The non-linear magnetization characteristics of recently developed ferrofluids complicate studies of wave dynamics and stability. A general formulation of the incompressible ferrohydrodynamics of a ferrofluid with non-linear magnetization characteristics is presented, which distinguishes clearly between effects of inhomogeneities in the fluid properties and saturation effects from non-uniform fields. The formulation makes it clear that, with uniform and non-uniform fields, the magnetic coupling with homogeneous fluids is confined to interfaces; hence, it is a convenient representation for surface interactions.

Detailed attention is given to waves and instabilities on a planar interface between ferrofluids stressed by an arbitrarily directed magnetic field. The close connexion with related work in electrohydrodynamics is cited, and the effect of the non-linear magnetization characteristics on oscillation frequencies and conditions for instability is emphasized. The effects of non-uniform fields are investigated using quasi-one-dimensional models for the imposed fields in which either a perpendicular or a tangential imposed field varies in a direction perpendicular to the interface. Three experiments are reported which support the theoretical models and emphasize the interfacial dynamics as well as the stabilizing effects of a tangential magnetic field. The resonance frequencies of ferrohydrodynamic surface waves are measured as a function of magnetization, with fields imposed first perpendicular, and second tangential, to the unperturbed interface. In a third experiment the second configuration is augmented by a gradient in the imposed magnetic field to demonstrate the stabilization of a ferrofluid surface supported against gravity over air; the ferromagnetic stabilization of a Rayleigh-Taylor instability.

When a long rectangular tube containing two immiscible fluids is slightly tilted away from the horizontal, a uniformly accelerating flow is produced with shear at the interface. The presence of shear leads to instability, which is characterized by the spontaneous and rapid growth of almost stationary waves if the fluid depths are equal and the density difference small. The conditions for the onset of Kelvin-Helmholtz instability, taking account of the accelerating flow and the presence of a velocity transition region at the interface, are investigated theoretically and comparison made with observations. The time at which instability occurs is quite well predicted by this theory, but the wavelength of the unstable waves is rather greater than predicted in the accelerating flow. The difference between the predictions and observations may be the result of finite amplitude effects or of the development of Tollmien-Schlichting instability before Kelvin-Helmholtz.

Oscillatory convective instability is shown to occur in a rotating fluid layer when convection is caused by surface-tension gradients at a free surface. The asymptotic equations, valid when the Taylor number approaches infinity, are solved analytically, and the critical Marangoni number is evaluated numerically. Fluids with Prandtl numbers above 0·201 will exhibit only stationary instability. Fluids with smaller Prandtl numbers will exhibit oscillatory instability with the critical Marangoni number varying as M0T½ where M0 depends on the Prandtl number and T is the Taylor number.

An analysis of the full, compressible, non-adiabatic boundary-layer equations is presented to describe the so-called ‘throat’ formed when a two-dimensional viscous layer, interacting with a supersonic inviscid outer stream, is accelerated or decelerated through sonic velocity defined in some mean sense. The basic analysis differs from previous momentum integral theories in that the dynamics of the viscous layer is described by the exact local expressions for the streamwise gradients of the flow variables that obtain from the boundary-layer conservation equations, rather than on streamwise derivatives of integral properties of these equations. The theory is then used to develop an extensive analogy with the classical analysis of the throat in the inviscid quasi one-dimensional streamtube. The theory shows that a single integral constraint exists at the throat, which relates the velocity and temperature profiles in the viscous layer to the motion of the inviscid outer flow. One consequence of this constraint is that, for a one-parameter family of profile shapes, the solution can be started at the throat station by specifying only a single variable, the free stream Reynolds number based on the physical thickness of the viscous layer at the throat station. For the hypersonic near wake, this simplification permits one to obtain an approximate solution for the downstream flow without first solving the detailed motion in the base recirculation region. The paper ends with a discussion of the numerical results for the Stewartson family of wake-like profiles.

Fluid material line growth in turbulent flow has been measured by tagging lines with small hydrogen bubbles in the nearly isotropic turbulence behind a regular grid in a water tunnel. The average three-dimensional line lengths were inferred by an intersection-counting method carried out on one-plane photographs. The measurements cover ‘small’ time intervals only.

The method of matched asymptotic expansions is used to determine the lateral flow of an ideal fluid past a slender body, when the flow is constrained by a pair of closely spaced walls parallel to the long axis of the body. In the absence of walls, the flow field would be nearly two-dimensional in the cross-flow plane normal to the body axis, but the walls introduce an effective blockage in the cross-flow plane, which causes the flow field to become three-dimensional. Part of the flow is diverted around the body ends, and part flows past the body in the inner cross-flow plane with a reduced ‘inner stream velocity’. An integro-differential equation of identical form to Prandtl's lifting-line equation is derived for the determination of this unknown inner stream velocity in the cross-flow plane. Approximate solutions are applied to determine the added mass and moment of inertia for accelerated body motions and the lift force and moment acting on a wing of low aspect ratio. It is found that the walls generally increase these forces and moments, but that the effect is significant only when the clearance between the body and the walls is very small.

The structure of fully developed turbulence in smooth circular tubes has been studied in detail in the Reynolds number range between 10,700 and 96,500 (R based on centre velocity and radius). The data was taken as longitudinal and transverse correlations of the longitudinal component of turbulence in narrow frequency bands. By taking Fourier transforms of the correlations, crosspower spectral densities are formed with frequency, ω, and longitudinal or transverse wave-number, kx or kz, as the independent variables. In this form the data shows the distribution of turbulence intensity among waves of different size and inclination, and permits an estimate of the phase velocity of the individual waves.

Data taken at radii where the mean velocity profile is logarithmic show that the waves of smaller size (higher (k2x + k2z)½) decrease in intensity more rapidly with distance from the wall than the larger waves, and also possess lower phase velocity. This suggests that the waves might constitute a geometrically similar family such that the variation of intensity with wall distance is a unique function with a scale established by (k2x + k2z)−½). The hypothesis fits the data very well for waves of small inclination, α = tan−1(kx/kz), and permits a collapse of the intensity data at the several radii into a single ‘wave-strength’ distribution. The function of intensity with wall distance which effects this collapse has a peak at a wall distance roughly equal to 0·6(k2x + k2z)−½). For waves whose inclination is not small, it would not be expected that the intensity data could collapse in this way since the measured longitudinal component of turbulence represents a combination of two turbulence components when resolved in the wave co-ordinate system.

Although the similarity hypothesis is strictly true only for data taken where the mean velocity profile is logarithmic, a simple correction procedure has been discovered which permits the extension of the similarity concept to the sublayer region as well. This procedure requires only that the observed total turbulence intensity at any station in the sublayer be reduced by a factor which depends solely on the y+ distance from the wall (i.e. on the distance from the wall, scaled by the viscid parameters of the sublayer). The correction factor is independent of Reynolds number and applies equally to waves of all sizes. In this way, all of the turbulence waves down to the very smallest of any significance, are found to satisfy slightly modified similarity conditions.

From the data taken a t Reynolds numbers between 96,500 and 46,000 wave ‘strength’ is seen to be distributed more or less uniformly over a range bounded at one extreme by the largest waves which the tube can contain (k2x + k2z ≅ (2/a)2, where a is the tube radius) and at the other extreme by the smallest waves which can be sustained against the dissipative action of viscosity (k2x + k2z ≅ (0·04v/Uτ)2, where Uτ is the shear velocity). As the Reynolds number of the flow is lowered, the spread between the bounds becomes smaller. If the data is projected to a Reynolds number of order lo3 the bounds coalesce and turbulence should no longer be sustainable.

This study concerns the hypersonic flow over blunt bodies in two specific cases. The first is the case when the Mach number is infinite and the ratio of the specific heats approaches one. This is sometimes referred to as the ‘Newtonian limit’. The second is the case of infinite Mach number and very large streamwise distance from the blunt nose with a strong shock wave, or the ‘blast wave limit’. In both cases attention is restricted to power law bodies. Experiments are described of such flows at M∞ = 7·55 in air.

The Newtonian flow over bodies of the shape y ∞ xm at zero incidence is shown to be divisible into three regions: the attached layer at small x, the free layer and the blast wave region. As m increases from zero, the free-layer region reduces in extent until it disappears at m = 1/(2+j) (j = 1 and 0 for axisymmetric and plane flow respectively). A difficulty arises in a transition solution of the type given by Freeman (1962b) connecting the free layer with the blast wave result. At m > 2/(3+j) the attached layer merges smoothly into the Lees-Kubota solution which replaces the blast-wave result in this range.

In the blast wave limit, solutions were obtained for flow over axisymmetric power law shapes in the range ½γ < m < ½. Second-order results taking account of the body shape are given. These solutions are compared with experimental results obtained in air at a free stream Mach number of 7·55 and stagnation temperature of 630 °K, as well as with numerical solutions at Mach number of 100. The numerical method is tested by comparing solutions corresponding to the experimental conditions with experiment.

The flow fields in two-dimensional, isoenergetic, viscous free mixing with constant β and with initial velocity profiles deviating slightly from those given by wakelike solutions of the Falkner-Skan equation for that β are considered. The similar solutions of the Falkner-Skan equation are investigated in more detail than in the past, e.g. we show that as β → −1 the flows approach the pure jet with the surrounding fluid at rest, and that there are new branch solutions for β < −1. We have investigated the spatial stability of these flows; it is found that for β > − 0·5 the only spatially stable solutions are the trivial ones f′(η) ≡ 1, but for −1 < β < − 0·5 there are non-trivial, jet-like solutions which are spatially stable. As to the new branch solutions for β < − 1, all are spatially unstable.

The paper discusses free convective flows above a horizontal plate, both theoretically and on the basis of experiments which yield quantitative data. The theory is applicable to the semi-infinite plate and is extended to cover the complete range of Prandtl number values including Pr → 0 and Pr → ∞. Experiments were carried out to demonstrate the existence of a laminar boundary layer above a horizontal plate at intermediate Grashof (respectively Rayleigh) numbers, and its extent along the plate. This layer breaks down into large-eddy instability some distance from the leading edge. The value of the critical Rayleigh number for this to occur, obtained experimentally using semi-focusing colour-Schlieren photography is in reasonable qualitative agreement with previously known data (Tritton 1963a,b).

The flow is examined in the neighbourhood of the trailing edge of slender aerodynamic shapes which terminate in either a cusp or a wedge. The manner in which the boundary layer reacts to the rapidly varying pressure field in such regions is analyzed using the method of matched asymptotic expansions. The case of a wedge is examined in greater detail and a criterion for separation to occur is established.