The spin-up of a homogeneous rotating fluid bounded at the top and/or bottom by a permeable medium has been proposed by Bretherton & Spiegel (1968) as a model for the spin-up in natural flows where turbulent processes transmit the direct effect of the boundaries deeper into the fluid than does the laminar Ekman layer. The theoretical analysis for the spin-up of a laterally unbounded fluid bounded by a permeable medium below is presented here. In addition, an experimental study of the process is presented. Theory and experiment agree reasonably well with a maximum difference of about 8% in the predicted and measured spin-up times. The effects of the side-wall boundary have been studied theoretically by Howard (1969). Experimental observations in the side-wall boundary layer confirm qualitatively the results of Howard's theory.

A concentrated electric current enters a region of fluid through an interface. It is shown that the magnetic field due to the current in general gives rise to rotational magnetic forces which must cause motions of the fluid. In particular the paper solves the axisymmetric non-linear problem in which a concentrated current enters a semi-infinite region of inviscid conducting fluid of constant density, inducing an inwards flow along the wall and a jet away from the wall opposite the current source. The case treated is the practically realistic one in which the effective magnetic Reynolds number is small and the current flows isotropically from the source. The first-order perturbation of this current distribution by electromagnetic induction is also calculated.

An analytical solution is possible because the non-linear equation of motion happens to be a linear equation in the square of the Stokes stream function. The motion is analytically related to viscous jet flows discussed by Slezkin, Landau and Squire.

This paper presents the results of a set of detailed experimental measurements on the resonant interaction of capillary-gravity waves for a case in which the entire propagation is in one direction. The influence of viscous attenuation is accounted for in the analysis. The measurements trace the entire spatial variation, or modulation envelope, of the amplitudes of the interacting modes from their inception near a wave-maker to their ultimate extinction through viscous dissipation, in excellent agreement with the theory. This is an unambiguous demonstration that at resonance and for the initial conditions specified at the wave-maker, a wave of uniform profile cannot exist.

Perturbation series are developed and mathematically justified, using a straightforward perturbation formalism (that is more widely applicable than those given in standard textbooks), for the case of the two-dimensional inviscid Orr-Sommerfeld-like eigenvalue problem describing quasi-geostrophic wave instabilities of parallel flows in rotating stratified fluids.

The results are first used to examine the instability properties of the perturbed Eady problem, in which the zonal velocity profile has the form u = z + μu1(y, z) where, formally, μ [Lt ] 1. The connexion between baroclinic instability theories with and without short wave cutoffs is clarified. In particular, it is established rigorously that there is instability at short wavelengths in all cases for which such instability would be expected from the ‘critical layer’ argument of Bretherton. (Therefore the apparently conflicting results obtained earlier by Pedlosky are in error.)

For the class of profiles of form u = z + μu1(y) it is then shown from an examination of the O(μ) eigenfunction correction why, under certain conditions, growing baroclinic waves will always produce a counter-gradient horizontal eddy flux of zonal momentum tending to reinforce the horizontal shear of such profiles. Finally, by computing a sufficient number of the higher corrections, this first-order result is shown to remain true, and its relationship to the actual rate of change of the mean flow is also displayed, for a particular jet-like form of profile with finite horizontal shear. The latter detailed results may help to explain at least one interesting feature of the mean flow found in a recent numerical solution for the wave régime in a heated rotating annulus.

Subcritically stable motion of long gravity waves of finite amplitude in a liquid layer flowing down an inclined plane is shown to be impossible. However, super-critically stable wave régimes for such flows are found and curves of constant wave amplitude in such régimes are obtained. The mechanism of non-linear stability is investigated by considering the energy transfer between the mean flow and the disturbances. The results obtained show that the mechanism of stability in a parallel flow with a free surface is quite different from that in a parallel flow without a free surface.

An integral method is used to investigate the interaction between a two-dimensional, single frequency finite amplitude disturbance in a laminar, incompressible wake behind a flat plate at zero incidence. The mean flow is assumed to be a non-parallel flow characterized by a few shape parameters. Distribution of the fluctuation across the wake is obtained as functions of those mean flow parameters by solving the inviscid Rayleigh equation using the local mean flow. The variations of the fluctuation amplitude and of the shape parameters for the mean flow are then obtained by solving a set of ordinary differential equations derived from the momentum and energy integral equations. The interaction between the mean flow and the fluctuation through Reynolds stresses plays an important role in the present formulation, and the theoretical results show good agreement with the measurements of Sato & Kuriki (1961).

Solutions are obtained for the self-similar form of the incompressible boundary-layer equations for all four second-order contributors, i.e. vorticity interaction, displacement speed, longitudinal and transverse curvature. These results are found to contain all previous self-similar solutions as members of the much larger family of solutions presented here. Numerical solutions are presented for a large number of cases, and several closed form solutions, which may have special significance for the separation problem, are also discussed.

The dynamical effects of a sudden increase of as much as 100°C in boundary temperature upon fully turbulent boundary layers at low Reynolds numbers in air have been investigated in a wind tunnel. A section of the floor or the roof of the tunnel could be heated, so that the rate of working of gravitational forces on the turbulence could be made to represent either a gain or a loss of turbulent mechanical energy. Techniques of hot-wire anemometry were employed which enabled the instantaneous temperature and the instantaneous velocity to be measured simultaneously at a point in the non-homogeneous turbulent flow field.

In the case of a strong discontinuity in the floor temperature, a fine-scale convective structure developed from the highly unstable interface between the heated air just above the surface and the turbulent boundary layer; and the motion in this region was sufficiently vigorous that the mean pressure in the vicinity of the floor was reduced and a local wall jet was generated. The deduced pressure distribution is regarded as evidence of coupling between the free and forced convection modes which may lead to a series of local wall jets downstream of the discontinuity.

In the case of a strong discontinuity in the roof temperature, the interface between the heated air and the turbulent boundary layer was stable; and the boundary-layer turbulence, acting to spread this stable gradient over the vertical extent of the boundary layer, was required to do work against the gravitational field. A rate of working against gravity which was an order of magnitude less than the rate of supply of turbulent energy from the mean shear proved sufficient to suppress the turbulence in a very short time.

This paper pertains to the steady condensation on to, or evaporation from, a liquid droplet suspended in a mixture of its vapour and an inert gas. The treatment is from a kinetic theory viewpoint. The Maxwell moment method is used with Lees’ two stream Maxwellian representations for the distribution functions, to obtain a closed form result valid through the whole range from free molecule to continuum. In the diffusion control limit the formula reduces to approximate results obtained by Maxwell, Fuchs and others. In the limit where no inert gas is present the formula reduces to a result obtained earlier by the author. The formulae presented here for the mass and energy flux can now be used to calculate the growth rate of very small droplets, under a wide range of conditions.

Is it possible to express the problem of calculating turbulent flame speeds as an eigenvalue problem that is analogous to the laminar flame speed problem? It is argued for grid turbulence that the answer is affirmative, and some benefits of pursuing such a calculation are exploited for the limiting case of a first-order reaction with vanishingly small heat release. The streamwise turbulent transport of reactant occupies a central role in the analysis. The equation governing the ensemble average of this quantity assumes different simplified forms in the limits of small-scale and large-scale turbulence. The criterion which is obtained for separating the small-scale and large-scale régimes differs from that of Damköhler and also from that of Kovasznay and Klimov. In the small-scale régime, turbulence produces a spatially varying diffusivity, the form of which can be ascertained only through an investigation of non-linear equations describing the statistical dynamics of production and decay of the velocity–concentration correlation. In the large-scale régime, which is of greater practical importance, the ensemble average of the streamwise turbulent reactant flux satisfies a linear ordinary differential equation whose solution for the growth and decay of the flux contains effects resembling wrinkling of the laminar flame, increasing of the effective diffusivity and augmentation of the effective reaction rate. An exact solution to the linear eigenvalue problem which arises in the large-scale limit reveals that turbulence enhances mean reactant consumption in the upstream portion of the flame and retards reactant consumption downstream. Formulas are given for the increase in flame speed and the increase in flame thickness that are produced by turbulence in the large-scale limit. Since the equations are relatively tractable in the large-scale limit, it is suggested that further study of these equations may yield improved descriptions of realistic turbulent flames.

A quantitative shallow water simulation technique for aerodynamic noise study is investigated. The technique is employed for the case of a free jet issuing from a nozzle with variable wall roughness.

The experimental results obtained are in remarkably good agreement with the theory. It is concluded that there is great potential for further work in even less well understood areas of aerodynamic noise research.