Analyses based on a three-dimensional vortex-filament model are presented for the unsteady pressure field generated by a ducted propeller. An oscillating part is identified in the kernels and absolute terms of the governing equations for the harmonic components, allowing two methods to be developed for the solution of the higher harmonics. The first method is exact and is applicable to ducted propellers with practical configurations (small chord-to-diameter ratio) while the second is approximate but more suitable for ducted systems with large chord-to-diameter ratios. The second method was applied to a configuration for which experimental data were available and good agreement was obtained for pressure harmonic amplitudes downstream of the propeller and for phase angles upstream of the propeller.

Special consideration was given to the Kutta-Joukowski condition at the duct trailing edge and a general constraint developed for the doubly coupled governing integral equations.

Melting from an electrically heated horizontal cylinder embedded in a paraffin (n-octadecane, fusion temperature 301·3 °K) has been studied experimentally. The shape of the solid-liquid interface has been determined photographically, and the local heat transfer coefficients have been measured using a shadowgraph technique. The experiments provide conclusive evidence of the important role played by natural convection in melting a solid due to an embedded cylindrical heat source. The four distinct pieces of quantitative evidence which contribute to this conclusion are the melt shape, surface temperature, local and average heat transfer coefficients and their variation with time.

The experimental findings prove the importance of natural convection in phase change problems involving melting and indicate that continued practice of neglecting the effects in the analysis of such problems does not appear reasonable. Natural convection should be considered in analysis and design of systems involving phase change.

The dynamics of an infinitely long one-dimensional vortex and a swirl are compared with the dynamics of a semi-infinitely long trailing vortex and trailing swirl. With increasing distance, the change in the axial velocity difference between the core of the trailing vortex and the surrounding region causes radial convection and some associated axial convection of angular momentum. In laminar or turbulent trailing vortices, we show that under most conditions of interest this is the dominant mechanism for the decrease in the velocities of swirl in the core and corresponding growth of the core. On the basis of theoretical considerations and experimental observations, we show that the axial velocity difference between the core of the trailing vortex and the surrounding region is necessary for the sustenance of turbulence in the vortex core. A theory of the turbulent trailing vortex is developed on the basis of these mechanisms and the results are compared with our experimental observations.

A study has been carried out of turbulent flow over a sinusoidally shaped solid boundary of large enough amplitude that the flow separates from the downstream side of the wave. Measurements are presented of the conditions under which separated flows exist, the extent of the separated region and the variation of the pressure and shear stress along and the velocity profile above the wavy surface. The results are consistent with the model D turbulent solution of the linear momentum equations discussed in Zilker, Cook & Hanratty (1977, hereafter referred to as I) in that reversed flows are possible for wave height to wavelength ratios 2a/λ > 0·033 and in that the range of flow rates for which reversed flows exist increases with increasing 2a/λ. For non-separated flows and for flows with thin separated regions the amplitude of the pressure variation changes linearly with wave height; however, for very large amplitude waves with thick separated regions it is much less sensitive to variations in wave height since the external flow that controls the pressure variation sees a wave profile consisting of a composite of the solid wave and the separated region. The variation of the velocity field along the wave surface in the non-separated region is similar to that predicted by linear theory for small amplitude waves. The flow separates in a region of increasing pressure and reattaches in the region where the pressure on the wave surface is a maximum. A large increase in the wall shear stress is noted immediately downstream of reattachment.

The interaction between magnetic fields and convection in a fluid heated from below is investigated in an axisymmetric cylindrical geometry. When Rm, the magnetic Reynolds number, is large the field is concentrated into a thin rope on the axis of the cylinder. For weak magnetic fields a larger Rayleigh number is necessary to produce a flux rope than that needed for infinitesimal convection. For larger total fluxes, however, the opposite is true and the system is subcritically unstable to steady motions. The results are contrasted with those found by Busse (1975) for the corresponding two-dimensional roll problem.

A rational theory is developed to describe the reattachment of a laminar shear layer in supersonic flow. In the neighbourhood of reattachment the flow develops a threetiered or ‘triple-deck’ structure analogous to that which occurs at a point of separation (Stewartson & Williams 1969) and, as in the separation problem, the local flow pattern may be found independently of the flow in the surrounding regions. The fundamental problem of the reattachment triple deck reduces to the solution of the incompressible boundary-layer equations in the lower deck, which is of streamwise and lateral dimensions O(R−⅜) and O(R−⅝), where R [Gt ] 1 is a representative Reynolds number for the flow. Pressure variations in this region are O(R−¼). Asymptotic solutions in terms of x, the scaled streamwise lower-deck variable, are derived to confirm the transition from a reverse flow profile at x = 0+, through reattachment, to a forward flow as x → ∞, the attainment of the required asymptotic form downstream (as x → ∞) being shown to depend crucially upon the correct choice of the finite part of the pressure in the lower deck at x = 0+. The lower-deck solution is singular at x = 0+ and assumes a complicated multi-structured form which is shown to match upstream with the solution in a largely inviscid region of dimension O(R−½) where the pressure is O(1) and the major part of the flow reversal takes place. Solutions are presented for reattachment at a wall and for symmetric reattachment behind a wedge or bluff body. In the former case the results also explain the apparent ignorance of upstream conditions in the expansive triple-deck solution formulated by Stewartson (1970) in the context of supersonic flow around a convex corner.

Axisymmetric high Reynolds number flows in tubes of slowly varying radius are shown to be governed to a first approximation and in suitable co-ordinates by a partial differential equation which, in a particular case, allows solutions independent of the streamwise co-ordinate. The solutions of the resulting ordinary differential equation give flows with inflexion points in the velocity profiles and reversed flow in some cases.

A comparison is made between the theoretically predicted and the observed stratification in a container which is traversed by a prescribed flux of fluid. Two different geometries were used illustrating respectively a useful procedure for the control of a stratified laboratory system and a mechanism which is believed to be geophysically significant, e.g. for the control of the stratification in certain estuaries. The behaviour of the fluid system was in all cases characterized by an almost stagnant interior with a boundary layer at the non-horizontal wall of buoyancy-layer type. Agreement between theory and experiment was satisfactory within experimental errors, say 10% of the overall temperature difference.

A series of experiments is described in which a fully submerged parallel-plate enclosure is subjected to regular incident waves. The resulting wave-interaction effects are defined in terms of a reflexion coefficient derived from wave-height measurements and a pressure coefficient derived from measurements of pressure in the depths of the enclosure. The latter parameter describes the pressure induced in the enclosure by the passage of regular waves above it and is of particular interest, at present, in having a bearing on the operation and performance of a sub-sea wave-energy converter currently under development. The outcome of these experiments is the partial verification of some recent theoretical work, including the demonstration of a pressure intensification at certain wave frequencies.

These experiments form part of a wider study concerned generally with the performance of immersed, pressure-driven, wave-energy converters.

In a recent paper (Evans 1976) a theory was presented for the behaviour of an oscillating two-dimensional cylinder of any shape which was capable of absorbing energy from a given regular sinusoidal wave. In particular an expression was derived for the efficiency of power absorption of the cylinder when oscillating in a single mode in terms of properties of the solution of the so-called radiation problem in which the cylinder is forced to oscillate in the appropriate mode in the absence of the incident wave train.

In the present paper this theory is extended to two independent cylinders of arbitrary shape each oscillating in a single mode and capable of absorbing energy in that mode. A general expression for the efficiency is derived which depends on properties of the solution to a new radiation problem, in which one cylinder is forced to oscillate in the presence of the other cylinder, which is held fixed in its equilibrium position. In this case, the efficiency also depends on cross-coupling coefficients related to the force on the fixed cylinder due to the motion of the oscillating cylinder.

It is shown that the cylinders can be tuned to absorb all the incident wave energy at a given frequency even for symmetric cylinders, in contrast to the single symmetric cylinder, for which the maximum efficiency has been shown to be 50%.

The general solution to the new radiation problem is derived in terms of the solution to the radiation problem for a single cylinder, by assuming that the cylinders are far enough apart for local wave effects to be negligible.

The special case of two widely spaced rolling vertical plates is considered in detail and curves showing the variation of efficiency with wavelength are given for a variety of plate spacings and points of rotation.

A class of nonlinear boundary layers in a hydromagnetic flow under differential rotation is analysed. The function of these layers is to provide smooth transition from the conditions within the electrically conducting container to those in the region far away from the boundary through the flow regime. The structure of the double-decker boundary layer depends on the diffusivity of the fluid, the conductance of the rigid boundary and the relative strength of the applied magnetic field. The method of multiple scales is used to obtain uniformly valid solutions with the conductance of the container varying from zero to infinity. It is found that even a small differential rotation (ε → 0) can induce perturbations of order ε½ or of order unity in the field functions.

In the solution given by Hall & Walton (1977) for Bénard convection in a two-dimensional box with slightly imperfectly insulated side walls it was shown that there were certain critical values 2Lc of the length 2L of the box at which two modes became unstable simultaneously. In this paper we show that in the neighbourhood of Lc a secondary transition takes place which may be a bifurcation or a smooth transition depending on the boundary conditions.