In studying the behaviour of a density-stratified shear flow difficulties are encountered at the ‘critical’ level where wave velocity equals fluid velocity.

Here a stratified shear layer of finite thickness is considered and a two-dimensional nonlinear steady-state problem is studied. It is assumed that blocking creates separate pockets of trapped fluid, each mixed to uniform density. These pockets are not in static equilibrium with the surrounding stratified fluid. They must be supported either by pressures dynamically developed in the curved flow along continuous streamlines outside the pockets or by centrifugal forces resulting from circulation within the pockets. The latter effect is considered only through evaluation of a crude ‘factor of importance’, FR, for the rotational effects and the pockets are assumed to be stagnant in the primary analysis.

For small but finite disturbance amplitude FR approaches zero, indicating that no correction of the primary analysis is required. A limiting Richardson number of unity appears. Above this limit the primary analysis gives no solutions and apparently the separate pockets of stagnant fluid merge to form a continuous stagnant insulating layer. This behaviour of the critical level (as a barrier to communication) resembles earlier results from transient linearized investigations although the two analyses have little in common except the existence of a critical level separating two fluid regions.

For moderate-to-large disturbance amplitudes the geometry of the flow pattern suggests Kelvin–Helmholtz billows. Rotational effects increase as the amplitude increases and may become significant at this stage. The primary analysis then becomes less accurate and cannot be used to exclude Kelvin–Helmholtz billows at Richardson numbers somewhat greater than unity.

This paper presents an analytical model for the aeroelastic instability of an infinitely long cylindrical shell in cross flow. The mean flow field is represented by a free-streamline model, and the perturbation flow field by a velocity potential associated with deformation of the shell cross-section; motions of the shell are described by Flügge's two-dimensional equations. It is shown that certain types of shell motions induce a negative aerodynamic damping, which increases with flow velocity; for sufficiently high flow, it overcomes the positive dissipative damping of the system, precipitating flutter, sequentially in the second, third and higher circumferential modes of the shell – each with specific orientation of the nodal pattern with respect to the free-stream vector. These analytical predictions are in agreement with observations in wind-tunnel experiments; quantitatively, predicted and measured flow-velocity instability thresholds are of the same order of magnitude.

The paradox reported by Brady & Acrivos (1981) of the non-existence of similarity solutions in the Reynolds-number range 10·25 < R < 147 for the flow in a tube with an accelerated surface velocity is resolved. It is shown that the source of the difficulty lies in the assumption that the tube is infinite in extent. For a finite tube, it is demonstrated that the presence of the closed end, even though far removed from the origin, affects in a fundamental way the structure of the flow throughout the entire tube. The change in the flow structure that occurs in a finite tube at R = 10·25 is caused by the fluid which is returning from the downstream end; it is shown further that the problem of determining the motion in a long finite tube is equivalent to that of selecting the initial condition for the boundary-layer equations that properly takes into account the presence of the reverse flow. By applying a method originally developed by Klemp & Acrivos (1976) for selecting this condition, the flow in a finite tube is determined numerically for Reynolds numbers up to 70. In addition, it is shown that the same change in structure brought about by the returning fluid occurs in a finite two-dimensional channel at R = 57, even though the corresponding similarity solutions exist for all values of R. The results suggest that similarity solutions should be viewed with caution because they may not represent a real flow once a critical Reynolds number is exceeded.

The analysis of Acrivos & Lo (1978) for the deformation and breakup of a slender drop placed symmetrically in an axisymmetric pure straining flow is extended to include the effects of the fluid inertia within the drop. It is shown that, although the flow pattern within the drop is very complicated, internal inertia always tends to stabilize the drop. This stabilizing effect is, however, so weak that, for all practical purposes, it can be ignored.

Measurements of the characteristics of small-amplitude shape oscillations of drops immersed in a host liquid have been carried out by acoustical means. The resonance frequencies of the first few modes have been measured, as well as the damping constant for the fundamental mode, as functions of the drop radius and viscosities of the two liquids. A qualitative photographic study during steady oscillations has revealed a simple internal fluid-particle flow field with no circulation. The theory available at the present time has been found to provide results which are in general agreement with experimental findings for low-viscosity liquids.

Collisions between two solitary waves are investigated using a numerical scheme. The phase shifts and maximum amplitude of a collision are checked with a corresponding perturbation calculation and compared with the available experiments. We found a wave train trailing behind each of the emerging solitary waves from a head-on collision. The properties of the wave train are in agreement with those of the perturbation solution. After the collision, the solitary waves recover almost all of their original amplitude for the length of time in our calculation. However, the difference (less than 2 % of their original value) persists and accounts for the energy residing in the wave train.

Detailed measurements are reported of mean-flow and turbulence characteristics of opposed jets discharging normally into a cross-flowing stream. They were obtained with pitch-to-diameter ratios of two and four, and for the limiting case of single opposed jets and for a separation of four jet diameters. Results are presented at downstream distances from two diameters from the plane of the jet centres.

The results for the symmetrically arranged jets show that the jets retain their identity for a velocity ratio of unity and pitch-to-diameter ratios of four and infinity. With a velocity ratio of 1·8, the single opposed jets bifurcate about a vertical plane to form two symmetric cores of mixed jet fluid. With the pitch-to-diameter ratio of two, the individual jets retain their identity and, in contrast with the results for a pitch-to-diameter ratio of four, where each jet divides to form two cores, only one core is formed for each jet. In general, the turbulence characteristics are determined by the mean flow, which is controlled largely by pressure forces.

This paper presents an infinite-series solution to the creeping viscous motion of a fluid through low- and moderate-aspect-ratio pores. The flow field is divided into two simply bounded regions: a cylindrical volume bounded by the walls of the pore and the entrance and exit planes, and an infinite half-space outside the pore. Analytic solutions are first obtained in each region for unknown functions representing arbitrary axial and radial velocity profiles at the pore entrance (exit). These unknown functions are then determined by matching the normal and tangential stress at the pore opening.

The results indicate that the velocity profile approaches to within 1·5 per cent of a Poiseuille profile after a short entrance distance of half the pore radius. In the far field the solution matches exactly the streamline pattern for a flow through an orifice of zero thickness obtained by Sampson (1891). The pressure drop across the pore exhibits linear dependence on the aspect ratio and is closely approximated (less than one per cent error) by a simple algebraic expression.

When two periodic permanent wave trains on shallow water intersect obliquely, the regions of intersection are two-dimensional waves of permanent shape. This shape varies from a nearly linear superposition of the two wave trains at large angles of intersection between the wave normals, to a structure predominantly transverse to the direction of propagation at small angles of intersection. The latter shape is found to be governed by the two-dimensional Korteweg–de Vries (Kadomtsev–Petviashvili) equation. The two-dimensional permanent waves are stable to periodic disturbances parallel to their direction of propagation, but are unstable to certain oblique periodic disturbances.