The upstream influence in an inviscid two-dimensional shear flow around a semicircular ‘cape’ (radius A) is computed using a piecewise uniform vorticity model of a boundary-layer current. The area of this layer upstream from the cape increases as the square root of time t when A is small, and increases as t for larger A. Complete blocking occurs when A is approximately three times the boundary-layer thickness, in which case all oncoming particles accumulate in a large upstream vortex. The numerical results obtained from the contour dynamical method also show the generation of large eddies downstream from the obstacle.

Treated in the present paper are the second-order effects, i.e. the effect of displacement thickness, longitudinal curvature, external shear and slip, on the two-dimensional laminar boundary-layer flow of incompressible fluid. The analysis is developed in terms of the stream-function co-ordinates proposed for the analysis of the rotational flow by the senior author previously. An inverse problem is set in the co-ordinates plane, and, within the framework of the second-order approximation, the problem is reduced to solving a parabolic partial differential equation for the total head. An implicit finite-difference scheme is then devised to solve the equation, and the practical computations are carried out for the flow along a flat plate or the one around a parabolic body, by making use of an electronic computer.

A series of experiments is described in which a fully-submerged circular duct situated with its axis vertical is subjected to regular incident waves. The resulting wave-interaction effects are defined in terms of reflexion coefficients derived from waveheight measurements, and a pressure coefficient derived from measurements of pressure in the depths of the enclosure. The experiments were conducted in a wide tank, so simulating open-sea conditions, and in a narrow tank where wall effects were important. The particular case when a transverse standing wave was induced above the duct was examined in detail.

These three-dimensional experiments complement a previous investigation into the performance of two-dimensional ducts and are of current practical significance in the context of sub-sea wave-energy conversion.

Detailed measurements of the flow over a compression corner were taken using hot-wire probes. The experiments were performed in supersonic flow (M = 2·64) under adiabatic wall conditions. The incompressible analogues of the boundary-layer profiles were obtained and their integral characteristics and shape factors correlated. Comparison with the self-similar profiles used by Lees & Reeves (1964) to describe interaction problems showed some similarities between the shape factors, but the measured negative shears in the separated bubble proved to be much less.

Large (gigajoule) amounts of energy can in principle be stored as kinetic energy in liquid metal circulating round a torus and can be extracted at the gigawatt level by Alfvén waves propagating along an imposed axial field. A major limitation on the energy that may be so stored is the disruption of these primary Alfvén waves by secondary flows in meridional planes, associated with out-of-balance centrifugal forces ahead of and behind the waves and non-uniform magnetic pressures at the wave fronts. Vorticity, created at the wave, itself propagates in secondary Alfvén waves.

This paper gives a linearized treatment of these secondary motions and the associated perturbations of the imposed axial field and compares the resulting disruption of the primary wave mode with crude estimates made in an earlier paper. The main case treated is the discharge of the stored energy into a matched resistor by an Alfvén step wave but the secondary consequences of standing primary waves are also explored. The nature of the solutions depends on the electromagnetic characteristics of the walls normal to the imposed field. The problem is mathematically interesting because it involves the joint solving of elliptic and hyperbolic equations that are coupled by the boundary conditions at these walls.

By what process can droplets be extracted out of the sea? This is an old problem, well-documented by precise field measurements of the size distribution of the spray aerosols. Lhuissier & Villermaux (J. Fluid Mech., this issue, vol. 696, 2012, pp. 5–44) study and characterize the bursting of an emerging bubble. They show that this single type of event can, by itself, generate the droplet size distributions in a sea spray. This is a remarkable result showing how, in a complex system, a statistical distribution can be entirely produced by the dynamics of one dominant phenomenon.

Rotating, stratified flows are important in a wide variety of both geophysical and engineering applications. Whilst ‘steady state’ flows of this type are generally very simple (in effect, rigid body rotation), the effect of abruptly altering (even a little) the rotation rate can induce significant temporal flow disruptions, made all the more complicated when the fluid is bounded inside a closed finite container, a problem studied both experimentally and theoretically by Foster & Munro (J. Fluid Mech., this issue, vol. 712, 2012, pp. 7–40).

Slow motion of a thin plate at a finite angle of attack in a rotating container filled with a viscous incompressible fluid is analysed. The Rossby and Ekman numbers are assumed to be small. The solution method is developed by studying horizontal translation of an elliptical plate. The plate is shown to carry a stagnant Taylor column with it as it moves. Detailed analysis of the structure of the vertical shear column bounding the Taylor column is circumvented by integrating the equations of motion across the shear column. A jump condition based upon mass conservation in the shear column which relates the geostrophic regions inside and outside the Taylor column results. This jump condition and its method of derivation can be used to analyse arbitrary (slow) motion of any thin plate at any angle of attack.

The fluid motion resulting when a disk moves using all six degrees of freedom at an infinitesimal angle of attack is discussed. The forces and moments on the disk are calculated and the streamlines of the geostrophic flow are displayed.

The rotating system of an infinite disk beneath an unbounded fluid can exhibit resonance if the disk performs torsional oscillations at a certain frequency. This effect is examined in detail, and the solution is shown to depend crucially upon the existence of a small, steady departure from the basic rotational state in the far field.

The flows caused by a uniformly expanding circular cylinder or sphere in a perfect gas at rest at various (from small to very large) expansion velocities are analysed by a method of successive approximations in which the first approximation represents the incompressible flow. The shock waves which form around the bodies are also treated. The results for a sphere, even up to the third approximation, agree closely with Taylor's (1946) calculations for all the expansion rates.