The magnetic induction equation is solved numerically in a sphere for a variety of prescribed fluid flows. The models considered are the so-called ‘αω dynamos’, in which both small-scale turbulence and large-scale shearing play a significant role. Solutions are obtained by marching the finite–difference equations forward in time from some initial field. For a critical value of the magnetic Reynolds number Rm solutions which neither grow nor decay are found.

Further calculations are performed with a ‘cut-off effect’ in which an attempt is made to simulate the effect of the Lorentz forces on the turbulence. For supercritical values of R, the magnetic field now stabilizes a t a finite value instead of increasing indefinitely. The form of the final field is compared with that produced at critical Rm in the absence of the cut-off effect.

A sharp wedge expansion flap was tested in the von Kámán Institute Long-shot tunnel at Mach 16 and data on the wall pressure and heat transfer were obtained. Pitot pressure measurements in the boundary layer just ahead of the expansion flap were also made. The surface data are compared with predictions from a characteristics solution for the boundary-layer expansion and from a simple heat-transfer theory.

The similarity equations for rotationally symmetric flow above an infinite counter–rotating disk are investigated both numerically and analytically. Numerical solutions are found when α, the ratio of the disk's angular speed to that of the rigidly rotating fluid far from it, is greater than −0.68795. It is deduced that there exists a critical value αcr, of α above which finite solutions are possible. The value of α and the limiting structure as α → αcr are found using the method of matched asymptotic expansions. The flow structure is found to consist of a thin viscous wall region above which lies a thick inviscid layer and yet another viscous transition layer. Furthermore, this structure is not unique: there can be any number of thick inviscid layers, each separated from the next by a viscous transition layer, before the outer boundary conditions on the solution are satisfied. However, comparison with the numerical solutions indicates that a single inviscid layer is preferred.

A continuously stratified fluid, when subjected to a weak periodic horizontal acceleration, is shown to be susceptible to a form of parametric instability whose time dependence is described, in its simplest form, by the Mathieu equation. Such an acceleration could be imposed by a large-scale internal wave field. The growth rates of small-scale unstable modes may readily be determined as functions of the forcing-acceleration amplitude and frequency. If any such mode has a natural frequency near to half the forcing frequency, the forcing amplitude required for instability may be limited in smallness only by internal viscous dissipation. Greater amplitudes are required when boundaries constrain the form of the modes, but for a given bounding geometry the most unstable mode and its critical forcing amplitude can be defined.

An experiment designed to isolate the instability precisely confirms theoretical predictions, and evidence is given from previous experiments which suggest that its appearance can be the penultimate stage before the traumatic distortion of continuous stratifications under internal wave action.

A preliminary calculation, using the Garrett & Munk (197%) oceanic internal wave spectrum, indicates that parametric instability could occur in the ocean at scales down to that of the finest observed microstructure, and may therefore have a significant role to play in its formation.

It is known that head seas cannot travel without deformation along a horizontal cylinder of full constant cross-section. Calculations are given which indicate that the waves are refracted away from the axis of the cylinder. Similar refraction effects are found for waves generated by a pulsating source on the cylinder, and also for the Kelvin wave pattern generated by a long ship of nearly constant cross-sectiop moving with constant speed in the axial direction.

The process of internal gravity wave generation by the simple harmonic flow (U = U0, cos ω0t) of a stably stratified fluid (Brunt–Väisälä frequency N) over an obstacle is investigated in some detail. Attention is primarily directed to the behaviour of the solution in various limiting cases, and to estimating the flux of energy into the internal wave field. In general, waves are generated not only at the fundamental frequency ω0, but also at all of its harmonics. But, for values of ω0/N greater than about one half, the waves of fundamental frequency are dominant. For values of ω0/N, less than about one half, the quasi-static approximation, in which the problem is considered as a slowly-varying version of the classical lee wave problem, is found to provide a viable estimate for the wave field. The general solution is found to compare favourably with the limited available experimental data.

The Laplace–Young equation is solved for axisymmetric menisci, analytically in terms of elliptic integrals for all possible types of pendular rings and liquid bridges when the effect of gravity is negligible, numerically for selected other cases in order to assess gravity's effect. Meniscus shapes, mean curvatures, areas and enclosed volumes are reported, as are capillary forces. It is shown that capillary attraction may become capillary repulsion when wetting is imperfect. The special configurations of vanishing capillary force and of zero mean curvature are treated. The range of utility of the convenient ‘circle approximation’ is evaluated.

The incompressible laminar flow in the neighbourhood of the trailing edge of an aerofoil undergoing sinusoidal oscillations of high frequency and low amplitude in a uniform stream is described in the limit as the Reynolds number R tends to infinity. The aerofoil is replaced by a flat plate on the assumption that leadingedge stall does not take place. It is shown that, for oscillations of non-dimensional frequency $O(R^{\frac{1}{4}})$ and amplitude $O(R^{\frac{9}{16}})$, a rational description of the flow at the trailing edge is based on a subdivision of the boundary layer above the plate into five distinct regions. Asymptotic analytic solutions are found in four of these, whilst in the fifth a linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

When a liquid-filled tube of radius b which is spinning about its axis with angular velocity ω is allowed to drain by opening one end, a cavity propagates in the tube with velocity U. This velocity has been measured with the tube in both vertical and horizontal positions for large values of the rat,io ω2b/g of the centrifugal to the gravitational force, g being the gravitational acceleration. It is found that the Rossby number Uωb becomes constant and independent of ω2/g in both cases, taking the value U/ωb = 0.52 in the vertical case and U/Ωb ≃ 0.4 in the horizontal case. Experiments conducted in a tube which is slightly inclined to the horizontal confirm that, although the Rossby number is constant when ω2b/g is large, the value adopted depends upon α, the inclination of the tube to the gravitational field.

The theory of the constant-temperature anemometer has been extended in order to obtain quantitative results for the frequency response. A simple electrical test against which to check the theory has been devised, and the validity of the anemometer equations is demonstrated. Important differences in design philo-sophies and modes of operation are indicated, and results are presented for a design in which high d.c. gain is employed in the servo amplifier. The square-wave response is briefly investigated, and it is concluded that commonly used criteria for determining the frequency response from it should be treated with caution.

To measure fluctuations with a hot-wire anemometer in flows containing both velocity and temperature perturbations, the hot wire must be operated at more than one temperature. Variation of the mean wire temperature causes, in general, a variation in the frequency response, as does variation of the mean flow conditions. It is shown that, by simultaneous variation of the gain of the servo amplifier in the anemometer, the frequency response may be held nearly constant over a useful range of both overheat and flow conditions.

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.

These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

The general problem of potential flow past a slender body of revolution is considered. The flow incident on the body is described by an arbitrary potential function and hence the results presented here extend those obtained by Handels-man & Keller (1967 α). The part of the potential due to the presence of the body is represented as a superposition of potentials due to point singularities (sources, dipoles and higher-order singularities) distributed along a segment of the axis of the body inside the body. The boundary condition on the body leads to a linear integral equation for the density of the singularities. The complete uniform asymptotic expansion of the solution of this equation, as well as the extent of the distribution, is obtained using the method of Handelsman & Keller. The special case of transverse incident flow is considered in detail. Complete expansions for the dipole moment of the distribution and the virtual mass of the body are obtained. Some general comments on the method of Handelsman & Keller are given, and may be useful to others wishing to use their method.