The instability of unbounded parallel inviscid flows which are neither plane nor axisymmetric is studied for disturbances with long wavelengths in the flow direction. The details of the variation of the flow velocity on any scale smaller than the wavelength are shown to have no effect on these disturbances and it is only the non-uniformity of the flow at infinity which is relevant. There is a class of disturbance which can only exist because of the non-uniformity, and it is governed by an equation similar to the Rayleigh equation for inviscid plane parallel flow. A number of the properties of the solution can be found and a large class of flows can be shown to be unstable. When the flow at infinity is linear in sectors it is easy to find simple solutions. Particular flows, which are either uniform in sectors with vortex sheets along the dividing radii or are continuous, but with a linear variation in each sector, are studied in detail and are shown to be unstable, even when the non-uniformity is confined to a narrow sector.

The drag on an axisymmetric body rising through a rotating fluid of small viscosity rotating about a vertical axis is calculated on the assumption that there is a Taylor column ahead of and behind the body, in which the geostrophic flow is determined by compatibility conditions on the Ekman boundary-layers on the body and the end surfaces. It is assumed that inertia effects may be neglected. Estimates are given of the conditions for which the theory should be valid.

The drag on a sphere has been measured as it moves through a slightly viscous fluid contained in a rotating cylinder that is short compared to the length of ‘Taylor columns’ created by the sphere motion. These results suggest that only when inertia effects are very much smaller than both viscous and Coriolis forces are the results of Moore & Saffman (1968) approached. Flow field observations show qualitative agreement with many of the features described in their paper but differ sufficiently to warrant a further, fairly extensive discussion. These differences are characterized by a marked fore and aft asymmetry in the shear layer and boundary-layer flows for all values of the parameters covered by this study.

A previous study of normal shock waves through numerical experiments with a simulated gas on a digital computer is extended to binary gas mixtures. The mixture is simulated by two sets of rigid elastic sphere molecules with the appropriate mass and diameter ratios. Velocity profile results for medium strength waves in a mixture of equal parts argon and helium are in qualitative agreement with the continuum calculations of Sherman (1960), but there is no initial acceleration of the argon in mixtures containing a very small initial mole fraction of this gas. The temperature profiles are similar to those for the velocity in that the argon profile lags behind the helium profile. However, when there is a small proportion of heavy gas, the profiles cross-over and the temperature of the heavy gas overshoots the Rankine-Hugoniot downstream value. For very strong shock waves, the overall shock thickness expressed in upstream mean free paths becomes larger, but the profiles are generally similar to those for the medium strength waves.

The existence of a ‘wake’ upstream of an obstacle moving slowly through a stratified fluid has been known for some time. The present study shows that a thin, flat plate moving slowly and horizontally through a linearly stratified salt-water mixture has, in addition, a boundary layer over the plate whose thickness increases upstream from the back of the plate.

The theory assumes that the ratio of diffusivity to viscosity is small, and that the plate moves so slowly that inertia forces are negligible; under these conditions, a similarity solution is derived describing the boundary layer over the plate. The study also shows that salt diffusion is important in a second, thinner boundary layer whose thickness increases from the front of the plate.

In the experiment, a plate was towed through a tank of linearly stratified salt water. From streak photographs of the boundary layer over the plate, it was possible to confirm quantitatively the similarity solution and to infer at very slow velocities the presence of the thin diffusion boundary layer.

A conference on ‘Stratified Fluids’ was held in Ann Arbor, Michigan, 11–14 April 1967, under the sponsorship of the National Science Foundation. The meeting was organized by Professor C.-S. Yih (University of Michigan) with the assistance of the other members of the scientific committee: T. B. Benjamin, W. R. Debler, L. N. Howard, R. R. Long, J. W. Miles, W. H. Munk and O. M. Phillips. Thirty papers were delivered on subjects involving the application of stratified fluid problems to geophysical phenomena, waves in stratified fluids, experimental and observational investigations, and stability. We give here a brief account of the proceedings. The papers delivered will not be published in a formal volume; references to where they can be found are given at the end of this article.

The magnetohydrodynamic flow between two parallel conducting planes is investigated for the case when the flow is driven by the current produced by electrodes placed one in each plane, the applied magnetic field being perpendicular to the planes. An exact solution is presented for the case of line electrodes placed opposite each other and an approximate method of determining the flow in this case for large Hartman number (M) is also given. It is shown that for large M the asymptotic form of the exact solution agrees with that obtained by the approximate method. The results are generalized to cover the case of line electrodes displaced relative to each other. A similar investigation is carried out for the case of two point electrodes opposite each other.

The problem of an unsteady axisymmetric expansion of a monatomic gas into a vacuum is considered in the limit of small source Knudsen number. It is shown that a solution of the Boltzmann equation for Maxwell molecules valid for large time can be constructed, which matches with the known equilibrium solution for an inviscid expansion of a fixed mass of gas into a vacuum provided that the region near the zero density front is excluded. This solution is formally the same as that obtained for the similar problem of steady spherical expansion into a vacuum—the variations along each particle path of the unsteady flow being the same as that in the steady flow.

Near the front, the expansion procedure breaks down and the equations require a different scaling. A modified form of the Boltzmann equation is obtained which leads to a corresponding set of moment equations. Unfortunately, the set of moment equations is no longer closed and no essential simplification has been made.

A layer of viscous liquid with a free surface is set in motion by the lower boundary moving simple-harmonically in its own plane. The stability of this motion is investigated. Since the primary flow is time-dependent, the time variable cannot be separated from at least one space variable, and a new approach must be used to investigate the problem. In this paper the stability of long waves is studied by a perturbation method which has not been applied before to problems of stability of unsteady flows, and it is found that the flow under consideration can be unstable for long waves.

Starting from Head's semi-empirical method for incompressible flow, two approaches to the prediction of turbulent boundary-layer development in compressible flow are explored. The first uses Head's incompressible method in conjunction with a compressibility transformation similar to Stewartson's transformation for laminar flow; the second carries over Head's physical arguments to treat the compressible flow directly. Measurements in supersonic flow, both on flat plates and downstream of an abrupt pressure rise, show broad agreement with the predictions of the second method but do not support the compressibility transformation. In particular, measurements on flat plates reveal that as Mach number increases the entrainment rate decreases to a lesser extent than the skin-friction coefficient. Whilst this result is consistent with the second treatment in this paper, it is difficult to reconcile with any of the compressibility transformations discussed, and the validity of these transformations in turbulent flow is therefore questioned.

Small amplitude waves on a shallow layer of water are studied from the point of view used in aerodynamic sound theory. It is shown that many aspects of the generation and propagation of water waves are similar to those of sound waves in air. Certain differences are also discussed. It is concluded that shallow water simulation can be employed in the study of some aspects of aerodynamically generated sound.

The second-order resonant interaction of two disturbances which are neutrally stable on a linear basis is investigated for cases when the mean flow is, first, an inviscid, homogeneous jet and, secondly, a stably stratified, antisymmetric shear layer for which the linear eigen-solutions are regular. For the former case, the periodic nature of the neutral disturbances is unaffected by the interaction. For the latter, the interaction can lead to an O(ε½) temporal growth rate of one disturbance, where ε is a characteristic disturbance amplitude.

Measurements of the pressure distribution around a sphere placed in aligned magnetic and velocity fields show that an increase in drag is mainly due to a decrease in the pressure on the base of the body. When magnetic forces are large compared to inertia forces, this decrease is due to a loss in total pressure along streamlines just outside the surface boundary layer and an acceleration of the flow to a velocity much larger than the reference velocity. Separation of a viscous boundary layer takes place behind the equator and still, to a large extent, controls the magnitude of the base pressure and the drag experienced by the sphere. A model consistent with these findings is presented.

The starting flow of a viscous fluid past a circular cylinder at Reynolds numbers 40 and 100 has been obtained by a numerical method. The method used is that developed by Payne (1957) but it has been extended here to cover a larger time interval.

At Reynolds number 40 Payne's result for the drag coefficient at time t = 6 is in reasonable agreement with Kawaguti's (1953) result for the steady case but if Payne's computation, is extended to time t ≈ 24, the result is in better agreement with Apelt's (1961) result for the steady case. Also, a further investigation into the case R = 100 shows that Payne's mesh size is too crude. Similar observations can be made concerning the size of the standing vortices downstream of the circular cylinder and how they grow in time.

The motion of a semi-infinite incompressible fluid caused by the sinusoidal oscillation of a plane flat plate is termed Stokes's problem. When the plate starts from rest in a still fluid a transient solution must be added to Stokes's well-known steady-state result. This paper presents a closed-form expression for the transient solution. Previous answers have contained a non-standard integral which could not be evaluated. The answer presented herein contains exponentials and error functions of a complex argument. These functions are readily available in newer mathematical tables. Graphs of the transient solution are presented for both sin (T) and – cos (T) boundary conditions. Velocity distributions in the fluid are also plotted and it is found that the transient period is essentially complete in one-half cycle for the cosine oscillation and in a full cycle for the sine wave case.