The hypersonic weak-interaction regime for the flow of a viscous, heat-conducting compressible fluid past a flat plate is analysed using the Navier-Stokes equations as a basis. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number, σ, of order unity, and a viscosity coefficient varying as a power, ω, of the absolute temperature. Limiting forms of solutions are studied for the free-stream Mach number, M, the free-stream Reynolds number (based on the plate length), RL, and the reciprocal of the weak-interaction parameter, (ξ*)−1 = [Fscr ](M, RL, ω, σ), greater than order unity.

By means of matched asymptotic expansions, it is shown that, for (1 − ω) > 0, the zone between the shock wave and the plate is composed of four distinct regions for which similarity exists. The behaviour of the flow in these four regions is analysed.

It is shown that islands can trap long-wave energy in a way similar to the capture of a particle by an atomic nucleus. The frequencies of the captured waves form a discrete set, being determined by the shape of the island and the contours of the surrounding sea bed. If the depth at great distances tends to a constant value, the trapped modes must leak some energy to infinity, though the consequent rate of decay may be exceedingly small. The initial energy of the trapped modes may be absorbed from incident radiation of the same frequency or from a sharp pulse. The particular example of a rectilinear pulse incident on a circular island is discussed in some detail.

The effect of the rotation of the Earth is to split the frequencies of a pair of waves progressing in opposite directions round the island. The splitting of the frequencies produces slow beats in the waves as seen at any fixed point. Slight asymmetry in the island induces a slow exchange of energy between each pair of progressive modes.

The present investigation was suggested by the occurrence of regular oscillations having a period of 6 min and a beat period of about 3 h in long-wave records taken at Macquarie Island, in the Southern Ocean.

A new type of solitary wave motion in incompressible fluids of non-uniform density has been investigated experimentally and theoretically. If a fluid is stratified in such a manner that there are two layers of different density joined by a thin region in which the density varies continuously, this type of wave propagates along the density gradient region without change of shape. In contrast to previously known solitary waves, these disturbances can exist even if the fluid depth is infinite. The waves are described by an approximate solution of the inviscid equations of motion. The analysis, which is based on the assumption that the wavelength of the disturbance is large compared with the thickness, L, of the region in which the density is not constant, indicates that the propagation velocity, U, is characterized by the dimensionless group (gL/U2) In (ρ1/ρ2), where g is the gravitational acceleration and ρ is the density. The value of this group, which is dependent on the wave amplitude and the form of the density gradient, is of the order one. Experimentally determined propagation velocities and wave shapes serve to verify the theoretical model.

A homogeneous fluid of viscosity v is confined between two co-axial disks (vertical separation H) which rotate relative to a rotating system (angular velocity Ω). The resulting velocity field is studied for values of the parameter v/2ΩH2 in the range 1·6 × 10−2 to 1·8 × 10−3. The Rossby number, defined as the ratio of the relative angular velocity of the disks to the angular velocity of the system, ranged from 0·038 to 0·0041. The dependence of the resulting velocity field (interior and boundary-layer flow) on geometrical parameters, imposed surface and bottom velocities, and Ω, is in good agreement with the calculations of Stewartson and Carrier. In particular, when the two disks rotate with the same angular velocity, the width of the vertical shear layer at the edge of the disks is found to be proportional to Ω−0·25±0·02. When the disks rotate in opposite senses, a shear layer in the vertical velocity is observed which transports fluid from one disk to the other and whose width is proportional to Ω−0·40±0·10. The magnitude and shape of the observed vertical velocity is in fair agreement with a numerical integration of the theoretical results.

A theory is developed to determine the shape of water-bells. The motion of the gas induced by the moving walls is taken into account in this analysis. A rapidly converging iterative procedure leads to a theoretical shape which agrees well with the experimental shape of the water-bell.

A unified picture of the linear dynamics of rotating fluids with given arbitrary stratification is presented. The range of stratification which lies outside the region of validity of both the theories of homogeneous fluids, $\sigma S < E^{\frac{2}{3}}$ and the strongly stratified fluids, σS > E½, is studied, where σS = vαgΔT/κΩ2L and E =v/ΩL2. The transition from one dynamics to the other is elucidated by a detailed study of the intermediate region E2/3 < σS < E½. It is shown that, within this intermediate stratification range, the dynamics differs from that of either extreme case, except in the neighbourhood of horizontal boundaries where Ekman layers are present. In particular the side wall boundary layer exhibits a triple structure and is made up of (i) a buoyancy sublayer of thickness (σS)−1/4E½ in which the viscous and buoyancy forces balance, (ii) an intermediate hydrostatic, baroclinic layer of thickness (σS)½ and (iii) an outer E¼-layer which is analogous to the one occurring in a homogeneous fluid. In the interior, the dynamics is mainly controlled by Ekman-layer suction, but displays hybrid features; in particular the dynamical fields can be decomposed into a ‘homogeneous component’ which satisfies the Taylor-Proudman theorem, and into a ‘stratified component’ which is baroclinic and which satisfies a thermal wind relation. In all regions the structure of the flow is displayed in detail.

A study of the formation of vortex rings when a liquid drop falls into a stationary bath of the same liquid has been made. The investigation covered liquids with a wide range in surface tensions, densities and viscosities. The results confirm the reported existence of optimum dropping height from which the drop develops into a superior vortex ring. The optimum heights are analysed, by a photographic study, in terms of the liquid drop oscillation. It is found that vortex rings are formed best if the drop is spherical and changing from an oblate to a prolate spheroid at the moment of contact with the bath. A Reynolds number has been determined for vortex rings produced at optimum dropping heights; these numbers are approximately 1000. A possible mechanism for the ring formation is suggested.

A theoretical study is made of a simple design for an underwater shock gun, which consists of a chamber in the form of a hollow circular cone, with a spherical sector of explosive charge fitted into the apex. When the explosive is initiated at the apex, the resulting sector of a spherical blast wave will be diffracted by expansion waves moving inwards after the leading shock has emerged from the rim of the cone.

The progress of the expansion wave-fronts is calculated, and the results show a surprising inability of the diffraction process to ‘eat into’ the full-strength sector of spherical blast. It is found to be possible to design such a gun so that it is capable of projecting a high intensity shock-pressure beam over a considerable range, using only a very small explosive charge.

We consider here the higher order effect of moderate longitudinal surface curvature on steady, two-dimensional, incompressible laminar boundary layers. The basic partial differential equations for the problem, derived by the method of matched asymptotic expansions, are found to possess similarity solutions for a family of surface curvatures and pressure gradients. The similarity equations obtained by this anaylsis have been solved numerically on a computer, and show a definite decrease in skin friction when the surface has convex curvature in all cases including zero pressure gradient. Typical velocity profiles and some relevant boundary-layer characteristics are tabulated, and a critical comparison with previous work is given.

Experiments were performed studying the formation of a dip on the surface of an initially stationary liquid draining from a cylindrical tank through an axisym-metrically placed circular orifice. Based upon the information obtained from the experiments, a simple analytical expression was derived predicting the height of the liquid surface in the tank at which this dip forms. A comparison was made between the experimental data and the results of the analysis and good agreement was found between theory and data.

In this article the problem of describing free convection near either horizontal cylinders or vertical axisymmetric bodies with fairly arbitrary body contours is studied. The solutions of two, coupled, partial differential equations, for the temperature and stream functions, are represented by series which are universal with respect to body contours within a specified class of body shapes (e.g. round-nosed cylinders). The series appear to converge rapidly so that a minimum of computational effort is required, even for classes of body shapes which do not admit the usual similarity transformations. For either horizontal, circular cylinders or spheres the series converge faster than expansions of the Blasius type and one-term approximations compare favourably with some of the existing experimental data.

An exact rear stagnation point solution is sought for a viscous, incompressible conducting fluid in the presence of a magnetic field. It is found that a steady solution exists only if [Nscr ] ≥ 2, where [Nscr ] = σB2/ρα is the interaction parameter of the flow based upon the normal component of the magnetic field at the wall. Here α is a positive rate of strain, which, for a finite body with length l and velocity U0, is of the order of U0/l.

The steady solution is found, and from its existence it is inferred that separation of the viscous boundary layer does not begin at the rear stagnation point when [Nscr ] ≥ 2, and that such separation can be prevented. This supports theoretical work by Moreau (1964) and experimental work of Tsinober, Shtern & Shcherbinin (1963).

When [Nscr ] < 2, the flow is necessarily unsteady, and in this case an asymptotic analysis (as t → ∞) similar to that of Proudman & Johnson (1962) is undertaken. For [Nscr ] < 1, the magnetic and non-magnetic flows are qualitatively alike, in that there is a growing inviscid region dominated by eddies, and an ultimately steady layer at the wall representing a viscous forward stagnation point flow.

For 1 < [Nscr ] < 2, the inviscid region again grows with time, but no eddies appear. It is thus suggested that for this range of [Nscr ] separation occurs without reversed flow.