A solution is developed for the flow of a vapour in a liquid enclosure in which different portions of the liquid wall have different temperatures. It is shown that the vapour pressure is very nearly uniform in the enclosure, and an expression for the net vapour flux is deduced. This pressure and the net vapour flux are readily expressed in terms of the temperatures on the liquid boundary. Explicit results are given for simple liquid boundaries: two plane parallel walls at different temperatures and concentric spheres and cylinders at different temperatures. Some comments are also made regarding the effects of unsteady liquid temperatures and of motions of the boundaries. The hemispherical vapour cavity is also discussed because of its applicability to the nucleate boiling problem.

The paper examines the role of heat diffusion as an internal noise source in aeroengines and as a source of noise in the mixing of hot jets. We consider a number of model problems and find that the sound induced by unsteady heat transfer can show an unusually weak dependence on the mean flow velocity U, the intensity scaling as U3 in three dimensions. At low enough velocities diffusion effects will overwhelm other noise sources, but we have failed in our search for a significant practical situation in which we can prove that sound generated by diffusion clearly dominates over that excited by unsteady aerodynamic forces; they are sometimes comparable.

We examine the possibility that diffusive monopole sources feature in the noise of hot jets using model problems in the linear case and using dimensional analysis in the nonlinear case, and conclude that no significant monopole exists when the specific heats are constant. But they are not constant at low frequencies when, for example, heat flows into and out of vibrational energy modes; then an important monopole source is present. This source shows an unusually complicated scale effect.

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.

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

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.

It is shown that spatially growing waves with complex wavenumber and real frequency can exist in a baroclinic flow and that these waves are substantially different from the more commonly studied temporally growing ones. They are bounded by a low wavenumber cut-off which separates them from the temporally growing waves. Their amplitude and phase change most rapidly near their steering level and are almost depth independent away from it. Most of the energy conversion from mean flow to the waves occurs at this level. It is suggested that these motions may be forced by steady disturbances such as bottom relief.

The theory is compared with recent observations of strong small-scale motions in a region of rough topography of MODE and in the vicinity of the Gulf Stream. The vertical structure can be well matched with the theory but the complex wavenumber appears to be a factor of 2–3 greater than that predicted.

A second approximation is developed for the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport profiles through the boundary layer are obtained by considering terms of up to third order in the perturbation parameter. A comparison with results based on a first approximation indicates that the effect of the third-order terms is to predict a smaller mass-transport velocity and that this difference is generally significant, particularly for waves extending to the intermediate depth range. The predicted correction to the first approximation is qualitatively supported by experimental evidence.

Formal expressions are derived for the effective thermal conductivity Kij of randomly dispersed suspensions undergoing shear. These are then evaluated for the cases of dilute suspensions of cylinders and of spheres when the bulk motion is a simple shear, the Péclet number Pe is large, and the particle Reynolds number is small enough for inertia effects to be negligible. It is shown that as Pe → ∞ the presence of shear can significantly affect the O(ϕ) contribution to Kij (ϕ being the volume fraction of the solids), which becomes independent of k, the thermal conductivity of the suspended material. This results from the presence of regions of closed streamlines surrounding each particle which, for sufficiently large Pe, attain an isothermal state and therefore act as regions of infinite conductivity.

The unsteady laminar flow due to the penetration of a horizontal jet of constant density into a stratified fluid is considered. A numerical solution of the Navier–Stokes equations under the Boussinesq approximation is obtained by means of an implicit finite-difference method. Results for different values of the Reynolds and internal Froude numbers are given and discussed.

Within the scope of the three-dimensional theory of homogeneous incompressible inviscid fluids, this paper contains a derivation of a system of equations for propagation of waves in water of variable depth. The derivation is effected by means of the incompressibility condition, the energy equation, the invariance requirements under superposed rigid-body motions, together with a single approximation for the (three-dimensional) velocity field.

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.

A surface gravity wave obliquely incident on a sloping beach is broken near the beach and has a smooth surface further out. Viewed in the frame of reference of the transition from the smooth to the broken part, the flow is steady, and the wave is oblique to the free stream. By placing a suitably shaped obstacle in a flume operated at high Froude number, such a wave can be generated. Experiments in which a wave of 18 cm height was generated are described and the wave shape and some of its characteristics presented. In particular, the dividing stream surface separating that part of the flow which curls over into the break from the part that flows smoothly over the obstacle is discussed.

Model surfboards can ride this wave unsupported, provided the correctly scaled weight loads them at the right centre-of-mass position. This makes it possible to determine the forces on the board without a balance. A comparison of the measured forces with estimates, particularly of the drag, indicate that viscous and surface-tension phenomena introduce only small scale effects in the Froude number modelling. While the results are not sufficiently accurate to draw definite conclusions about the effects of surf board shape, they indicate clearly that surf board flows may be modelled with quantitative success in the laboratory.

The mass, momentum and energy-transfer equations are solved to determine the response of a rectangular enclosure to a fire or other high-temperature heat source. The effects of non-participating radiation, wall heat conduction, and laminar natural convection are examined. The results indicate that radiation dominates the heat transfer in the enclosure and alters the convective flow patterns significantly. At a dimensionless time of 5·0 the surface of the wall opposite a vertical heated wall has achieved over 99% of the hot-wall temperature when radiation is included but has yet to change from the initial temperature for pure convection in the enclosure. At the same time the air at the centre of the enclosure achieves 33% and 13% of the hot-wall temperature with and without radiation, respectively. For a hot upper wall the convection velocities are not only opposite in direction but an order of magnitude larger when radiation transfer between the walls is included.

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.

The motion of a bore over a sloping beach, earlier considered numerically by Keller, Levine & Whitham (1960), is studied by an approximate analytic technique. This technique is an extension of Whitham's (1958) approach for the propagation of shocks into a non-uniform medium. It gives the entire flow behind the bore and is shown to be equivalent to the theory of modulated simple waves of Varley, Ventakaraman & Cumberbatch (1971).

An analysis is presented for the non-inertial descent of an inclined sinkage element (a rectangular prism) through a viscous fluid onto a rigid surface. The effects of sinkage-element deformability, slip velocity and time-dependent loading conditions are considered. Unlike previous analyses no assumptions are made a priori about the form of the pressure distribution during, or the effect of corners on, inclined sinkage. The results for rigid square plates are compared with those of previous analyses and with the limited amount of experimental data available. Results are also presented for a deformable sinkage element, which is used to model the action of an individual tyre tread element on a wet pavement. An inclination function based on available data on the tyre surface shape in the footprint region is used. The loading function for this case is based on measured values of tyre footprint pressure.

This paper is a summary of the first Euromech Colloquium to be held on Magnetohydrodynamics (MHD). It was organized in conjunction with the Centre National de la Recherche Scientifique and held at Grenoble from 16–19 March 1976 with 60 participants from 10 countries present. Papers were presented on laminar and turbulent MHD duct flows; heat transfer and two-phase flows in MHD; the effects of magnetic fields on instabilities and turbulence; the motion of and forces on solid objects in MHD flows; flow-measurement methods, and applications of MHD in the metallurgical industries, in sodium technology and in liquid-metal power generation. Our main conclusion is that there are many industrial applications of the existing body of research findings in MHD, but that quite new research problems have arisen as a result of the new applications, and that these need investigation. MHD lives!

The time development of two-dimensional fluid motion induced by a line sink in a rectangular, density stratified reservoir with a free surface is given. It is shown that the initiation of such a sink gives birth to a spectrum of internal expanding shear fronts with a progressively decreasing vertical wavelength. These fronts move out from the sink and travel towards the far wall, where they are reflected. This process ceases once the front with a vertical wavelength equal to the steady withdrawal-layer thickness has reached the end wall. The fronts so introduced continue to move back and forth, expanding to standing waves if the viscosity of the fluid is small enough. The evolution and nature of the withdrawal layer are shown to depend critically on the relative magnitude of the convective inertia and viscous forces, the number of reflexions from the rear wall and the Prandtl number.

A mathematical model for the unsteady fluid-dynamic response of the semicircular canals is developed. The endolymph is assumed to be an incompressible Newtonian fluid and the presence and effects of both the utricle and the cupula are specifically accounted for. A first approximate solution is obtained using a singular perturbation method. It is shown that the canal can be modelled as a heavily damped, second-order system which behaves as an angular-velocity meter. A comparison of the model response with experimental results is made; fairly good agreement 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.