which grew in all directions rn they were swept downstream by the mean flow. A typical lateral spread angle of the spots is 10° to each side of t.he plane of symmetry. Conditional sampling methods were used to form ensemble-averaged data yielding the average shape of a spot and the mean flow field in its vicinity. Far downstream a spot exhibits conical similarity and all quantities measured seem to be independent of the type of disturbance which generated the spot in the first place.

In plan view, the spot has an arrowhead shape whose leading interface is convected downstream somewhat more slowly than the free-stream velocity near the plane of symmetry and at approximately half the free-stream velocity at the extreme spanwise location. The trailing interface is convected at a constant velocity throughout (UTE = 0·5 U∞). In this way the spot entrains laminar fluid through both interfaces, resulting in its elongation it proceeds downstream. The flow near the surface accelerates abruptly as the leading interface passes by, however the acceleration continues within the spot and the velocity attains a maximum near the trailing interface. There is therefore a continuous increase in skin friction towards the trailing interface. Further away from the surface the passage of the spot is marked by deceleration followed by acceleration after the ridge of the spot passes the measuring station. All changes in velocity occur monotonically without causing inflexions or kinks in the ensemble-averaged velocity profiles. Although the displacement and momentum thicknesses change quite rapidly within the spot, the shape factor is practically constant in the interior region (H = 1·5); and the velocity profiles may be very well represented by the universal logarithmic distribution. The spanwise velocity component W is everywhere directed outwards (i.e. away from the plane of symmetry) and increases with increasing z. The component of velocity normal to the surface is directed towards the plate near the leading interface and away from it in the remaining part of the spot.

Two-point velocity correlation measurements suggest that the spot may be represented by an arrowhead vortex tube which is convected downstream with a velocity equal to 65 yo of the free-stream velocity. Pluid which is entrained near the plane of symmetry acquires a helical motion towards the extremities of the spot. This motion helps to explain the lateral as well as the longitudinal spread of the spot.

The two-dimensional motion of a fluid confined between two long horizontal planes, heated and salted from below, is examined. By a combination of perturbation analysis and direct numerical solution of the governing equations, the possible forms of large-amplitude motion are traced out as a function of the four non-dimensional parameters which specify the problem: the thermal Rayleigh number RT, the saline Rayleigh number ES, the Prandtl number σ and the ratio of the diffusivities τ. A branch of time-dependent asymptotic solutions is found which bifurcates from the linear oscillatory instability point. In general, for fixed σ, τ and RS, as RT increases three further abrupt transitions in the form of motion are found to take place independent of the initial conditions. At the first transition, a rather simple oscillatory motion changes into a more complicated one with different structure, at the second, the motion becomes aperiodic and, at the third, the only asymptotic solutions are time independent. Disordered motions are thus suppressed by increasing RT. The time-independent solutions exist on a branch which, it is conjectured, bifurcates from the time-independent linear instability point. They can occur for values of RT less than that at which the third transition point occurs. Hence for some parameter ranges two different solutions exist and a hysteresis effect occurs if solutions obtained by increasing RT and then decreasing RT are followed. The minimum value of RT for which time-independent motion can occur is calculated for fourteen different values of σ, τ and RS. This minimum value is generally much less than the critical value of time-independent linear theory and for the larger values of σ and RS and the smaller values of τ, is less than the critical value of time-dependent linear theory.