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.

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.

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.

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!

A detailed experimental study of developing turbulent flow in a rectangular duct was made using a laser-Doppler anemometer. The purposes of the work were to obtain data of value to fluid mechanicists, particularly those interested in the development and testing of mathematical turbulence models, and to evaluate the performance of the anemometer. For the first purpose, contours of axial mean velocity and turbulence intensity were measured in the developing flow, and all three mean velocity components and five of the six Reynolds stresses were obtained in the nearly fully developed flow.

The symmetry of the present flow appears to be better than that of previous measurements and the range of measurements is more extensive. In addition, the laser-Doppler anemometer has the potential advantage, particularly in the measurement of secondary velocities, of avoiding probe interference.

Some experimental results on incompressible viscous fluid flow in the gap between two concentric rotating spheres are discussed. The flow field in the spherical gap has been studied qualitatively by flow visualization (photographs) and quantitatively by measurements by the hot-wire technique. For a wide range of Reynolds numbers, the friction torque was measured for several gap widths and a relatively simple method of determining the torque theoretically is given. At higher Reynolds numbers instabilities appear. Their different behaviour for relatively small and large gap widths is demonstrated. For the larger gap widths, the different appearance of the Taylor–Görtler vortices, the reason for their generation, their regimes of existence as well as their influence on the friction torque are thoroughly treated. Detailed information is given on the new effect of the dependence of the wavelength of the vortices on the Reynolds number.

The axisymmetric motion of a compressible fluid in a rapidly rotating cylinder is considered using a linear approach and boundary-layer techniques. The deviation of the fluid motion from rigid-body rotation is caused either by an applied temperature distribution on the side wall, a differential rotation of the top and bottom end plates or sources and sinks of fluid distributed on the end plates. The horizontal end plates are assumed to be thermally insulated, while the side wall is conducting. The critical parameter governing the problem is found to be E−½(γ − 1) PrG0/4γ, where E is the Ekman number, γ the ratio of specific heats, Pr the Prandtl number and G0 the square of a rotational Mach number. If this parameter is larger than unity, the coupled effect of the compressibility of the fluid and the thermal condition on the end plates suppresses the flow in the cylinder. The flow in the inner inviscid core is strongly coupled with the Ekman-layer flow through the boundary conditions on the end plates, something which does not occur if the fluid is Boussinesq nor if the fluid is compressible and the end plates are conducting.

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

The lateral migration of a solid spherical particle suspended in a fluid flowing between parallel vertical walls is investigated theoretically using a method developed by Cox & Brenner (1968). Buoyant and neutrally buoyant, freely rotating and non-rotating particles in the fluid flow are considered as is also the case of a sedimenting particle in a quiescent fluid. The results obtained are applied to the special cases of plane Poiseuille flow and of plane shear flow, these situations being investigated in detail.

A mathematical model is developed with which the reading from a piezometer ring may be predicted from the individual wall static measurements and from this the conventional form of ring is shown to be unreliable in asymmetrical flow. An alternative form of ring known as the Triple-T is analysed and shown to provide a true mean pressure in all cases. It is recommended that this form be used in all future test work. Tests demonstrating the validity of the theory are described.