Expressions are obtained for the jump in vorticity across a discontinuity surface which is not a contact surface. Admitting arbitrary motion of the fluid and the discontinuity, the most general of these is established on a purely kinematical basis. More specific expressions are obtained by successively enforcing the momentum equation of the flow and the conditions of conservation of mass and momentum across the discontinuity. Eventually Hayes's (1957) result for a gasdynamic discontinuity is recovered.

It has been found that ventilated cavities extending behind hydrofoils, plates, and other two-dimensional bodies, oscillate when the air supply rate is sufficient to reduce the cavitation number to about one-fifth of its natural value. As the rate increases further, higher modes of oscillation occur in which the cavity–water interface supports several waves that are convected downstream towards the wake, which, owing to a pinching-off action replacing the usual entrainment sink, consists of a sequence of large bubbles drifting downstream. A theory of such flows that allows both for the convected velocity fluctuations in the cavity, and for the transport of bubble volume down the wake, is given in this paper. Coupled with a rather simple phenomenological relation between the pressure fluctuations within the cavity and the departure of the pinched-off rear portion of the cavity—explained in terms of the action of the re-entrant jet—this theory successfully predicts the resonance frequencies obtained in experiments by Silberman & Song.

The theory also provides a solution of the more general problem of determining the fluctuations in the pressure distribution over the whole surface of the body, when it is in a prescribed unsteady motion along its axis of symmetry (the theory is confined to symmetrical bodies and flows). Thus the growth in drag due to a sudden increment in the upstream velocity can be predicted, and also the damping forces acting on the body when it is forced to oscillate at a given frequency. It is shown that in all cases the body is unstable.

One important feature of the mathematical model chosen is that it completely avoids the presence of a time-dependent sink at infinity—with its associated infinite pressures—by conserving total volume of wake and cavity in just the same way as vorticity is conserved in unsteady aerofoil theory.

The physical mechanisms underlying the relaxation process leading to thermal equilibrium behind ionizing shock waves in argon have been studied through use of optical techniques. The non-equilibrium condition in the relaxation region was investigated experimentally by measuring the shift in the fringes due to a change in the refractive index of the medium with a Mach–Zehnder interferometer. Both electron- and mass-density profiles from the shock front to the equilibrium region were determined. The experimental work has been supplemented by a theoretical analysis of the ionization mechanism to explain the measured profiles and relaxation times.

The results of a detailed mean velocity survey of a smooth-wall turbulent boundary layer in an adverse pressure gradient are described. Close to the wall, a variety of profiles shapes were observed. Progressing in the streamwise direction, logarithmic, ½-power, linear and $\frac{3}{2}$-power distributions seemed to form, and generally each predominated at a different stage of the boundary-layer development. It is believed that the phenomenon occurred because of the nature of the pressure gradient imposed (an initially high gradient which fell to low values as the boundary layer developed) and attempts are made to describe the flow by an extension of the regional similarity hypothesis proposed by Perry, Bell & Joubert (1966). Data from other sources is limited but comparisons with the author's results are encouraging.

A solution is offered for the relative phase relationship of bed, depth and surface waves observed in alluvial channels, and is found to be in good agreement with observation in laboratory flumes. The solution does not depend on an assumption of a phase lag between the velocity and sediment movement. The emphasis of the paper is on the mechanics of bed-wave formation.

This paper studies the two-dimensional convective motion in a rectangular cavity, the two vertical sides of which are maintained at different temperatures. This system is studied for the special case in which the temperature difference ΔT between the two vertical walls is so large that the transfer of heat from one vertical wall to the other is achieved almost entirely by convection. Heat transfer by conduction is assumed to be of importance only in thin boundary layers adjoining the walls. For a cavity of height H, the boundary layers on the two vertical walls are found to have thickness proportional to [ell ], where [ell ]4 = κνH/γgΔT, and the condition for the boundary-layer regime to be established is that [ell ] be small compared with the width of the cavity. An approximate solution of the problem is obtained for the case of large values of the Prandtl number ν/κ, and found to be in satisfactory agreement with experimental results obtained by Elder (1965).

The magnetohydrodynamic lubrication flow in an externally pressurized thrust bearing is investigated both theoretically and experimentally. The ordinary magnetohydrodynamic lubrication theory for this bearing is extended to include fluid inertia effects. Very good agreement is obtained between theory and experiment.

A theory of finite-amplitude secondary flow between concentric rotating cylinders has been published by Davey (1962). A necessary feature of the theory is the generation of harmonics of the spatial periodicity in the axial direction of the velocity field. A method has been devised to measure the amplitude of each harmonic separately and experimental results for the fundamental and first three harmonics are presented here for Taylor numbers up to 100 times the critical value. The agreement with Davey's theory is excellent, and the agreement extends far beyond the range where the theory is expected to be valid. It is shown that all the harmonics are in phase with the fundamental. This result requires that jets and shock-like structure must be present in the velocity field.

The separation points which occur in the Newtonian theory of hypersonic flow are treated by locally modifying the shock-layer equations. This approach leads to direct verification of the free-layer theory for separation on certain bodies with discontinuous curvature. Separation points on bodies with continuous curvature have already been treated by matching the upstream shock-layer solution to the downstream free-layer solution. The agreement that is found between these results and those of the present approach provides further confirmation of the free-layer theory.

A technique for the quantitative measurement of fluid velocities in the range 0–5 cm/sec is described. The technique uses a pH indicator, is applicable in aqueous solutions and permits visualization and measurement of three-dimensional flow fields.

The Navier-Stokes vorticity equation is solved numerically for the circulation induced in a vertical plane, by a constant stress acting on a liquid, enclosed in a basin of uniform depth and vertical sides.

Solutions of the linearized vorticity equation are obtained for all Reynolds numbers (τsD2/4ρν2 where νs is the surface stress, ρ is the density, ν is the kinematic viscosity, and D is the depth of the liquid) and solutions of the complete vorticity equation for Reynolds numbers 0–400.

The notable feature of the solutions is the totally different end circulations. At the upwind end the flow becomes very slack, and the vorticity equation has a boundary-layer limit, while at the downwind end a damped wave occurs and the equation has an inviscid limit.

At Reynolds numbers between 400 and 600, the streamlines at the downwind end lead to a condition of hydrodynamic instability, in approximate agreement with some experimental observations by G. H. Keulegan.

Periodic oscillations are found in a one-dimensional model of thermal convection. The model consists of a fluid-filled tube bent into rectangular shape and standing in a vertical plane. The fluid is heated at the centre of the lower horizontal segment and cooled at the centre of the upper horizontal segment. When a certain parameter exceeds unity, a periodic motion of the fluid is found in which the flow is always in the same direction but in which the speed varies. Inertia is unimportant for this oscillation, which depends upon the interplay between frictional and buoyancy forces.

The paper deals with the refraction of a plane shock wave by an interface between two different gases. It is shown that the equations of motion can be reduced to a single polynomial equation of degree 12. Detailed numerical results are presented for the air-CH4 and the air-CO2 interfaces, which are respectively ‘slowfast’ and ‘fast–slow’ combinations. When the results are compared with experiment good agreement is obtained. The numerical data are multi-valued, but it is found that it is always the weakest solution that agrees with the experimental data. The multiple roots of the equation are often found to be associated with the appearance of degenerate and irregular wave systems and some attempt is made to analyse and discuss these systems.